1
Monetary policy operations and the Financial System
Tutorial
Ulrich Bindseil
January 2016
This tutorial complements the book Monetary policy operations and the financial system for
the use in classrooms, or for anyone willing to try out classroom exercises on monetary
policy implementation topics. In the field of monetary policy operations, there are many
very simple models (the financial account system, how to control short term interest rates
within a monetary policy implementation framework; funding market access of banks and
multiple equilibria; mechanics through which a financial crisis destabilizes markets, etc.)
which capture elements of reality, and which are suitable for classroom calculus.
The tutorial follows the structure of the book with its 17 chapters and contains essentially
three types of questions: (1) Questions which require a text answer that can be precisely
found in the book; (2) exercises requiring simple calculus or the use excel; (3) text quotes,
examples of non-conventional measures (mostly taken from the euro area), or data which
readers are invited to analyze or interpret. The solutions in part II of the tutorial provide, for
the first type of questions, only a reference to the relevant parts or page numbers of the
book. For the other two types, at least a sketch of the solution is provided. Literature to
which a reference is made can be found in the book’s literature list (or otherwise a full
reference is made here in the tutorial). Normally, it is sufficient to have read the book up to
the relevant chapter to be able to answer the questions. In rare cases one needs to have
read beyond - which is then indicated in the question. Obviously: trying to answer the
questions before looking at the solutions is the best way to learn.
I wish to thank the many students that went through previous versions of this tutorial. They
were essential in reducing the number of errors, and in identifying which exercises are
useful.
The Excel spreadsheets with solutions (relevant for around 10% of the exercises) can be
downloaded at my lecture website at the Technical University of Berlin. It is not strictly
necessary to use these excel spreadsheets, as the relevant formulas and simulations are
simple and can be programmed in any other spreadsheet program, programming language
or math tool like e.g. Matlab.
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Table of content
Page
Questions Solutions
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Basic terminology and relationship to monetary macroeconomics
Monetary policy in a closed system of financial accounts
Short-term interest rate as the operational target of monetary policy
Three basic techniques of controlling short term interest rates
Several liquidity shocks, averaging, and the martingale property
Standing facilities and the interest rate corridor
Open market operations
Reserve requirements
Collateral
Optimal frameworks in normal times
The nature of a liquidity crisis
Collateral availability and monetary policy
Open market operations and standing facilities in a financial crisis
The lender of last resort (LOLR) role of the central bank
LOLR and central bank risk taking
LOLR, moral hazard and liquidity regulation
The international lender of last resort
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5
11
12
14
15
16
17
18
19
20
23
24
25
28
30
32
35
37
50
53
56
58
59
61
63
65
66
72
74
78
82
85
89
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Q1: Basic terminology and relationship to monetary macroeconomics
Q1.1 Define the main types and sub-types of monetary policy instruments.
Q1.2 To what extent is there a “continuum” of central bank market operations between the extreme,
ideal-type standing facility and open market operation?
Q1.3 Draw a matrix with the two dimensions {outright operations, credit operations} and {open
market operations, standing facilities} and fill the four fields of the matrix with examples.
Q1.4 What is the relationship between the operational target of monetary policy, its ultimate target,
the transmission mechanism, and the monetary policy instruments?
Q1.5 What does “monetary policy implementation” consist in? What is, in contrast, “monetary
macroeconomics”, and what is the borderline between the two? How has the “dichotomy” between
the two fields of central banking been blurred in theory, and how in practice?
Q1.6 Poole (1970, “Optimal Choice of Monetary Policy Instruments in a Simple Stochastic Macro
Model’, Quarterly Journal of Economics, 84, 197–216) defined an ‘instrument’ to be a ‘policy variable
which can be controlled without error’ and considered three possible approaches to its specification
(p. 199): “First, there are those who argue that monetary policy should set the money stock while
letting the interest rate fluctuate as it will. The second major position in the debate is held by those
who favour money market conditions as the monetary policy instrument. The more precise
proponents of this general position would argue that the authorities should push interest rates up in
times of boom and down in times of recession, while the money supply is allowed to fluctuate as it
will. The third major position is taken by the fence sitters who argue that the monetary authorities
should use both the money stock and the interest rate as instruments...the idea seems to be to
maintain some sort of relationship between the two instruments.” How would you assess this from
the point of view of the terminology proposed in chapter 1, and on substance?
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Q2: Representing monetary policy implementation in a closed system of financial accounts
Q2.1 Consider the following system of financial accounts.
A. What monetary policy implementation technique does the central bank seem to apply (full
answer requires having read chapters 2-4 of the book)?
B. How are the following events reflected in this system of financial accounts? You may want to
distinguish immediate effects and possible subsequent effects reflecting the reactions of
economic actors (in particular of the central bank) to the initial event.
a. The central bank buys new headquarters for 1
b. Due to progress in electronic payment technologies, banknote demand shrinks by 80%
c. Because of a financial panic, the households substitute all bank deposits with banknotes.
d. The CB decides to substitute all its securities holdings with reverse open market
operations (as it decided to change its monetary policy implementation technique)
e. The real assets of the corporate sector lose 50% of their value due to an earthquake
Real assets
Banknotes
Deposits banks
Bank equity
Corporate equity
Corporate bond
Government bond
Total assets
Real assets
Total assets
Real assets
Total assets
Corporate bonds
Government bonds
Deposits with CB
CB Deposit facility
Total assets
Corporate bonds
Government bonds
Central bank credit
Total assets
Households
60
Equity
10
10
10
2
1
7
100
Total liabilities
Government
20
Debt
20
Total liabilities
Corporations
20
Equity
Debt
20
Total liabilities
Banks
7
Deposits of HH
8
Equity
5
Central bank credit
0
20
Total liabilities
Central bank
10
Banknotes
5
Deposits of banks (RR=0)
0
CB Deposit facility
15
Total liabilities
100
100
20
20
2
18
20
10
10
0
20
10
5
0
15
5
Q2.2 Consider the following system of financial accounts.
Household
Real assets
Banknotes
Deposits
E-D -B
B
D
Equity
E
Corporate & Government sector
Real assets
B+D
Bonds issued
B+D
Banks
Bonds
Excess reserves
D+B-P
max(0, P-B)
Credit to banks
Bonds
max(0, B-P)
P
Deposit
Central bank credit
D
max(0, B-P)
Central bank
Banknotes
Excess reserves
B
max(0, P-B)
(a) How does the length of the balance sheets of the four entities depend on B, D, P?
(b) What are in reality the approximate proportions between B, D, P and the lengths of the
various balance sheets of the sectors of the economy? What has in particular been simplified
away in the balance sheets above?
(c) How would the financial accounts change if the household sector also contains households
who are indebted?
Q2.3 Starting from the same financial accounts as in Q2.2, assume now that the banking system
consists in a continuum of banks in the unit interval, and that household deposits are distributed
linearly but not uniformly across banks in this unit space. The linear deposit distribution curve D(x)
with x in [0,1] being defined as
D(x) = D + (0.5-x)s
The parameter s in [0,2D] is the “slope” factor (note that if s=2D, then the bank x=1 has no deposits
at all; the bank x=0 is always the most deposit rich bank and would in this case have deposits of 2D).
In Q2.2 s had obviously been set to 0. The larger s, the more uneven is the distribution of deposits
with the banking system. We assume that initially, s=0, but then something happens (e.g. a liquidity
crisis breaks out, and households start to re-allocate their deposits with banks) and s takes a positive
value. Therefore, we assume that the banks’ assets are still uniform across banks at B+D, and central
bank credit has to fill the funding gaps resulting from the assumed unexpected change of s away
from zero and its impact on deposits (but not on the total assets per bank).
(a) Draw the curve Di(x) for the four combinations of parameter values of {D,s,B,P} indicated in
the table below. Comment on the four curves.
Total Deposits D
Inequality parameter s
Banknotes B
Portfolio P
Scenario 1
1
1
1
1
Scenario 2
1
1
1
2
Scenario 3 Scenario 4
0.5
1
1
2
1.5
1
1
1
(b) Define as Ri(x) the amount of central bank credit taken by bank x. Assume absence of
interbank markets. Provide the formula for this function and draw it for the same four
combinations of parameter values. Comment on the four curves. Draw the balance sheet of
bank x.
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(c) Assume now that there is an interbank market. Define as Mi(x) the amount on interbank
credit provided by bank x in scenario i (Mi(x) can be positive or negative, in the latter case it
means that bank x is a debtor on the interbank market). What are the conditions for an
active interbank market?
(d) How does in general the interbank market volume depend on D, s, B, P (assuming that
interbank market transaction costs are always below the spread between central bank credit
provision interest rates and the remuneration rate of excess reserves)? Provide intuition to
your answers.
(e) Assuming a perfectly efficient interbank market, what are, for the four parameter
combinations shown in the table above, the (i) interbank market volumes; (ii) total recourse
to central bank credit; (iii) Total excess reserves of the banking system; (iv) total length of the
central bank balance sheet?
(f) If money markets break down, how do these results change?
(g) Starting from the first parameter combination, i.e. {D,s,B,P}={1,1,1,1}, illustrate that the
interbank volume first increases and then decreases with the size of the central bank
securities holdings. How does the recourse to central bank credit (R) and excess reserves
(XSR) evolve as a function of the central bank’s outright portfolio P? Differentiate the cases
of efficient and broken interbank markets.
(h) The model predicts that more cross-bank deposit inequality (s) often increases interbank
market volumes. Why is this conclusion questionable in case higher deposit inequality is
driven by negative views of households on some banks?
Q2.4 Consider the following balance sheet of the Reichsbank of 1900 and 1922, Deutsche
Bundesbank as of December 1998, and of the Bank of Latvia as of December 2001
Reichsbank, average weekly financial statements in 1900, in billion RM
Gold and silver
817
Banknotes
1139
Banknotes of other issuing banks
14
Other liabilities (net)
150
Government bills
23
Discounted trade bills
800
Lombard lending
80
Current accounts of banks
513
Residual
68
Total assets
1802
Total liabilities
1802
Net foreign assets incl. gold
Government bills
Discounted trade bills
Lombard lending
Total assets
Reichsbank, end 1922, in billion RM
1
Banknotes
1184
Other liabilities (net)
660
1
Current accounts of banks
1846
Total liabilities
1280
36
530
1846
Bundesbank, end 1998, in billion DM
112
Banknotes
Other liabilities (net)
Credit operations with domestic banks 235
CB bills issued
Current accounts of banks
Total assets
347
Total liabilities
260
33
5
49
347
Bank of Latvia, Dec 2001, in million Lats
563
Banknotes
Other liabilities (net)
Credit operations with domestic banks
39
Current accounts of banks
Total assets
602
Total liabilities
484
55
63
602
Net foreign assets incl. gold
Net foreign assets incl. gold
(a) For each of these central bank balance sheets, please provide:
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(i)
The level of total autonomous factors;
(ii)
the total liquidity provision through monetary policy operations;
(iii)
the original liquidity deficit of the banking system;
(iv)
the liquidity deficit post outright monetary policy operations;
(v)
the “leanness” of the balance sheet?
(b) What do you find striking with regard to each the four balance sheet structures?
Q2.5 What did James Tobin mean by the term “fountain pen money”?
Q2.6 What are the various possible limits to the creation of fountain pen money?
Q2.7 Why should a granular banking system make fountain pen money creation by individual banks
more difficult?
Q2.8 Consider the following system of financial accounts, in which both banks are creating fountain
pain money in parallel:
Real Assets
Deposits Bank 1
Deposits Bank 2
Bank Equity
Banknotes
Real assets
Lending to corporates
Lending to households
Lending to corporates
Lending to households
Credit operations
E-D-B-F
D/2 + C/2
D/2 + C/2
F
B
D+B+F
Households / Investors
Household Equity
Credit from bank 1
Credit from bank 2
E
C/2
C/2
Corporate / Government
Credits from banks
D+B+F
D/2 + B/2 +F/2
C/2
Bank 1
Household deposits / debt
Credit from central bank
Equity
D/2 + C/2
B/2
F/2
D/2 + B/2 +F/2
C/2
Bank 1
Household deposits / debt
Credit from central bank
Equity
D/2+C/2
B/2
F/2
B
Central Bank
Banknotes
B
Assume the following four possible constraints for the creation of fountain pen money:
(a) Capital adequacy requirements: assume that banks must not have less than 8% capital,
and that capital charged on all bank assets are 100%
(b) Reserve requirements on household deposits are 5%
(c) Collateral: lending to corporates is central bank eligible collateral, whereby a haircut of
20% is applied.
(d) Both reserve requirements apply as in (a) and collateral rules as in (c).
For each of these constraints on their own, what is the maximum amount of central bank money
creation? Which is the binding constraint?
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Q2.9 The following system of financial account reflects the German 2013 financial and wealth
accounts, in % of Germany’s 2013 GDP (DeStatis, Deutsche Bundesbank, 2014, “Sektorale und
Gesamtwirtschftliche Vermögensbilanzen, 1999-2013”, Statistisches Bundesbamt, Wiesbaden), with
selective amendments made to ensure full internal consistency from the perspective of this exercise.

“Real assets” are all assets that are non-financial, i.e. including intellectual rights etc.

The sum of equity held as assets is only 190, while total equity as liability item is 528. The
difference of 338 is the liability equity of Households (296) and the Government (42) sector,
which is owned by nobody else than the sector itself (while all liability-equity of the NFC and
financial corporate sectors is owned by other sectors of the economy).

To simplify, net positions against the Rest of the World (RoW) are shown as “real assets”.

The Bundesbank is shown separately below, but is also part of the financial corporate sector.
The Bundesbank will not be relevant as separate entity in the rest of the exercise.
Real goods
Fixed financial claims
Equity holdings
Total
Real goods
Fixed financial claims
Equity holdings
Total
Real goods
Fixed financial claims
Equity holdings
Total
Real goods
Fixed financial claims
Equity holdings
Total
Real goods
Fixed financial claims
Equity holdings
Total
Real goods
Claims towards banks
Securities
Claims to Rest of the world
Other claims
Total
Non-financial corporates
98 Debt
39 Equity
39
177
State
75 Debt
17 Equity
11
103
Financial corporates (banks, insurance, etc.)
5 Debt (including deposits)
192 Equity
114
311
Households
159 Debt (including deposits)
154 Equity
26
339
Sums from the four sectors
338 Debt
402 Equity
190
930
Deutsche Bundesbank (included in financial corporates)
0 Banknotes
2 deposits of banks
2 Equity
13
1
18
56
121
177
61
42
103
241
70
311
43
296
339
402
528
930
6
8
4
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(a) What do you find most striking in these actual financial accounts? What do you think about
the financial stability of the various sectors?
(b) The accounts are not detailed enough to identify precisely which sector has which claims
against (or shares of) a specific other sector. Assume general proportionality of financial
claims and liabilities cross sector, and derive on that basis the precise inter-sector positions.
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(c) Assume now that as a consequence of a negative external shock, all real assets decline by a
percentage x, and that this percentage is sufficiently small that equity in the economy can
take the loss and no sector on aggregate loses its solvency (and we assume that the sectors
are constituted by homogeneous entities). How do the financial accounts look like after this
shock? Make sure that not only first round effects are considered, but the eventual effects
reflecting all interdependences (i.e. including subsequent effects transmitted via equity
holdings).
(d) What is the critical value of a percentage real asset value decline x* in which a first sector
becomes on aggregate insolvent?
(e) What happens beyond the point of insolvency of one sector (no need for an exact solution)?
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Q3: The short term interest rate as the operational target of monetary policy
Q3.1 What are desirable properties of an operational target of monetary policy?
Q.3.2 Verify that short term interbank interest rates are a suitable operational target of monetary
policy. Why is the overnight interest rate preferable to say the three months interest rate?
Q3.3 Derive the “non-accelerating” nominal interest rate from an arbitrage relationship between the
four goods “money today” and “wheat today”, “money tomorrow” and “wheat tomorrow”. What are
important simplifying assumptions of this arbitrage logic, that require to be refined when applying it
in central bank practice?
Q3.4 Why is the monetary policy decision making body of the FED called the “Federal Open Market
Committee”, although it decided (at least until 2009) on short term interest rates, such that it could
better have been named “Federal Short Term Interest Rate Committee”?
Q3.5 Friedman (1960: 50–1) argues that open market operations alone are a sufficient tool for
monetary policy implementation, and that standing facilities (such as the US discount facility) and
reserve requirements could thus be abolished:
The elimination of discounting and of variable reserve requirements would leave open market
operations as the instrument of monetary policy proper. This is by all odds the most efficient
instrument and has few of the defects of the others . . . The amount of purchases and sales
can be at the option of the Federal Reserve System and hence the amount of high-powered
money to be created thereby determined precisely. Of course, the ultimate effect of the
purchases or sales on the final stock of money involves several additional links . . . But the
difficulty of predicting these links would be much less . . . The suggested reforms would
therefore render the connection between Federal Reserve action and the changes in the
money supply more direct and more predictable and eliminate extraneous influences on
reserve policy.
Friedman (1982) argues largely along the same lines and seems to suggest an ‘open market
operations volume target’ (1982: 117):
Set a target path for several years ahead for a single aggregate—for example M2 or the
base. . . . Estimate the change over an extended period, say three or six months, in the Fed’s
holdings of securities that would be necessary to approximate the target path over that
period. Divide that estimate by 13 or 26. Let the Fed purchase precisely that amount every
week in addition to the amount needed to replace maturing securities. Eliminate all
repurchase agreements and similar short-term transactions.
Why have these policy advices never been set into practice?
Q.3.6 What were the main “reserve position doctrine” concepts applied by the Federal Reserve
across time? What could have been the specific problems with each of those?
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Q4: Three basic techniques of controlling short term interest rates
Q4.1 What is the basic idea behind the “fundamental equation” of controlling the overnight interest
rate in a corridor system? What explicit or implicit assumptions does this equation depend on?
Q4.2 What are the respective advantages and disadvantages of the three alternative approaches to
interest rate control presented in chapter 4?
Q4.3 Consider the balance sheets in exercise Q2.4 – what approaches to monetary policy
implementation did these central banks apply?
Q4.4 Assume the bank and the central bank balance sheets shown below. Moreover, assume that
deposits of banks with the central bank are not remunerated, and the central bank lending facility is
charged at a rate of 1%. The central bank chooses the amount of open market operations OMO in
the morning, then the interbank market takes place with the overnight rate i being established, and
finally μ materializes, which is an N(0,1) distributed random variable.
a) What level of OMO has the central bank to choose if it wants i to be (i) at 0.5; (ii) at 0.25; (iii) at
0.10?
b) Now assume that μ is decomposed into μ = μ1 + μ2 and that μ1 materializes before, and μ2 after
the interbank session. Also assume that the two are independently and identically N(0,1)
distributed. What level of OMO does the central bank need to choose (early in the day) if the
central bank wants the expected value of i to be (1) at 0.5; (2) at 0.25; (3) at 0.10. Use excel to
find an approximate answer. What is the volatility of the overnight rate in each of these cases?
c) How do these findings depend on the absolute and relative volatility of the two autonomous
factor shocks?
Government bonds
Loans to corporates
Deposits with CB
Government bonds
CB borrowing facility
100-OMO
50
Max(OMO-50- μ,0)
Bank
Deposits of HH
CB Borrowing facility
Central bank
OMO
Banknotes
Max(-(OMO-50- μ),0))
Deposits of banks
100 - μ
Max(-(OMO-50- μ),0))
50 + μ
Max(OMO-50- μ,0)
Q4.5 A corridor system with two facilities that are both liquidity providing or absorbing. The
classical approach of the Reichsbank up to at least 1914 consisted to steer short term interbank rates
in a corridor set by two liquidity providing standing facilities: a discount facility (in which banks could
submit trade bills satisfying certain criteria) and a Lombard facility, priced at 100 basis points above
the discount facility, which provided collateralised lending against a very broad collateral set. In
2015, the Fed announced a system after lifting off from the zero lower bound which Potter (Money
Markets and Monetary Policy Normalization, April 15, 2015, speech by Simon Potter, Executive Vice
President, FRBNY, “Remarks at the Money Marketeers of New York University”, New York City)
describes as follows:
“Specifically, the Federal Reserve intends to target a range for the federal funds rate that is 25 basis
points wide, and to set the IOER [Interest on excess reserves] rate and the offering rate associated
with an ON RRP [overnight reverse repo] facility equal to the top and bottom of the target range,
respectively. It intends to allow aggregate capacity of the ON RRP facility to be temporarily elevated
to support policy implementation. It can also adjust the IOER rate and parameters of the ON RRP
facility, and to use other tools such as term operations, as necessary for appropriate monetary
control….The Federal Reserve intends to use adjustments to the IOER rate—a rate it directly
administers—as the main tool for moving the fed funds rate and other short-term interest rates into
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its target range…. The IOER rate is essentially the rate of return earned by a bank on a riskless
overnight deposit held at the Fed, thus representing the opportunity cost to a bank of using its funds
in an alternative manner, such as making a loan or purchasing a security. In principle, no bank would
want to deploy its funds in a way that earned less than what can be earned from its balances
maintained at the Fed. Even though banks are the only institutions eligible to earn IOER, arbitrage
should lift market rates up to the level of the IOER rate. In practice, however, with the large levels of
excess reserves in the system, certain institutional aspects of money markets—including bank-only
access to IOER, credit limits imposed by cash lenders and other impediments to market competition,
and the costs of balance sheet expansion associated with arbitrage activity—appear to create
frictions that have made IOER act more like a magnet that pulls up short-term interest rates than a
firm floor beneath them. …The FOMC will supplement the magnetic pull of changes in the IOER rate
with an ON RRP facility to help control the federal funds rate. Under the facility, the Desk will offer
general collateral reverse repurchase agreements at a specified offering rate to a broad set of
counterparties—including several types of nonbank financial institutions that are significant lenders
in U.S. money markets.”
(a) How do such techniques generally insure that the interbank rates are kept with a corridor of
same-sided standing facilities?
(b) Do you believe that this technique allows for a very precise control of overnight rates?
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Q5: Several liquidity shocks, averaging, and the martingale property of overnight rates
Q5.1 What is the meaning of the “martingale property” of overnight interest rates intraday, and in a
reserve averaging system?
Q5.2 What are possible impediments to the martingale properties in the first and in the second case,
respectively?
Q5.3 Assume a central bank with banknotes outstanding of EUR 10 billion and a Lombard facility at
1% and a deposit facility at 0%. Consider the following daily sequence of events:

OMO operation takes place (overnight maturity)

A first autonomous factor shock materialises, which is N(0,1/q billion) distributed

A morning trading session with half weight of total daily trading volume takes place

A second autonomous factor shock materialises, which is N(0,1 billion) distributed

An afternoon trading session with half weight of total daily trading volume takes place

A third autonomous factor shock materialises, which is N(0,q billion) distributed (the three
shocks are independently distributed; a, 1 are the variance)
Build an excel tool which allows you to answer approximately the following questions:
a) In a symmetric corridor system, what is the volatility of the morning, the afternoon, and the
overall overnight rate for values of q of 0.5, 1, 2?
b) Assume that the central bank targets an overnight rate of 0.25. What OMO amount does it
need to choose to achieve it for values of q 0f 0.25, 0.5, 1, 2, 4, 8? What is the volatility of the
overnight rate in each of these cases? In how can one derive from that an important
advantage of a symmetric corridor system?
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Q6: Standing facilities and the interest rate corridor
Q6.1 Explain the difference between a discount- and a Lombard facility. How did the two typically
coexist in pre WW1 central banking?
Q6.2 Why is the Fed been using the term “discount facility” for its Lombard credit facility?
Q6.3 Why did monetarist strongly dislike standing facilities?
Q6.4 Why was the discount window stigmatised for so long in the US?
Q6.5 What are relevant considerations when choosing the optimal width of the interest rate corridor
set by standing facilities in a symmetric corridor system?
Q6.6 Explain the idea of a “TARALAC” standing facility. In which sense is it more effective and simple
in stabilising overnight rates around the desired level?
Q6.7 What is the main difference between the US Fed discount window (“primary credit”) and the
Eurosystem “marginal lending facility”?
Q6.8 On 22 December 1998, i.e. 10 days before the introduction of the euro, the ECB announced the
interest rates applied to its standing facilities, including a transitory measure: “With respect to the
interest rates on the ESCB's standing facilities, which are designed to form a corridor for movements
in short-term money market rates, the Governing Council decided that the interest rate for the
marginal lending facility will be set at a level of 4.5% and the interest rate for the deposit facility at a
level of 2%. …. However, as a transitory measure, between 4 January 1999 and 21 January 1999, the
interest rate for the marginal lending facility will be set at a level of 3.25% and the interest rate for
the deposit facility at a level of 2.75%. This measure aims at smoothing the adaptation of market
participants to the integrated euro money market during the initial days of Monetary Union. The
Governing Council intends to terminate this transitory measure following its meeting on 21 January
1999.” What would have happened in your view without this transitory measure?
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Q7: Open market operations
Q7.1 Why were both the US Fed and monetarist so enthusiastic about open market operations for
many decades?
Q7.2 What is the role of open market operations in the pre-2007 consensus?
Q7.3 How would you assess the relative merits of credit- and outright- open market operations? How
could they be combined efficiently? In which sense could the optimal combination between the two
depend on the circumstances?
Q7.4 How would you assess the relative merits of fixed and variable rate tenders?
Q7.5 Why should tender procedures avoid discretionary elements in the allotment decision?
Q7.6 Between 1999 and 2008, the ECB conducted all its credit operations with a maturity of more
than a month as pure variable rate tenders with pre-announced amounts. In contrast, during the
same period, the ECB applied various different procedures in its weekly main refinancing operations
(fixed rate tender, variable rate tender with minimum bid rate, fixed rate tender with full allotment).
Why this difference between the shortest and the longer maturities?
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Q8: Reserve requirements
Q8.1 Why is the fulfilment of reserve requirements not measured more frequently than once a day,
e.g. once a minute? Why is it not measured less frequently, e.g. once a year?
Q8.2 What are key parameters to specify a reserve requirement system?
Q8.3 What objectives have been attributed to reserve requirements in the past and present? What
does the choice of objective implies for the choice of specification?
Q8.4 How convincing do you find the various possible objectives of reserve requirements? Please
explain.
Q8.5 What views did monetarist have on reserve requirements? And Keynes in his “Treaties on
Money” (1930)? What is left today of these views?
Q8.6 Consider the ECB announcement of its reserve requirement system made on 8 July 1998: “The
Governing Council sees three main functions which a minimum reserve system could usefully
perform in Stage Three. First, it may contribute to the stabilisation of money market interest rates.
Second, such a system will contribute to enlarging the demand for central bank money and thus
creating or enlarging a structural liquidity shortage in the market; this is considered helpful in order
to improve the ability of the ESCB to operate efficiently as a supplier of liquidity and, in the longer
term, to react to new payment technologies such as the development of electronic money. Third, the
ESCB's minimum reserve system may also contribute to controlling the expansion of monetary
aggregates by increasing the interest rate elasticity of money demand.” How would you assess these
three objectives with hindsight?
Q8.7 On 8 December 2011, the ECB announced the decision “To reduce the reserve ratio, which is
currently 2%, to 1% as of the reserve maintenance period starting on 18 January 2012. As a
consequence of the full allotment policy applied in the ECB’s main refinancing operations and the
way banks are using this option, the system of reserve requirements is not needed to the same
extent as under normal circumstances to steer money market conditions.” While the press release
provides an argument why the higher levels are no longer needed, it does not explain the benefits of
lowering reserve requirements. How would you complete the reasoning?
17
Q9: Collateral
Q9.1 Why should a central bank refrain from providing uncollateralized credit?
Q9.2 What are desirable properties of central bank collateral (and why)? What are the differences to
the desirable properties of collateral for interbank repo operations?
Q9.3 Under what circumstances can losses arise even in collateralised lending? What risk control
measures can be designed to address this? Against what can these protect, and against what can
they not?
Q9.4 Why would assets with lower credit quality tend to deserve higher haircuts, even after adjusting
valuation? Why would assets with longer duration deserve higher haircuts?
Q9.5 Consider two eligible assets of the same duration (say 2 years), asset 1 being a AAA rated
sovereign bond and asset 2 being a BBB rated corporate bond. Asset 1 is credit risk free and liquid
and can be liquidated without market impact in 3 business days. Asset 2 is less liquid and therefore it
is realistic that liquidation without market impact takes 10 business days. Assume that the common
(risk free yield curve) related market risk factor is normally distributed, and that the related one day
price change is N(0,1%). Asset 2 is in addition subject to the following risk factors: the uncertainty on
the true asset value at the moment of valuation is N(0,4%), the daily uncertainty stemming from
spread and credit migration risks is N(0,2%). Assume that the daily price innovations are uncorrelated
across time. Assume that the risk tolerance of the central bank has been defined as “preventing with
95% probability that the asset value at liquidation falls short of the last valuation post haircut”. What
are the appropriate haircuts on the two assets?
Q9.6 Assume an economy in which households would only hold banknotes and no bank deposits,
such that the entire banks’ balance sheet would be financed with equity and central bank credit.
Assume that the shadow cost of equity is captured in a 6% spread over risk free rates and that the
central bank provides its credit at 4%. Also assume that banks have two type of assets, held in equal
quantities: liquid and non-liquid assets. The central bank imposes on liquid assets a haircut of 10%
and on illiquid assets a haircut of 30%. What amount of equity will the bank need? What will be its
average funding costs? How will banks (assuming that they have no operating costs and are subject
to full competition) price the loans to liquid and illiquid projects (assets)? What is the average
funding cost of the real economy? In which sense is haircut policy in such a setting equal to monetary
policy? Provide two alternative ways (via the central bank credit interest rate and via collateral
haircuts) to tighten effective monetary conditions by one percentage point. In which sense can it
influence the industry allocation of credit?
Q9.7 Section 6.4.2 (c) of the Eurosystem’s General Documentation specifies that: “The Eurosystem
limits the use of unsecured debt instruments issued by a credit institution or by any other entity with
which the credit institution has close links as described in section 6.2.3. Such assets may only be used
as collateral by a counterparty to the extent that the value assigned to that collateral by the
Eurosystem after the application of haircuts does not exceed 5% of the total value of the collateral
submitted by that counterparty after the haircuts”. Show in a financial accounts system that indeed
banks can create in this way “fountain pen collateral”. What risks would this create for the central
bank?
18
Q10: Optimal frameworks for monetary policy implementation in normal times
Q10.1 What are desirable properties of monetary policy implementation frameworks?
Q10.2 If you compare the operational framework of the Reserve Bank of Australia (narrow corridor,
no reserve requirements, daily open market operations) with the one of the Eurosystem in normal
times (wider corridor, one month reserve requirement period, weekly open market operation) –
which approach seems preferable in your view an on what could the choice depend?
Q10.3 How would you describe the pre-2007 consensus on monetary policy implementation
technique? What issues seemed to remain unclear?
Q10.4 The book covers mainly the case of industrialised countries’ central banks, and chapter 10
issues relating to their ‘optimal’ operational framework. What would you believe are additional key
issues of ‘optimality’ for emerging market central banks?
Q10.5 C. Ho (2008, “Implementing monetary policy in the 2000s: operating procedures in Asia and
beyond”, BIS Working Paper No. 253) concludes (p. 26) that “Another perhaps even more striking
finding of this paper is that even within just the last couple of years, there have been many changes
and new developments in virtually all aspects of monetary policy implementation – from the
redefinition of policy rates and operating targets, to the adoption of new instruments, to a complete
overhaul of the reserve requirement framework. It is therefore also clear that no operating
framework can be the “right” one for all times. Central banks everywhere – in industrial and
emerging economies alike – have continued to refine their frameworks and procedures and to
innovate where necessary, responding to changing needs in changing times.” How do you assess this
conclusion, and in particular that “no operating framework can be the ‘right’ one for all times”?
19
Q11: The nature of a liquidity crisis
Q11.1 Assume the following balance sheet of an indebted company. (You can use excel to
approximate some of the answers).
Assets
100-e
Company x
Senior debt
Equity
80 –max(0,e-20)
20-min(e,20)
(a) What is the probability of default for senior debt, assuming that e is normally distributed and
has an expected value of -5% and a standard deviation of (i) 5%, (ii) 15%, (iii) 25%? Assume
that default occurs when equity is negative.
(b) Assuming that investors are risk neutral and that the required remuneration rate for risk free
assets (established by the central bank) is 4%, what is the remuneration rate of debt for the
three alternative values of the standard deviation of e which compensates for the expected
losses?
(c) Assume now that there is a one off realised shock of e=-10. In the next period, asset value
uncertainty is again an identically independently distributed e being N(-5, σ2). What is now the
remuneration rate of debt that compensates for expected losses, again depending on the
standard deviation of asset value shocks?
(d) In how far does the profitability of the corporate depend on asset price volatility (even with
risk neutral investors)?
Q11.2 Consider the following table indicating total Government financing needs and total eventual
related increases of the debt/GDP ratio in the respective euro area country relating to the sovereign
debt crisis. (data from: H. Maurer and P. Grussenmeyer, 2015, Financial assistance measures in the
euro area from 2008 to 2013: statistical framework and fiscal impact”, ECB Statistics Paper Series,
No. 7).
(a) How would you interpret the data?
(b) What is the relationship between these measures of Government support and the role of
central bank credit?
Country
DE
IE
GR
ES
FR
IT
Financial needs in % GDP
(from table 2 in MG,
2015; 2008-2013)
8.8
37.3
24.8
4.8
0.0
0.2
Cumulated deficit effect due to
Government interventions (from
Table 4 in MG, 2015), in % of GDP
1.4
25.2
12.1
4.3
-0.1
-0.1
Q11.3 Assume the lemons market model of section 11.2 and that before the outbreak of a financial
crisis, the following parameter values apply: δ =0.4, p=0.9, and VG=1.2.
(a) Will an active credit market prevail under such circumstances?
(b) On the basis of the three parameters, explain why a financial crisis can lead to a break-down
of credit markets. Provide illustrations from the current financial crisis.
(c) Starting from the values above and varying each parameter individually: what are the critical
values of each of the parameters?
20
Q11.4 Why would you expect haircuts to increase in a financial crisis? What is the effect on leverage?
When could some collateral type become ineligible in interbank repos?
Q11.5 Why do bid ask spreads posted by market makers typically increase in a financial crisis?
Q11.6 Assume the following bank balance sheet.
Assets
Assets
D+1
Liabilities
Short term funding from Investor 1
Short term funding from Investor 2
Equity
D/2
D/2
1
Assume that a share Lambda, Λ (0<Λ<1) of assets is fully liquid (i.e. it can be sold without any
fire sale losses). Assume also that the other assets, i.e. a share (1-Λ) of assets, are totally
illiquid, i.e. if one would try to fire sell them, one would not generate a cent of liquidity, but
only generate losses. Assume also that the central bank applies a homogeneous haircut h on
all assets, and that all assets are eligible as central bank collateral.
(a) Derive a sufficient condition for a unique no-run equilibrium.
(b) Is funding stability ensured if Λ=0.4, h = 0.8, and D=2?
(c) What is the maximum sustainable amount of short term funding?
(d) Assume now that in a liquidity crisis Λ’=0. What would the central bank need to do to
maintain a unique no-run equilibrium (starting from the parameter values of b))?
Q11.7 Consider the following case of a bank threatened by a bank run
Assets
Liquid assets
Semi- liquid assets
Non-liquid assets
Λ(2+E)
Π(2+E)
(1-Π-Λ)(2+E)
Liabilities
Depositor 1
Depositor 2
Equity
1
1
E
Moreover, assume the following haircut and fire sales discounts, with f < h2:
Liquid assets
Semi-liquid assets
Non-liquid assets
Central bank haircut
h1
h2
h3
Fire sale discount
0
f
1
(a) What is the condition for a single no-run equilibrium?
(b) Assume now that Λ=0.25, Π = 0.25, f = 10% and h1 = 0%; h2 = 20% and h3 = 50%. What value
of E will the bank choose?
(c) What if f=25%?
(d) What if Λ=0, f= 50% h3 = 80%?
Q11.8 Why is there a risk that a liquidity crisis pushes the economy into a deflationary trap? Explain
this on the basis of an extended Wicksellian arbitrage equation.
Q11.9 What measures can central banks take to address the risks of the economy falling into a
deflationary trap in a financial crisis?
(a) ex ante
(b) ex post
Q11.10 In particular German economists have warned repeatedly that the crisis response of the ECB
would be inflationary. Examples (I wish to thank Adalbert Winkler for collecting these quotes): J.
Starbatty, 22 April 2010: „I think that the inflation rate will increase strongly: to above 5%. All
evidence shows that countries that have high debt levels tend to inflation”; H-O Henkel, 25 Mai 2010:
“An increase of inflation is in front of the door”; S. Homburg, 18 December 2011, answering to a
journalist’s question “Is a higher inflation rate unavoidable in the future?” S. Homburg: “Yes. So far,
21
the ECB has purchases sovereign bonds while at the same time absorbing the money supply
elsewhere. But when Italy gets stressed, then the ECB will no longer be able to sterilize the bond
purchases which would then be necessary. And if she is no longer able to do so, then unavoidably the
monetary base, the quantity of money, and eventually prices will increase. Currently the inflation
rate is 2.8%, so clearly above the target level of 2%. In principle the ECB would have to tighten its
interest rate policy already now”. J. Stark, 23 March 2012: “History has shown that any particularly
strong increase of central bank balance sheets has lead in the medium term to inflation” J. Starbatty,
10 September 2012: “In the long term there is only one reason for inflation: financing of fiscal deficits
by central banks. Current recessionary tendencies may still hide that. But that this creates inflation is
as certain as the Amen in the church”. MJM Neumann, 6 November 2012: expects a “creeping
inflation rate of up to 6%”. R. Vaubel, 11 October 2012: “I expect that we will get in coming years
inflation rates of up to 5% and more. This is because the monetary base has been increased since
2010 by more than 50%. I do not believe that the ECB will be able to turn this back in time”.
At least so far these economists were wrong, as inflation rates in the euro area trended down and
both headline and core inflation reached new lows in early 2015 (core at 0.6%, headline negative).
(a) What may explain that the inflation fears of these economists have not (yet) materialized?
(b) How would you rank their different arguments in terms of merits?
(c) Could they still be right in the long term with their inflation worries?
Q11.12. The following chart shows NFC overall cost of funding (see the book, page 174), the 5Y OIS
rate, and the average monthly EONIA rate during the crisis years. What does the evolution of the
three time series tell us? What does the evolution of their relative level tell us?
Q11.13 Before 2013, the ECB never lowered the rate of its deposit facility to below 0.25%, despite
the fact that it started with non-conventional monetary policy measures in 2007 and continued to
launch various such measures throughout all the crisis years. Only in 2013, the ECB set the deposit
facility rate to 0%, and in 2014 even to -0.10% (in June) and -0.20% (in September). How would you
interpret that various non-conventional monetary policy measures were taken by the ECB before it
strictly reached the ZLB?
22
Q12: Collateral availability and monetary policy
Q12.1 For what reasons does central bank collateral become scarcer in a financial crisis?
Q12.2 How can increased collateral scarcity affect monetary policy transmission in a financial crisis?
Q12.3 What can the central bank do to reduce collateral scarcity in a financial crisis and thereby
contribute to restore the intended stance of monetary policy at a given interest rate level?
Q12.4 Assume the following representative bank balance sheet. In normal (crisis) times, fire sale
discounts of credit claims is 100% (100%) and of corporate bonds 25% (50%). Central bank haircuts
are set in normal times to be 100% on credit claims (i.e. credit claims are not eligible central bank
collateral) and 50% on corporate bonds.
(a) What is the maximum sustainable level of d in normal times (assuming that the banks are
myopic and do not anticipate crisis times)?
(b) Assume that banks indeed chose to maximise their funding through short term deposits.
How would the central bank need to adjust its collateral framework in crisis times to
preserve a stable funding structure of banks and to prevent bank runs?
Assets
Credit claims
Corporate bonds
(d+2)/2
(d+2)/2
Liabilities
Short term funding from Investor 1
Short term funding from Investor 2
Long term debt
Equity
d/2
d/2
1
1
Q12.5 In a press release on 4 September 2008, the ECB announced to increase haircuts applied to
ABS when used by banks as collateral in Eurosystem credit operations. ABS “will be subject to a
haircut of 12% regardless of their residual maturity and coupon structure. This corresponds to the
level of haircuts that was previously assigned to assets in this liquidity category with a fixed coupon
and a residual maturity of over ten years. Furthermore, assets in this liquidity category that are given
a theoretical value …will be subject to an additional valuation haircut. This haircut will be applied
directly to the theoretical value of the asset in the form of a valuation markdown of 5%, which
corresponds to an additional haircut of 4.4%.” How would you assess these measures, taking into
account their timing? Was this decision compatible with the “inertia principle” of Bagehot?
Q12.6 on 15 October 2008, the ECB announced that it would “lower the credit threshold for
marketable and non-marketable assets from A- to BBB-, with the exception of asset-backed securities
(ABS), and impose a haircut add-on of 5% on all assets rated BBB-. How would you explain these
decisions?
23
Q13: Open market operations and standing facilities in a financial crisis
Q13.1 Besides improving collateral availability, how can central banks adjust their credit operations
in financial crises to make them more convenient?
Q13.2 What purposes can outright purchase programmes pursue in a financial crisis?
Q13.3 What are suitable operational targets for outright purchase programmes? Can you give
examples of outright purchase programmes with well-defined and not so well-defined operational
targets?
Q13.4 How would you measure the success of outright purchase programmes? Distinguish between
operational, intermediate, and ultimate targets. What are the main difficulties?
Q13.5 Should the success of outright purchase programme depend on whether the securities
purchased come from the holdings of banks or from of the holdings of households? What if banks are
subject to leveraging constraints? Draw the financial accounts of the economy and show what
difference it makes where the securities come from.
Q13.6 On 15 October 2008, the ECB announced that “the Eurosystem will also enhance its provision
of longer-term refinancing as follows: All longer-term refinancing operations will, until March 2009,
be carried out through a fixed rate tender procedure with full allotment.” How would you explain
this decision?
Q13.7 On 8 December 2011, the ECB announced to conduct two credit operations with duration of
36 months, specified as fixed rate full allotment operation. These were the longest monetary policy
credit operation ever done by a central bank, and the keen interest of banks to participate also made
them the largest ever (each had a volume of close to half a trillion). What speaks normally against
such operations, and what spoke in their favour in the euro area of December 2011?
Q13.8 Various LSAPs aimed at overcoming low inflation in the context of the ZLB (e.g. the
Government bond purchase programmes of the FED, BOE, BoJ and ECB). What effects on yields do
you expect from such programmes? Distinguish between a “stock”, a “flow”, and a fair value effect,
and elaborate also on the time path of interest rates that you expect to materialise.
Q13.9 Outright purchase programmes of a “credit easing” type aim also at compressing spreads of
securities towards risk free Government bonds. To what extent can such spread compression be
distortive and thereby undermine the efficient allocation of resources?
Q13.10 On 10 May 2010, the ECB announced its “Securities Market Programme”. Accordingly, “the
Governing Council of the European Central Bank (ECB) decided … to conduct interventions in the
euro area public and private debt securities markets (Securities Markets Programme) to ensure
depth and liquidity in those market segments which are dysfunctional. The objective of this
programme is to address the malfunctioning of securities markets and restore an appropriate
monetary policy transmission mechanism. …. In making this decision we have taken note of the
statement of the euro area governments that they “will take all measures needed to meet [their]
fiscal targets this year and the years ahead in line with excessive deficit procedures” … In order to
sterilise the impact of the above interventions, specific operations will be conducted to re-absorb the
liquidity injected through the Securities Markets Programme. This will ensure that the monetary
policy stance will not be affected.”
(a) How should one understand in this announcement the term “stance of monetary policy”?
(b) How would you assess the announcement of sterilisation in this context?
(c) How do you assess the reference to a statement by Governments?
(d) What would you expect to be the operational, intermediate, and ultimate target of the SMP?
24
Q14: The lender of last resort (LOLR) role of the central bank
Q14.1 What are the fundamental reasons for central banks to act as lender of last resort?
Q14.2 Explain why the LOLR role is also to some extent effective under central bank inertia, i.e.
without the central bank taking active LOLR measures. What determines the limits of this built-in
LOLR?
Q14.3 What are key “active” LOLR measures?
Q14.4 What are the distinct features of ELA, compared with normal central bank credit operations?
What are generally accepted central bank principles applied to ELA?
Q14.5 How would you assess the merits of “constructive ambiguity” regarding the provision of ELA?
Q14.6 Consider the following heterogeneous banking system (with “exogenous” modelling of funding
liquidity risk).
Government bonds
Corporate bonds
Loans to corporates
Deposits with CB
Total assets
Government bonds
Corporate bonds
Loans to corporates
Deposits with CB
Total assets
Government bonds
Corporate bonds
Lending to banks
Total assets
80
20
100
0
200
Bank 1
Deposits of HH
Borrowing from CB
Equity
Total liabilities
Bank 2
20 Deposits of HH
80 Borrowing from CB
100 Equity
0
200 Total liabilities
Central bank
50 Banknotes
50 Deposits of banks
140 +η Equity
240 +η Total liabilities
100 - 0.75η + μ
70 +0.75η - μ
30
200
100 - 0.25η - μ
70 + 0.25η + μ
30
200
200 +η
0
40
240 +η
Assume moreover that    10 and    5 and that the haircut vector of the central bank is {0%,
20%, 100%}.
a) What is the distance to illiquidity (DTI) and the Probability of Liquidity (PL) or Probability of
illiquidity (PI = 1- PL) of the two banks?
How does the system of accounts and the DTI and PL change under the following (independent)
scenarios:
b) Corporate bonds loose 30% of their value;
c) The central bank purchases 50 more of corporate bonds (proportionally to bank holdings);
d) The central bank starts accepting loans to corporates as collateral, applying a haircut of 50%;
e) The central bank lowers corporate bond haircuts to zero;
Finally:
f)
Under what circumstances is the central bank involved in absolute intermediation of the
banking system? How likely is that?
25
Q14.7 On 16 September 2008, the Fed provided a credit to AIG, the biggest American Insurer: “The
Federal Reserve Board on Tuesday, with the full support of the Treasury Department, authorized the
Federal Reserve Bank of New York to lend up to $85 billion to the American International Group (AIG)
under section 13(3) of the Federal Reserve Act. The secured loan has terms and conditions designed
to protect the interests of the U.S. government and taxpayers. The Board determined that, in current
circumstances, a disorderly failure of AIG could add to already significant levels of financial market
fragility and lead to substantially higher borrowing costs, reduced household wealth, and materially
weaker economic performance. The purpose of this liquidity facility is to assist AIG in meeting its
obligations as they come due. This loan will facilitate a process under which AIG will sell certain of its
businesses in an orderly manner, with the least possible disruption to the overall economy.” What
was particular in this operation? Why the reference to section 13.3 of the Federal Reserve Act?
Q14.8 On 14 September 2007, Northern Rock requested liquidity support facility from the Bank of
England. According to the Financial Times of that day: “It will lift the uncertainty that has been
hanging over Northern Rock’s future for much of the past month because it could not access the
wholesale funding upon which it is heavily dependent. It will also allow Northern Rock to reassure
thousands of customers that their deposits are secure.” However, actually these announcements
triggered a bank run with people queuing in front of branches to withdraw cash, i.e. the
announcement to provide ELA contributed to worsen a panic, instead of stabilising the situation.
How can this be explained?
Q14.9 Consider the balance sheet charts on pages 232-234 of the book. Which phases of the balance
sheet lengthening of CBs do you associate with the LOLR, and which ones do you explain differently?
Q14.10 Assume the following financial system
Assume the following financial accounts.
Real assets
Banknotes
Deposits
Real assets
Corporate bonds
Loans to corporates
Corporate bonds
Loans to corporates
Credit to banks
Corporate bond holdings
Household
E-4
Equity
E
2+ η
2- η
Corporate sector
4
Corporate bonds issued
2
Loans from banks
2
Bank 1
1– P/2
Depositors
1+μ-η/2
1
Central bank credit 1- μ + η /2 –P/2
Bank 2
1 – P/2 Depositors
1- μ - η /2
1
Central bank credit 1+ μ + η /2 –P/2
Central bank
3-P+ η
Banknotes
2+η
P
Central bank credit
1
Assume that the initial desire of the central bank to hold an outright portfolio is zero (P=0) and that
also the households’ financial asset allocation shocks μ, η stand initially at zero.
Assume moreover that the central bank applies a haircut h when accepting corporate bonds as
collateral. This haircut is initially 20%. The haircut the central bank applies to credit claims is 40%.
(a) How does relative and absolute central bank intermediation depend on μ, η?
(b) How does “distance to illiquidity” change with P? How do changes in the haircut influence
“distance to illiquidity?
26
Q14.11 Assume the following financial accounts.
Real assets
Deposits
Banknotes
Bank equity
Real assets
Bonds
Bonds
Credit to banks
Bonds
Household
Equity
E-D-B
D
B
F
Corporate/Government
D+B
Bonds issued
Bank 1
D/2 + B/2 + F/2 – P/2
Depositor 1
Depositor 2
Central bank credit
Equity
Bank 2
D/2 + B/2 + F/2 – P/2
Depositor 1
Depositor 2
Central bank credit
Equity
B-P
P
E
D+B
D/4
D/4
(B-P)/2
F/2
D/4
D/4
(B-P)/2
F/2
Central bank
Banknotes
B
Assume moreover that fire sale costs of bonds are 60% and central bank collateral haircuts on them
are 75%. How does the leveraging ability of the central bank depend on D, B, P?
27
Q15: LOLR and central bank risk taking
Q15.1 Would you expect the central bank risk budget to increase or to decrease in a financial crisis?
Q.15.2 Would you expect the central bank risk budget to increase or to decrease due to the
adjustment measures taken by the central bank in a financial crisis?
Q15.3 Bagehot claimed in 1873 that “only the brave plan [of the Bank of England] is the safe plan”.
Why would this be the case, and under what circumstances?
Q15.4 Consider the following example.
Government bonds
Corporate bonds
Loans to corporates
Deposits with CB
10
10
70
0
Bank
Deposits of HH1
Deposits of HH2
Borrowing from CB
Equity
40
40
10
10
Assume moreover that the haircut vector of the central bank is {0%, 20%, 50%} and that the fire sale
discounts in normal times are {0%, 10%, 40%}. These fire sale discounts are also the basis for
calculating the cost of default C (which we assume to imply immediate liquidation of all assets), and
therefore C=29 in normal times.
a) Is the funding structure of the bank stable?
b) What is the probability of central bank losses? In what sense is this probability a function of
haircuts (vary the haircuts proportionally)?
c) What changes if the fire sales loss vector is {0, 30%, 50%} in terms of how central bank losses
depend on haircuts?
Q15.5 Assume the following bank balance sheet.
Assets
D+d
Bank
Deposits of HH1
Deposits of HH2
Long term credit
d/2
d/2
D
Also assume a central bank collateral haircut of h and fire sale losses of f per asset unit sold, with f <
h. Under what circumstances is the risk talking of the central bank as a function of h upward sloping?
Q15.6 On 5 Mach 2009, the ECB issued a press release on its end 2008 Annual accounts and a note
on Monetary Policy Operations in 2008, in, which also explained the following. “In autumn 2008, five
counterparties defaulted on refinancing operations undertaken by the Eurosystem, namely Lehman
Brothers Bankhaus AG, three subsidiaries of Icelandic banks, and Indover NL. The total nominal value
of the Eurosystem’s claims on these credit institutions amounted to some €10.3 billion at end-2008.
The monetary policy operations in question were executed on behalf of the Eurosystem by three
NCBs, namely the Deutsche Bundesbank, the Banque centrale du Luxembourg and de Nederlandsche
Bank. The Governing Council has confirmed that the monetary policy operations in question were
carried out by these NCBs in full compliance with the Eurosystem’s rules and procedures, and that
these NCBs had taken all the necessary precautions, in full consultation with the ECB and the other
NCBs, to maximise the recovery of funds from the collateral held. The counterparties in question
submitted eligible collateral in compliance with the Eurosystem’s rules and procedures. This
collateral, which mainly consisted of asset-backed securities (ABSs), is of limited liquidity under the
present exceptional market conditions and some of the ABSs need to be restructured in order to
allow for efficient recovery. Under current market conditions, it is difficult to assess when the
eventual resolution will be achieved by the Eurosystem. The Governing Council decided that any
shortfall, if it were to materialise, should eventually be shared in full by the Eurosystem NCBs in
accordance with Article 32.4 of the Statute of the ESCB, in proportion to the prevailing ECB capital
28
key shares of these NCBs in 2008. The Governing Council also decided, as a matter of prudence, that
the NCBs should establish their respective shares of an appropriate total provision in their annual
accounts for 2008 as a buffer against risks arising from the monetary policy operations which were
conducted with the counterparties mentioned above. The size of the total provision will amount to €
5.7 billion, and it is already accounted for in the net result figures stated above. The level of the
provision will be reviewed annually pending the eventual disposal of the collateral and in line with
the prospect of recovery.”
On 20 February 2013, the Bundesbank issued a press release on the same subject: “Since autumn
2008 the Bundesbank has gradually resolved the pledged securities, in some cases having to
restructure them. In 2012, Diversity and Excalibur, the two largest positions in the LBB collateral
portfolio, were sold, amongst other assets. The process of winding down the pledged securities is
now complete. The situation after more than four years of resolving collateral is as follows. With
proceeds from sales as well as interest and redemption payments totalling €7.4 billion, a
considerable percentage of the original claims against LBB have been covered. After subtracting
these €7.4 billion from the original claim of €8.5 billion, a difference of €1.1 billion is left over. After
accounting for interest claims and costs totalling €0.8 billion, a residual claim of €1.9 billion is left
over and will go into the German LBB bankruptcy proceedings. In addition, the Bundesbank is a
creditor in the US LBHI bankruptcy proceedings; it has a nominal guaranteed claim of $3.5 billion
against LBHI. Payments are expected from both bankruptcy proceedings. For this reason, the
Eurosystem’s provisions for counterparties in default, calculated according to the principle of
prudence, and of which LBB is the largest position, were able to be reduced from €5.6 billion at end2008 to €0.3 billion at end-2012.”
What are the ley lessons from this episode for central bank collateral frameworks?
29
Q16: LOLR, moral hazard and liquidity regulation
Q16.1 In a report in 2009, the UK Financial Services Authority (p. 68) acknowledged that: “[T]here is a
trade-off to be struck. Increased maturity transformation delivers benefits to the nonbank sectors of
the economy and produces term structures of interest rates more favourable to long-term
investment. But the greater the aggregate degree of maturity transformation, the more the systemic
risks and the greater the extent to which risks can only be offset by the potential for central bank
liquidity assistance.” What are the actual costs of potential central bank reliance which really justify
the perception of a trade-off?
Q16.2 How would you define “Moral hazard”? What is the distinction from “legitimate” optimisation
behaviour? In which sense can substantial liquidity and maturity transformation of banks be
considered “moral hazard”?
Q16.3 What are key challenges in liquidity regulation?
Q16.4 Sunday July 13, 1931 was a decisive day in German economic and financial history: it was the
day in which Germany failed to find a solution for its banking crisis. After that, banks never reopened normally, gold convertibility of the Mark ended, and Germany defaulted on its foreign debt.
Only around 20 years later, and the unprecedented human and political disaster of the “Third Reich”,
normalisation occurred. Hans E. Priester (1932, Das Geheimnis des 13 Juli, Verlag von Georg Stilke,
Berlin) describes a part of the decisive meeting in the Reichsbank as follows (own translation, p. 6263):
„After a short welcome by Chancelor Brüning, state secretary Trendelenburg summarized the
situation. There would be two ways to save Danat bank: a merger or supportive solidarity by
all other banks. Otherwise, only a closure of Danat bank would remain. A discussion followed.
The banks unanimously rejected the idea of solidarity as the situation of Danat bank was
completely non-transparent…. Eventually, the banks were ready to help Danat bank with 250
million Reichsmark, but only if the funding would come from the Reichsbank and in any case
the Reichsbank would have to give up its restrictive policies. The President of the Reichsbank
Dr. Luther completely rejected this proposal, and announced to the contrary that the
restrictive policies would be sharpened even further in the future. Neither himself nor Brüning
mentioned that the political negotiations with France [regarding inter-central bank loans]
played an important role to explain his position. Harsh words were exchanged, including by
Dr. Luther. He refused to tolerate that all of the burden was dumped on the Reichsbank, who
would not be the drudge the banks seemed to perceive in it. She would not be ready to let
itself be misused, as the first condition for maintaining the German economy would be that
the central bank would remain faultless. If he would provide further discount loans, he would
not be able to maintain the 40% gold cover ratio. … The banks should think about the signal
an under-fulfilment of the gold cover ratio would imply. Unrest would be created, which could
easily be the starting point of a domestic bank run…. Also for political reasons, the Reichsbank
would not be in a position to engage in such support measures before the central bank
meeting in Basel next Monday…. Luther had spoken himself into a state of strong excitement.
He stood there wildly gesticulating, in his hand his bible, the Reichsbank law. The
representatives of the banks and the ministries were perplex, as they did not know enough
about the political issues who had brought Luther towards such conclusions. … Geheimrat
Bücher of the AEG asked Luther ironically, what would be the benefit of a faultless
Reichsbank, if the rest of the economy had broken down. He added that one should not only
insist on legal articles, as unusual times also require unusual measures. The Reichsbank would
be the institution that was responsible for the functioning of the German credit system. She
would had the duty to do whatever was possible, to avoid the collapse of the German credit
building. But Dr. Luther constantly insisted that the Reichsbank would not contribute funding
in any sense to the rescue of Danat bank.”
30
(a) What analogies and differences between the failed rescue of Lehman in September 2008,
and the discussions on Danat Bank in July 1931 do you see?
(b) How would you generally assess the merits of “collective private” solutions brokered by the
central bank to solve liquidity problems of single institutions (similarly to the case of the
LTCM rescue brokered by the Fed NY in [1998], or the liquidity support that German banks
gave temporarily to Hypo Real Estate in 2007, brokered by the Deutsche Bundesbank)?
(c) How important would you believe is it that the central bank sticks to the rules in LOLR
operations, as a matter of principle (as argued by the President of the Reichsbank, Hans
Luther)?
(d) In which sense would Reichsank LOLR to Danat Bank has been a “misuse” of the Reichsbank,
as argued by Luther?
(e) What difference did the Gold standard make, and in which sense was the Gold standard the
eventual main problem to an unconstrained LOLR by the Reichsbank (this question can best
be answered after reading also chapter 17 of the book)?
Q16.5 M. Carlson, B. Duygan-Bump, and W. Nelson (“Why do we need both liquidity regulation and a
Lender of Last resort? A perspective from Federal Reserve Lending during the 2007-2009 Financial
Crisis”, BIS Working Paper No. 493) conclude that “while central banks can to some extent control
the potential moral hazard associated with lending by pricing credit risk correctly or, more practically,
by driving credit risk to zero by taking on lots of collateral, this approach may actually hinder their
ability to address liquidity troubles at times. Consequently, it will also be important to establish
sufficiently low-cost resolution regimes to reduce the cost of allowing an institution to fail, and that
institutions be allowed to fail – rather than lent to by a LOLR – when their illiquidity is the
consequence of solvency rather than liquidity concerns.” What is the precise link between credit risk
taking of the central bank when doing LOLR and bank solvency?
31
Q17: The international lender of last resort
Q 17.1 Consider the case of a monetary area such as the euro area, with a system of national central
banks (NCBs) and the ECB. The following accounts represent this case, whereby only two NCBs are
distinguished (A and B)
a) Comment on these initial financial accounts. How could one explain the main
asymmetries between the two countries?
b) Assume now that doubts arise on the solvency of the banking system of one country (or
people realise that the deposit insurance in one country is less good than in other
countries etc.). Represent the following five shocks in the system of financial accounts:
i.
households shift deposits of 5 from A to B banks
ii.
household shifts deposits from B to A banks amounting to 32
iii.
decline on interbank lending to A banks to zero
iv.
households withdraw banknotes from A banks for 6
v.
NCB A injects reserves into the A banks by purchases of corporate claims of 4
c) How would you represent a current account transaction in this system of financial
accounts (hint: you need to split the household account into an A country and a B
country household)? Assume a surplus of country B of 10.
Euro area households
Deposits with A banks
Deposits with B bans
Banknotes
Real assets
Loans
Deposits with NCB A (RR)
Loans
Net interbank claims
Deposits with NCB B (RR)
Eurosystem credit
Net intra –Eurosystem claims
Eurosystem credit
10
Equity
40
10
40
A country banking system
20
HH Deposits
5
Eurosystem refinancing
Net interbank liability
B country banking system
40
HH Deposits
10
Eurosystem refinancing
10
NCB A
5
Banknotes
Deposits of banks
3
NCB B
20
Banknotes
Current accounts of banks
Net intra – Eurosystem liabilities
100
10
5
10
40
20
3
5
7
10
3
32
Q 17.2. Consider the case of a monetary area such as the euro area, with a system of two
national central banks (but no ECB). The accounts below represent this case, with two stylised
countries “Greece” and “Germany” which are initially identical. Assume that this represents the
situation at end of 2009.
Deposits with Greek banks
Deposits with German banks
Banknotes
Real assets
Deposits with Greek banks
Deposits with German banks
Banknotes
Real assets
Real assets
Loans
Deposits with NCB A (RR=5)
Loans
Deposits with NCB B (RR=5)
Eurosystem credit
Intra –Eurosystem claims
Eurosystem credit
Intra –Eurosystem claims
Eurosystem credit
“Greek” households
10
Equity
10
5
25
“German” households
10
Equity
10
5
25
Euro area corporate sector
50 Real assets
“Greek” banking system
25
HH Deposits
5
Eurosystem refinancing
“German” banking system
25
HH Deposits
5
Eurosystem refinancing
“Bank of Greece”
10
Banknotes
Deposits of banks
0
Intra –Eurosystem liabilities
“Deutsche Bundesbank”
10
Banknotes
Deposits of banks
0
Intra – Eurosystem liabilities
“Eurosystem”
20
Banknotes
Deposits of banks
50
50
50
20
10
20
10
5
5
0
5
5
0
10
10
(a) Assume now that Greece has in 2010 a current account deficit of 2 and a capital account
deficit of 4. The current account deficit results from real asset transactions between
households (whereby the Greek household uses his account with the Greek bank to pay for
the net import of real assets), while the capital account deficit results from deposit transfers
of which one half is done by the Greek, and one half by the German households (i.e. each
household transfers 2 deposit units from one bank account to the other). How do the
accounts look like at the end of 2010?
(b) Assume that the central bank accepts Loans of banks to corporates as collateral but imposes
a haircut of h. What is the critical level of the haircut h at which the flows above become
constrained by the collateral scarcity of the Greek banking system?
(c) Assume that after 2010, the same capital and current account flows continue. When will the
consolidated Eurosystem balance sheet start to lengthen (i.e. when will the Eurosystem start
to do “absolute” central bank intermediation, instead of only “relative” one)?
Q17.3 Some observers have criticised that the TARGET2 system (which is the cross border payment
system in the euro area) and the associated creation of Intra-Eurosystem claims and liabilities is
problematic as it undermines “hard” budget constraints. The conclusion is drawn by these observers
that the intra-Eurosystem claims should be capped (i.e. a maximum limit should be imposed). How
do you assess this proposal?
33
Q17.4 Consider the following example of a stylised state balance sheet.
Assets
1
State A
Short term foreign currency loans – investor 1
Short term foreign currency loans – investor 2
Equity
d/2
d/2
1-d
Assume that the Government can generate liquidity in the short term, but at some increasing costs.
Assume that the cost of liquidity function f(x) is a mapping from the state’s assets ordered according
to liquidity in [0,1] into marginal liquidation costs within [0,1], whereby f(0) = 0 and df(x)/dx ≥ 0. Also
define F(x) the integral of f(x). The maximum amount of short term liquidity that the Government
may generate is therefore 1-F(1).
(a) Under what conditions does this state have stable access to international capital markets?
(b) What are “assets” and “equity” in the case of a sovereign?
(c) What are possible analogies to asset value shocks and a deterioration of asset liquidity for
banks?
(d) Assume now that f(x) = x^α. What is the highest possible level of short term funding as a
function of α?
(e) Assume now that d=0, 0.25, 0.5, 0.75, 1 and α=0.1, 0.5, 1, 5. In which cases does the
Government has a stable funding basis?
Q17.5 According to a Bloomberg News Article of 24 May 2011, “European Union demands may
require Greece to sell 15 billion euros of assets by the end of 2012, a year ahead of schedule, in order
to win a new three-year loan package, a person familiar with the talks said today. EU Economic and
Monetary Affairs Commissioner Olli Rehn said creating a vehicle to manage Greece’s privatization
program was being considered. … “The possibility to create a trust fund or a privatization agency is
one option we’re exploring among several,” Rehn told reporters in Vienna today. The government
said it would sell its stake in Hellenic Postbank SA and the country’s ports in the first phase of the
asset-sale program. The state’s direct 34 percent stake in Postbank has a market value of about 275
million euros. The government also said it would create a sovereign-wealth fund composed of state
assets to accelerate the sale process. The government plans to complete the stake of Hellenic
Postbank by the end of the year, and to sell 75 percent stakes in Piraeus Port Authority and
Thessaloniki Port Authority SA. It also intends to extend the concession for Athens International
Airport this year.” What are the strength and weaknesses of state asset sales in a Government
funding / Balance of Payments crisis?
Q17.6 In June 2015, Greek authorities introduced administrative measures in Greece to protect the
funding of Greek banks. Show in a financial accounts system that both balance pf payment deficits
and banknote withdrawals create funding gaps with banks that can only be closed with central bank
credit. What key challenges would you expect for a capital controls framework to operate in a
monetary union like the euro area?
34
Solutions
S1: Basic terminology and relationship to monetary macroeconomics
S1.1 See page 9-10 of the book.
S1.2 The “purest” open market operation, and the most remote to a standing facility, is a bilateral
outright purchase or sale of a security (or commodity, like gold) in the financial market using
standard practices also applied between banks. A pure standing facility in today’s sense is a credit
operation with well-defined access criteria and procedures, accessible to eligible counterparties at
any moment during the day, and overnight maturity and full allotment at the pre-announced interest
rate. The following steps can each be seen as moving from the pure open market operation to the
pure standing facility, and the continuum results from the fact that the steps can be gradual on some
of the dimension.

Instead of a bilateral trade in the “open” financial market using standard interbank practice,
conduct an auction procedure with pre-defined access conditions and (idiosyncratic)
procedures;

Instead of outright purchases of securities, do credit operations;

Shorten the maturity of credit operation to overnight;

Conduct the credit operation as fixed rate tender (instead of as variable rate tender); more
generally, be oriented towards interest rates, instead of towards quantities;

Conduct the operation with full allotment;

Conduct the operation late in the day (as intra-day credit anyway tends to be interest rate
free, an end of day overnight operation tends to be economically equivalent to offering
access at any moment during the day).
One could say that an open market operation in the form of a fixed rate full allotment with overnight
maturity and conducted at day end is practically equivalent to a liquidity-providing standing facility
for overnight credit.
S1.3 The matrix is as follows.
Open market operation
Standing facility
Outright operations
Credit operations
Purchase in the standard market
(or through an auction) of a
certain fixed quantity of a security
(Example: ECB’s Public Sector
Purchase Programme, PSPP, 2015)
Auction central bank three months
credit once a months in a variable
rate tender with pre-announced
volume (Example: ECB’s LTRO, as
conducted between 1999 and
2008)
Discount window in pre-1914
central
banking
(selling
commercial bills to the central
bank with the price being
determined by the discount rate
fixed by the central bank)
Modern
liquidity
providing
standing facilities, e.g. “marginal
lending facility” of the ECB
35
S1.4 See page 12-13 of the book.
S1.5 See pages 12-13 of the book
S1.6 From the point of view of the terminology as proposed in chapter 1 of the book, Poole mixes an
‘instrument’ (a term the book uses for e.g. standing facilities and open market operations) with the
concept of an ‘operational target’, which is a variable that the policy decision making body of the
central bank sets, and which is then targeted on a day-by-day basis through central bank market
operations.
On substance, the following critical remarks are permitted:
First, the ‘money stock’ is neither an ‘instrument’ nor an ‘operational target’ but if anything an
intermediate target or an information variable. It cannot at all be steered on a day-to-day basis.
Second, the ‘fence sitters’ is what this paper of Poole aims at contributing to: a model which justifies
such an intermediary approach, depending on what shocks hit the economy. However, from today’s
perspective, we would say that this idea of ‘fence-sitting’ and of the associated model of Poole was
more an academic exercise, and that it cannot be applied to practical central banking. In reality, short
term interest rates are a meaningful operational target, and the money stock is not. The only
relevant question is what information content is attributed to the money stock in the
macroeconomic model of the central bank. The macroeconomic model is a key input to the decisions
on the setting of short term interest rates as operational target.
36
S2: Representing monetary policy implementation in a closed system of financial accounts
S2.1
(A) The implementation technique seems to be based on a symmetric corridor approach (as
recourse to both facilities seems to be zero). Liquidity is steered through outright purchases
and sales in a way to achieve neutral liquidity before recourse to central bank facilities.
(B) Transactions are reflected as follows
(a) Real assets of corporates and corporate debt decline by one; Corporate bonds held
by central bank decline by one; A new “real asset” item is added to the central bank
balance sheet with a value of 1. (Of course the central bank does not pay the
corporate directly with a corporate bond. Instead, the central bank will initially credit
the central bank deposit account of the bank of which the corporate is a client. But
the corporate will then in a second step want to reduce its excess cash, and redeem
with it some of its bond, as this allows to reduce the related interest rate cost).
(b) Household: banknotes down by 8 to 2, deposits of households with banks up by 8; CB
balance sheet shortens by 8 as banknotes go down by 8; to shorten also its asset
side, we assume that the central bank sells corporate bonds of 8. Banks take these
corporate bond from the central bank, and pay for them with the cash they got from
the inflow of deposits of 8. This is how accounts look like afterwards (we do not
show the corporate and government sectors, as they are unaffected).
Real assets
Banknotes
Deposits banks
Bank equity
Corporate equity
Corporate bond
Government bond
Corporate bonds
Government bonds
Deposits with CB
CB Deposit facility
Corporate bonds
Government bonds
Central bank credit
Households
60
Equity
10 -8
10 +8
10
2
1
7
Banks
7 +8
Deposits of HH
8
Equity
5
Central bank credit
0
Central bank
10 -8
Banknotes
5
Deposits of banks (RR=0)
0
CB Deposit facility
100
10 +8
10
0
10 -8
5
0
(c) Banknotes held by household increase to 20, deposits go down to zero. Banks take
recourse to central bank credit for 10 to substitute for the deposit outflows. The CB
balance sheet lengthens by 10, as banknotes and CB credit both increase by that
amount.
(d) The central bank sells all Corporate and Government bonds (15 in total) to the banks,
the banks have to refinance those with additional central bank credit. The central
bank undertakes an asset switch, while banks see their balance sheet lengthen by 15.
(e) Corporations see their asset value being reduced from 20 to 10, and see their equity
being wiped out and also the value of debt has to decline from 18 to 10 (write-offs
applied to the holders of these securities). For banks that means that corporate
bonds decline from 7 to 7*10/18 = 3.89, i.e. by 3.11. Their equity declines
37
accordingly from 10 to 6.89. The central banks’ corporate bonds decline from 10 to
10*10/18 = 5.56 and CB equity becomes negative (having been zero before), namely
an asset side equity of 4.44. Finally, also the household suffers a shrinkage of
corporate bod values by a factor 10/18 (i.e. by -0.445 to 0.555) on its corporate
bonds and experiences the same drop of its equity. Moreover, the households has
large losses on corporate and bank equity (as he is the only holder of this equity). In
fact the only loss that does not end up directly with the household is the central bank
loss. This will however end later on with it, in the form of higher taxes to compensate
for the absence of seignorage for some years. The financial accounts look as follows
after applying these changes.
Real assets
Banknotes
Deposits banks
Bank equity
Corporate equity
Corporate bond
Government bond
Real assets
Total assets
Corporate bonds
Government bonds
Deposits with CB
CB Deposit facility
Total assets
Corporate bonds
Government bonds
Central bank credit
Equity gap
Total assets
Households
60
Equity
100 -2-3.11-0.445
10
10
10 -3.11
2-2
1-0.445
7
Corporations
20-10
Equity
2 -2
Debt
18 -8
20
Total liabilities
20
Banks
7 -3.11
Deposits of HH
10
8
Equity
10 -3.11
5
Central bank credit
0
0
20
Total liabilities
20
Central bank
10 -4.44
Banknotes
10
5
Deposits of banks (RR=0)
5
0
CB Deposit facility
0
4.44
15
Total liabilities
15
38
S2.2
(a) Impact on length of BS (in the table “R” = “Real assets held by household)
Factor: →
B↑ (HH choice)
D↑ (HH choice)
P↑ (CB choice)
Household
No impact as asset switch with
D or R
No impact as asset switch
with B or R
No effect
Corporate sector
Depends
on
substitute asset:
Depends on the
substitute asset:
No effect
Length of balance
sheet of: ↓
Banks
CB
the
HH’s
HH’s
If HH:B↑+D↓: Neutral.
If HH:D↑+B↓: Neutral.
If HH:B↑+R↓: Increases (as
corporate takes over real
assets from HH).
If HH:D↑+R↓: Increases (as
corporate takes over real
assets from HH).
If HH:B↑+D↓: Neutral.
If HH:D↑+B↓: Neutral.
If HH:B↑+R↓: Increases
If HH:D↑+R↓: Increases
Balance
lengthens
If HH:D↑+B↓: shortens
sheet
always
If HH:D↑+R↓: neutral
Shortens bank BS
Asset side switch,
balance
sheet
length unchanged
(b) Take the example of the euro area (see table 2.2 on page 35 of the book – this data refers to
June 2011) – the length of the Eurosystem central bank balance sheet was around EUR 1.9
billion with banknotes of EUR 0.8 billion. Deposits are around EUR 21 trillion; The length of
the household balance sheet is around 19 trillion; banks’ balance sheet have a length of
around EUR 30 trillion (note that “monetary financial institutions” include the central bank).
Important simplifications in the stylised financial accounts: Households are also leveraged,
i.e. take credit from banks; some sectors are missing: Government; non-bank financials; Rest
of the world.
(c) As follows (the debt of the household is called “L”) . If the households uses the credit to buy
real assets (e.g. real estate), then this goes at the expense of the length of the balance sheet
of the corporate sector:
Real assets
Banknotes
Deposits
Real assets
Bonds
Loans to households
Household
E+L-D –B
Equity
B
Loans from banks
D
Corporate sector
B+D-L
Bonds issued
Banks
D+B-P-L
Deposit
L
Central bank credit
E
L
B+D-L
D
B-P
39
If the HH uses the bank credit to hold more deposits, then instead:
Real assets
Banknotes
Deposits
Real assets
Bonds
Loans to households
Household
E -D -B
Equity
B
Loans from banks
D+L
Corporate sector
B+D
Bonds issued
Banks
D+B-P
Deposit
L
Central bank credit
E
L
B+D
D+L
B-P
In none of these cases, the central bank balance sheet is affected (therefore it is not shown).
S2.3
(a) The charts can be drawn easily in Excel – see the excel file Q2 3. These are the deposit curves
across individual banks for the four proposed combinations of the four parameters.
Notes: D1 (x) and D2(x) are identical. Under both D3(x) and D4(x), the banks with the weakest
deposit base have no deposits at all. D3(x) can be interpreted as the result of a reallocation of
household financial assets out of bank deposits into banknotes. D4(x) can be interpreted as a
re-allocation of household financial assets from deposits of weak banks to deposit of strong
banks (a run on individual banks, presumably by those households having accounts with
weak banks opening accounts with strong banks and transferring their deposits).
(b) Define Ri(x) now as the recourse of bank x to central bank credit under scenario i. The
formula for Ri(x) is: Ri(x) = B-P-(Di(x)-D) = B-P-(0.5-x)s. In the same excel file the recourse to
the central bank curves are drawn, for the same four scenarios also examined under (a).
40
Notes: In the initial case R1 the position of banks vis-à-vis the central bank (before money
markets) is symmetric, i.e. some banks are short, others are long. Therefore, there are
opportunities for interbank trading, and eventual recourse to the central bank after a
perfectly efficient interbank market would have cleared is zero (as B-P=0). The same applies
for R4. Because of the higher value of s, there is even more scope for interbank trading. In the
cases R2 and R3, in contrast, all banks are “on the same side” relative to the central bank even
before interbank markets, and therefore there is no reason to expect the existence of an
interbank market.
The bank x’s balance sheet looks as follows:
Bonds
Excess reserves
D+B-P
max(0, -(B-P-(0.5-x)s))
Deposit
Central bank credit
D+(0.5-x)s
max(0, B-P-(0.5-x)s)
(c) An interbank market takes place if some banks are in a surplus to the central bank and some
in a deficit (before interbank trading). This is the case if R(0) < 0 and R(1) >0, i.e. B-P-0.5s < 0
and B – P + 0.5s > 0. This means that -0.5s < B-P < 0.5s. The size of the interbank market for a
given s is maximised if the liquidity neutral bank x* is right in the middle, i.e. x* = 0.5 => B-P =
0  B=P, which means that we are in the symmetric corridor case. Another necessary
condition for an interbank market to take place is that interbank market transaction costs,
including those relating to credit risk concerns, are not too high, and in any case do not
exceed the spread between the rate at which the central bank provides credit to banks and
the remuneration rate offered by the central bank for excess reserves.
(d) One can show that if a liquidity neutral x* exists in [0,1], then x* = 0.5-(B-P)/s (if 0.5-(BP)/s>1, then all banks have excess liquidity, and if 0.5-(B-P)/s<0, then all banks need to take
recourse to central bank credit; in both cases there is no bank with a neutral liquidity
position towards the central bank and M=0). If x* = 0.5, then the interbank volume (under
efficient markets) will be M=s(0.5^3)=0.125s. If x* deviates from 0.5, then market volumes
shrinks with the square of the proportional deviation of x* from 0.5, because, graphically
spoken, both sides of the triangle, the surface of which represents the market volume, shrink
proportionally. Therefore the shrinkage factor is ((0.5 - abs(x*-0.5))/0.5)^2. Therefore, the
interbank market volume formula is:
M = s(0.5^3)((0.5 – abs((B-P)/s))/0.5)^2 = 0.5s(0.5–abs((B-P)/s))^2.
41
(e) The results are shown in the following table. For (i) apply formula derived in (d); If interbank
markets function perfectly, then all aggregate balance sheet figures will correspond to the
ones that hold in the aggregate model. Therefore: (ii) max(B-P, 0); (iii) max(P-B, 0); (iv) B +
max(P-B, 0).
(f) The results are shown in the following table. If money markets break down, then both the
recourse to central bank borrowing and the excess reserves held by banks with the central
bank increase by what was – under functioning markets – the interbank volume. Therefore, if
the interbank volume under functioning markets was M for some parameter constellation,
then (ii) max(B-P,0) + M; (iii) max(P-B, 0) + M; (iv) B + max(P-B,0)+M.
Table resulting from the formulas above:
1
2
3
4
Input parameters
Total Deposits D =
1
1
0,5
1
inequality parameter s
1
1
1
2
Banknotes B
1
1
1,5
1
Portfolio P
1
2
1
1
0,125
0*
0
0,25
Recourse to CB credit
0
0
0,5
0
XS Reserves
0
1
0
0
Length of CB balance sheet
1
2
1,5
1
Recourse CB credit
0,125
0
0,5
0,25
XS Reserves
0,125
1
0
0,25
Length of CB balance sheet
1,125
2
1,5
1,25
Functioning MM
Interbank volume
Broken MM
*In this case x* is outside [0,1] and therefore the formula for x* does not apply, but x*=0
(g) We vary P from 0 to 2 in steps of 0.5 to obtain the following central bank recourse (before MM) curves
(functions of x cross banks). This provides some intuition on how the triangles evolve.
42
The following two charts show the evolution, as a function of P, of the MM volume, total excess
reserves and total recourse to the central bank for efficiently functioning and broken money markets,
respectively.
M, R, XSR as a function of P, for functioning MM:
M, R, XSR as a function of P, for broken MM:
Evolution of BS length as a function of P, for functioning and broken money markets, respectively:
43
The following table shows data for five different values of P.
1
2
3
4
5
Total Deposits D =
1
1
1
1
1
inequality parameter s
1
1
1
1
1
1
0,5
1
0,75
1
1
1
1,25
1
1,5
0
0,5
0
1
0,03125
0,25
0
1
0,125
0
0
1
0,03125
0
0,25
1,25
0
0
0,5
1,5
0,5
0
1
0,28125
0,03125
1,03125
0,125
0,125
1,125
0,03125
0,28125
1,28125
0
0,5
1,5
Banknotes B
Portfolio P
Functionning MM:
Interbank volume
Recourse to CB credit
XS Reserves
Length of cB balance sheet
Broken MM
Recourse CB credit
XS Reserves
Length of CB balance sheet
(h) If s increases because of households’ suspicion that some banks are weak, then probably also
strong banks are worried about their weaker competitors and will not lend to them in the
interbank market. Therefore, a significant increase in s will likely be correlated with a switch
from efficient to broken markets, and therefore also the simulations assuming broken
markets are more relevant.
S2.4
(a) The definitions of the various central bank balance sheet concepts can be found in Chapter 2 of
the book. In short:
(i)
The level of total autonomous factors = total net sum of all balance sheet items that
are not under the control of the monetary policy function, i.e. all items except
monetary policy items and sight deposits of domestic banks with the central bank;
netted typically on the liability side of the balance sheet;
(ii)
the total liquidity provision through monetary policy operations = the (net asset) sum
of monetary policy operations, i.e. both outright and reverse;
(iii)
the original liquidity deficit of the banking system = autonomous factors + reserve
requirements = liquidity that needs to be provided through MPI including outright
operations; In historical central bank balance sheets, one should also account for a
large demand for working balances by banks, which one may regard as a component
of the liquidity deficit that needs to be satisfied by liquidity provision through
monetary policy operations.
(iv)
the liquidity deficit post outright monetary policy operations = liquidity needs that
need to be covered by central bank credit operations, i.e. after outright monetary
policy operations = AF + RR – outright MPOs;
(v)
the “leanness” of the balance sheet = total length of BS / banknotes
Be aware that assigning certain balance sheet items to either “autonomous factors” or “monetary
policy” is not necessarily trivial. For example, “government bonds” can reflect (i) an investment
portfolio; (ii) a facility granted to the Government; (iii) a monetary policy portfolio. In the first two
44
cases it would be classified as autonomous factor, in the last case obviously as monetary policy item.
A classification can normally be achieved by reading in e.g. the annual report of the central bank its
further explanations. Below we solved these ambiguous cases in one way or the other, as it can be
seen in the calculus provided within the matrix. Another issue is that in principle one would need to
know reserve requirements (which itself is not a balance sheet item) to calculate the liquidity deficit.
Again ideally one can find out the level of reserve requirements from publications of central banks.
The following table provides the results for the five central banks and the five measures:
Measure →
Central bank ↓
Total
autonomous
factors
Total
liquidity
provision through
MPOs
Original liquidity
deficit
Liquidity deficit
post
outright
operations
Leanness
of
balance sheet
Reichsbank 1900
1139+150-81714-23 -68 = 367
800+ 80 = 880
376 + 513 = 889*
889
1802/1139 = 1.58
Reichsbank 1922
1280 + 36 – 1 –
1184 = 131**
660+1 = 661
131+530 = 681
681
1846/1280 = 1.44
Bundesbank 1998
260+ 33—112 =
181
235 – 5 = 230
181 + 49 =
230***
230
347/260 = 1.33
484+55-563 = -24
39
-24+63 = 39
39
602/484 = 1.24
Latvia, 2001
* We interpret current accounts in the case of the Reichsbank as inevitable demand for reserve balances and therefore as a
component of the liquidity deficit.
** We interpret the large outright holdings of T-bill as result of a funding facility offered to the Government by the
Reichsbank – this implies the classification as autonomous factor
*** In these cases we interpret current account as being equal to reserve requirements
(b) Striking features of balance sheets
Reichsbank 1900: large size of voluntary reserves, suggesting a not so efficient payment system
and/or a high number of small depositors with the central bank. Large precious metal reserves
relative to the monetary base, and reliance on discounting as monetary policy tool.
Reichsbank 1922: depleted precious metal reserves, instead lots of Government bills of a presumably
not so healthy sovereign, implying that in reality the Reichsbank may have had negative capital. Still
reliance on discounting of trade bills as tool to provide liquidity.
Bundesbank 1998: Lean balance sheet, reliance on central bank credit operations for MPI.
Bank of Latvia, 2001: More foreign reserves than banknotes, compatible with currency board
framework. Very small liquidity deficit.
S2.5 With fountain pain money, James Tobin meant the fact that in principle bank directors can, by
signing loan contracts and at the same time crediting the account of the client for the amount lent,
create “money” (in the sense of sight deposits with banks) by a mere signature.
S2.6 Limits to the creation of fountain pen money: (i) household preferences and the fact that
fountain pen money is not cost free to create (banks require higher interest rate on loans than they
pay on deposits, such as to be able to cover their operating costs and to be compensated for risk
taking. (ii) capital adequacy (risk-weighted assets or leverage ratio); (iii) reserve requirements and
collateral constraints, jointly, limit also the simultaneous creation of fountain pen money by banks;
(iv) in case of a diverging speed of fountain pen money creation by say two banks, the one creating it
faster will need to increase its refinancing with the central bank and will eventually run into collateral
issues even without reserve requirements.
45
S2.7 Assume a banking system composed of two banks only. Two banks may co-ordinate and create
fountain pen money more or less in parallel, and this effectively will soften some of the constraints.
For a granular banking system, the outflow of large parts of created fountain pen money is
unavoidable, and co-ordination is more difficult. Therefore, for example, collateral haircuts alone are
sufficient to limit money expansion.
S2.8 (a) Capital adequacy requirements. 8% capital, 100% risk weighting of all assets. Therefore:
(D/2 + B/2 + F/2 + C/2)*0.08 ≤ F/2 => C ≤ + 0.92F/0.08 - D-B
(b) Reserve requirements on household deposits are 5%. Therefore, a bank’s balance sheet now
looks as follows, whereby we assume that the bank refinances the additional liquidity needs with the
central bank. In so far, provided central bank liquidity provision is elastic, there does not seem to be
a direct limit following from reserve requirements.
Lending to corporates
Lending to households
Required reserves
Bank i
Household deposits / debt
D/2 + B/2 +F/2
C/2
Credit from central bank
0.05*(D/2 +C/2)
Equity
D/2+C/2
B/2 + 0.05*(D/2+C/2)
F/2
If the central bank refuses to provide additional central bank credit, then a constraint kicks in directly
(and a necessary condition for fountain pen money creation is that banknotes decline, which may be
achieved with very high interest rates).
(c) Collateral: lending to corporates is central bank eligible collateral, whereby a haircut of 20% is
applied. This is not relevant in the case that credit creation by the two banks moves in parallel, as
central bank funding does not increase as a consequence of parallel credit creation. This is different
in the case only one bank would try to expand.
(d) Both reserve requirements apply as in (a) and collateral rules as in (c). Available collateral is:
0.8*(D/2 + B/2 +F/2). This must be larger or equal the central bank funding: B/2 + 0.05*(D/2+C/2). So
we have to solve the following inequality for the amount C: 0.8*(D/2 + B/2 +F/2) ≥ B/2 +
0.05*(D/2+C/2) => C ≤ 20*(0.8*(D + B +F)-B) – D/2  C ≤ 15.5D +16F – 4B
S2.9
(a) The very different equity ratios are striking. Households are by far the least leveraged, followed
by NFCs. Most leveraged are financial corporates. Another striking difference is the relevance of
real assets versus financial assets, with the highest share of real assets held by the state,
followed by households and NFCs with both having broadly one half of their balance sheet in the
form of real assets. Finally, financial corporates have obviously the by far lowest share of real
assets. What the composition of assets in terms of real vs. financial, for a given level of equity,
means for financial stability, is not a priori clear. Both financial and real assets can lose value, and
which ones are more risky will depend on circumstances and the financial interdependencies.
This will be illustrated further in (c). The following table shows the shares of real assets and the
share of equity in total balance sheet length of the four sectors.
Share of real goods
Share of equity
NFC
56%
68%
State
73%
41%
FCs
2%
22%
HHs
47%
87%
(b) Exact inter-sector financial linkages are easily calculated in excel under the assumption of
proportionality. The following table that can be found with underlying formulas in the excel
spreadsheet. Each row of the table provides one sector (and the total) from the asset
46
perspective, while each column shows the column sector’s respective liability to the row-sector.
The left part of the table covers equity, while the right hand part of the table covers debt.
↓ Assets' perspective
Equity:
All sectors
All sectors
190
NFCs
39
State
11
FCs
114
HH
26
NFC
121
25
7
72
17
State
0
0
0
0
0
Liabilities' perspective
Debt:
FCs
HH
All sectors
70
0
402
14
0
39
4
0
17
42
0
192
10
0
154
NFC
56
5
2
27
22
State
61
6
3
29
24
FCs
241
23
10
115
92
HH
43
4
2
20
16
Let us call the matrix of exposures to equity E, with E(i,j) being the claim on equity of sector i
on sector j, in the order of the table above. Call D(i,j) be the corresponding matrix of fixed
financial claims and debt.
The full effects of declines of real asset values can be calculated using matrix algebra, or by
substitution. We follow the latter, simpler but less elegant approach below. Note that R, FFC,
EA, D, EL stand for different balance sheet positions, namely for real assets, fixed financial
claims, equity as asset item (i.e. holdings of stocks and shares), debt and equity as liability
item, respectively. The indices stand for the relevant sectors. We know that:
ELHH = RHH + FFCHH + EAHH – DHH, with EAHH = 17/121 ELNFC + 10/70 ELFC
ELNFC = RNFC + FFCNFC + EANFC – DNFC, with EANFC = 25/121 ELNFC + 14/70 ELFC
ELS = RS + FFCS + EAS – DS, with EAS = 7/121 ELNFC + 4/70 ELFC
ELFC = RFC + FFCFC + EAFC – DFC, with EAFC = 72/121 ELNFC + 42/70 ELFC
We assume now that x is below a certain threshold, such that Debt and Fixed financial claims
are not negatively affected yet by the negative real asset shock. We substitute the net (FFCD) figures from the financial accounts, and put the initial real assets R, but with a multiplier
(1-x)R to obtain:
ELHH = (1-x)159 + 111 + 17/121 ELNFC + 10/70 ELFC
ELNFC = (1-x)98 -17 + 25/121 ELNFC + 14/70 ELFC
ELS = (1-x)75 - 44 + 7/121 ELNFC + 4/70 ELFC
ELFC = (1-x)5 -49 + 72/121 ELNFC + 42/70 ELFC
This is a system of four linear equations with four unknowns. Because of the ultimate nature
of liability side equity of the state and of households, the easiest solution is to solve first the
two equations - two unknown systems of the NFCs and FCs:
ELNFC = (1-x)98-17+25/121ELNFC +14/70ELFC and ELFC = (1-x)5 -49 +72/121 ELNFC +42/70 ELFC
 ELNFC = (121/96)(1-x)98 –(121/96)17 +(14*121)/(70*96)ELFC and ELFC = (70/28)(1-x)5
(70/28)49 + (72*70)/(121*28)ELNFC
 ELNFC =123.5(1-x) -21.4 + 0.252 ELFC and ELFC = 12.5(1-x) -122.5 + 1.49 ELNFC
 ELNFC = 102.1 - 123.5x + 0.25 ELFC and ELFC = -110 - 12.5x + 1.49 ELNFC
 ELNFC = 74.38 -126.65x + 0.376 ELNFC
 ELNFC = 121 – 202 x
Moreover: ELFC = -110 + 1.49*119.1 + (-12.5 -1.49*202) x
 ELFC = 68 – 314 x
Now we can also complete the equity of the two “ultimate” sectors, HH and S:
ELHH = (1-x)159 + 111 + 17/121 ELNFC + 10/70 ELFC
 ELHH = 295 – 232x
ELS = (1-x)75 - 44 + 7/121 ELNFC + 4/70 ELFC
 ELS = 39-105 x
47
Finally, we can now also express the Equity positions on the asset side of the four entities as
EAHH = 17/121 ELNFC + 10/70 ELFC
 EAHH = 26-73x
EANFC = 25/121 ELNFC + 14/70 ELFC
 EANFC = 38-104x
EAS = 7/121 ELNFC + 4/70 ELFC
 EAS = 11-30x
EAFC = 72/121 ELNFC + 42/70 ELFC
 EAFC = 111-308x
We can write now all the financial accounts such as to be prepared to reflect an x% decline in
all asset values. For example the accounts of NFCs will look as follows:
Non-financial corporates
Real goods
98(1-x)
Debt
56
Fixed financial claims
39
Equity
121-202 x
Equity holdings
39- 104x
Total
177-202x
177-202x
We can present the entire financial account in a more compact way as follows. There is a
need to be careful in interpreting effects of real asset value declines on totals in the last row.
Remember that all the results were calculated on the basis of the assumption that no sector
was insolvent. Once real asset value declines go beyond a certain threshold where this is no
longer the case, the table no longer applies as such. The threshold of x (beyond which this
table no longer applies) will be provided in the next part of this exercise.
HH
State
NFC
FC
Total
Assets
Liabilities
Totals
Real
Fixed Equity
Debt
Equity
BS total
BS total
assets x-term claims assets
x-term
x-term asset
x-term liability x-term
159
-159
154
26
-73
43
295
-232
339
-232
338
-232
75
-75
17
11
-30
61
42
-105
103
-105
103
-105
98
-98
39
39
-104
56
121
-202
176
-202
177
-202
5
-5
192
114
-308
241
70
-314
311
-313
311
-314
337
-337
402
190
-515
401
528
-853
929
-852
929
-853
(c) Financial corporates (FCs) are most vulnerable to real asset value declines in the sense that they
end up first in insolvent territory. Indeed, as can be read in the table above from the two
columns on equity liability, a real asset value decline by more than 22% would make the
aggregate FC sector insolvent. This may surprise in view of the fact that the FC sector has the by
far lowest direct exposure to real assets. However, secondary effects via equity exposure matter
(even in the present example where we did not consider the case of losses on fixed financial
claims), and the low equity ratio of the Financial corporates is eventually decisive.
(d) Once the equity of one sector is exhausted, then the secondary effects of the real asset value
declines transmitted from this sector to the other sectors changes, with no longer the debt
exposure shares of the other sectors being the transmittance coefficients, but the equity shares.
Solving for the properties of the system from the point of insolvency of the first sector to the
point of insolvency of the second, is in principle identical to (b) for the case that all sectors are
still solvent (actually, one can “reset” the exercise to restart from the new real asset values after
the 22% decline, and the new equity of the insolvent sector is now its debt (as if the insolvent
sector is a sector that is financed only by equity). The table below shows these initial accounts (in
compact representation). The debt liabilities of Financial corporates have been reclassified as
equity, and the corresponding switch has been done on the asset side of all sectors (applying the
shares in the Financial corporate debt according to the table in sub-exercise (a)). The variable x is
still defined as a percentage decline in real asset values taking into account the very initial level
of real assets.
48
Assets
Real
assets
HH
State
124
58
NFC
76
FC
Total
4
262
Liabilities
Fixed
Equity
Debt
x-term claims assets
x-term
-159
62
102
-75
7
15
-98
-5
-337
Equity
x-term
43
61
243
19
16
39
56
76
77
161
161
317
0
160
241
579
Note that we have not assumed any additional damage from the insolvency of the financial
sector (while in reality there would be such extra damage, which we could calculate using
empirical estimates from the literature, and input into the table above).
Once one has established how the system reacts to further real asset value declines (using the
same technique as in sub-exercise (b)), one can complete the “x-term” columns above for equity,
and one can calculate when the second sector gets insolvent. Then again the system changes
properties as also the second sector transmits further real asset declines via the debt shares of
the other sectors, etc.
49
S3: The short term interest rate as operational target of monetary policy
S3.1 See page 10 of the book (four properties listed – note that on page 36 of the book, only three
properties are listed, which is an inconsistency).
S3.2 Short term, say overnight interest rates, (i) can be controlled by the central bank, since the
central bank can control both the supply of and the demand for reserves (not perfectly, but almost);
(ii) it is economically relevant as through the expectations hypothesis short and long term interest
rates are linked, and long term interest rates determine funding costs of the economy (and the rate
of returns on savings) and thereby, essentially via the Wicksellian arbitrage logic, impact on inflation;
(iii) it is a clearly defined variable (either in the form of an overnight interbank interest rate target, or
in the form of a central bank policy rate that will determine market rates) that can be decided and
communicated by decision making bodies; (iv) it gives clear guidance to market operations experts in
the central bank on what they need to do.
S3.3 The Wicksellian arbitrage logic is derived on pages 39-40 of the book. At least four sets of
simplifying assumptions are inherent in the simple Wicksell arbitrage diagram.
First, the system will most of the time be outside steady state equilibrium. Adjustment dynamics are
non-trivial and will invoke more challenging modelling. Prices and real rates of return on capital are
hit constantly by exogenous shocks. This implies that one needs to differentiate between the
expected (ex ante) and the actual (ex post) real rate of return on capital, E(rt) and rt (e.g. the actual
rate of return on wheat is affected by weather conditions). Moreover, when non-anticipated price
pressures (relative to expected prices) occur, adjustment of prices is typically sticky. Amongst other
things, this implies that the real rate of return on capital needs to be distinct from the real rate of
return on money investments – in particular ex post. Indeed, the fact that ex ante it=E(rt)+E(πt) does
not imply that ex post it = rt + πt. The real rate of return on money investments is equal to (ex post) it
– πt. The real rate of return on capital is (ex post) rt. There is a third concept that needs to be
distinguished, which is the ex-ante real rate of return on money investments which is it – E(πt). In an
ex ante arbitrage steady state equilibrium, this should be equal to E(rt). However, in reality, this is not
the case as ex ante adjustments to reach an arbitrage equilibrium are imperfect and slow. The
following table summarises the four concepts of real rates that need to be distinguished, as they will,
for the reasons mentioned above, not be identical in reality. (It may be noted that we have assumed
that the nominal interest rate on money is identical ex post and ex ante. This holds as long as debtors
do not default.)
Four concepts of the real rate of interest
capital good investment
money investment
Ex ante
E(rt)
it-E(πt)
Ex post
rt
it- πt
The general idea of the dynamics triggered by a perceived arbitrage opportunity is as follows:

If it > E(rt) + E(πt) => it is profitable to sell real goods and hold more money investments =>
demand for goods today ↓ => disinflationary pressures => actual inflation will fall below
expected inflation: πt < E(πt)

If it < E(rt) + E(πt) => buy more real goods for real investment projects, hold less money
investments (or be short in money, i.e. borrow money), => demand for goods today ↑ =>
inflationary pressures => actual inflation will turn out to be above expected inflation: πt >
E(πt)
50
While this intuition is clear, it is not obvious to fully specify this dynamic process in a discrete two
point in time arbitrage diagram. Modern macroeconomic monetary theory aims at capturing such
dynamics.
Second, in reality there is not only one good (“wheat”) which is at the same time a consumption and
an investment good, but there is a wide range of goods with very different properties. Investment
goods are supposed to determine the real rate of return on capital, while consumer goods determine
inflation. Consumer and investment good prices are eventually linked, but in reality such links will be
imperfect and exhibit time lags.
Third, nominal funding costs of the real economy are not identical to the short term nominal
interest rate that the central bank sets. Nominal funding costs of the real economy can be estimated
by producing a weighted average of funding rates, the weights reflecting the share of that type of
funding in the total funding of the real economy. The weighted average nominal lending rate of the
economy can be thought to reflect three main factors: (i) The short term interbank interest rate
which is normally controlled precisely by the central bank; (ii) The slope of the risk free benchmark
yield curve; (iii) The various instrument specific liquidity and credit risk premia. The challenge for the
central bank is then no longer limited to the estimation of the real rate of return on capital goods
(such as to be able to shift the nominal short term interest rate across time in parallel to it), but in
addition to estimate and take into account the varying spread between the weighted average
funding costs of the real economy and the risk free interest rate.
Fourth, it has to be kept in mind that the actual availability of credit to the real economy cannot
necessarily be measured by contemplating interest rates alone (e.g. Stiglitz and Weiss, 1981; in the
book the adverse selection model in section 11.2, pages 149-150). Indeed, funding markets for some
indebted companies can break down completely due to an increase of uncertainty and information
asymmetries.
These four complications are the reason for why the theory of optimal short term central bank
interest rate setting is complex, diverse and inconclusive, and also why central banks have large
economics departments and cannot follow simplistic mechanic formulas in interest rate setting.
S3.4 For the reasons provided on pages 44-45 in the book, the Fed seemed to have gotten convinced
after the first world war, at least officially, that monetary policy implementation is about controlling
the amount of (excess) reserves of banks with the central bank (or the monetary base) through
liquidity providing and absorbing open market operations (ideally outright purchases or sales of
treasury securities). Therefore, the monetary policy decision making would consist in deciding
essentially about quantities of open market operations, and hence the policy committee was called
“Federal Open Market Operations”.
S3.5 Because these views are based on a number of misunderstandings and would lead to extreme
volatility of interest rates and strong erratic monetary policy impulses. Reserve position doctrine,
including in the variant of M. Friedman, is wrong in particular for the following reasons.
First, the monetary base cannot reasonably be controlled in the short run. An operational target
variable should be a variable that can be controlled in the very short run by the central bank and for
which a concrete figure is set by the decision-making committee for the inter-meeting period to (a)
tell the central bank’s implementation experts what to do, and (b) indicate the stance of monetary
policy to the public. However, this obviously does not make sense for the monetary base. Its
normally biggest component, banknotes in circulation, is in the short term purely demand-driven,
with innovations to demand rarely linked to macroeconomic developments. Its second component,
current account holdings, is mainly determined by reserve requirements. Under a lagged reserverequirement system, required reserves are given.
51
The monetary base also should not be controlled in the short run. First, the monetary base is a
heterogeneous aggregate since it is composed of banknotes and reserves (which are themselves
subdivided into required and excess reserves). Why should changes in these three completely
different components be equivalent in terms of requiring the sum of the three to be controlled?
Moreover, the predictability and stability of the money multiplier is very doubtful, especially in the
event that one wishes to base policy actions on it. In particular, the multiplier is unlikely to remain
stable when interest rates move towards zero, since banks then no longer really care about holding
excess reserves. To that extent, when monetary growth is deemed insufficient and excess reserves
are injected to make the banks expand credit, the result will be first that, in an efficient market,
short-term inter-bank interest rates drop to zero (if there is no deposit facility). The fact that interest
rates have dropped to zero is, of course, relevant and, if judged to be permanent for a longer period
of time, medium- and longer-term rates also will drop and economic decisions will be affected.
However, once inter-bank rates have fallen to zero and the central bank continues to increase excess
reserves through open market operations at zero interest rates, not much more should happen: that
is, the money multiplier should fall with every further reserves injection. It is to that extent difficult
to really construct a case where an injection of reserves by the central bank through open market
operations sets in motion monetary expansion independently from the interest rate channel.
Third, any attempt to control in the short run the monetary base leads to extreme volatility of
interest rates since the market will, due to stochastic and seasonal fluctuations in the demand for
base money, permanently either be short or long of reserves, as already observed by Bagehot (1873).
One of the core ideas of central banking is to provide an ‘elastic currency’, that is, one in which the
important transitory fluctuations in base money demand no longer need to disturb economic
conditions via interest rate effects. What matters for the key economic decisions, namely, to save or
consume, to borrow or invest, are mainly medium and long term interest rates. With extreme
volatility of short-term rates, the volatility of medium and longer-term rates will also increase. Such
volatility will create significant noise in economic decisions, and hence lead the economy away from
equilibrium.
S3.6 The main “reserve position doctrine” concepts applied by the Federal Reserve across time are
explained in the book on pages 47-49.
52
S4: Three basic techniques of controlling short term interest rates
S4.1 The “fundamental equation” states that the overnight interbank market rate should consist in a
weighted average of the standing facility rates, i.e. the deposit facility rate and the borrowing facility
rate, the weights being the probabilities perceived by market participants of having at the end of the
maintenance period an excess or tightness or reserves relative to minimum reserves, respectively:
i = P(“short”)*ib + P(“long”)*iD
“Short” means the event that reserves are short of required reserves, and “long” means the event
that reserves are in excess of required reserves. For example, in the symmetric corridor approach,
the central bank keeps the two probabilities equal (at 0.5) via open market operations, so that the
interbank interest rate should remain in the middle of the interest rate corridor. Important
simplifying assumptions are:

No additional costs or access restrictions to either facility. Typically, borrowing from the
central bank requires providing collateral, which may be scarce and not cost free. Therefore
the true costs of being short are likely to be somewhat higher than ib.

Interbank rates have in addition a credit risk premium, which will bias the interbank rate to
slightly above the mid point of the corridor.

Money market participants do not necessarily have access to the standing facilities.
Therefore, unless the banks that have access to the facilities are perfect cost-free
intermediaries, market rates may be subject to an additional bias (a material phenomenon
affecting the Fed funds rate in the US since 2012).

In case of an averaging period for the fulfilment of reserve requirements, an asymmetry is
introduced because reserve over-fulfilment is unlimited (a bank can in theory fulfil on the
first day of the reserve maintenance period the entire reserve requirements for the
maintenance period) while banks must never end the day with negative reserve balances (i.e.
under-fulfilment of reserve requirements cannot exceed the size of reserve requirements).
This can create a systematic upwards trend of interest rates (Perez-Quiros and Mendizabal
2006).
S4.2 Symmetric corridor approaches generally maximise interbank market activity, in particular
relative to one sided approaches (see also Q2.3).
Symmetric corridor approaches with discretionary allotment have the advantage relative to
discretionary allotment asymmetric approaches (e.g. targeting an interest rate of 1.25% in a corridor
from 1.00% to 2.00%) that they require only to forecast the expected value of autonomous factors,
and not higher order moments.
An advantage of approaches with discretionary allotments relative to the full allotment approach is
the central bank can ensure that its ability to predict the sum of aggregate autonomous factors as
they will be relevant for the banking system on aggregate can be used to determine allotment
volumes in open market operations and therefore liquidity conditions.
The symmetric corridor approach based on fixed rate full allotment has the advantage that it is more
automatic and does not require any forecasting of autonomous factor and decision making on the
allotment amount of open market operations on the side of the central bank. However, the banking
system will not be able to forecast and aggregate autonomous factors in the same way as the central
bank can. This can create additional volatility of overnight interest rates.
One sided, standing facility based approaches have the advantage that they allow for a close control
of the operational target, the short term interest rate, without precise autonomous factor forecasts
53
of the central bank and without the need for the banks to bid in a way that is consistent with
aggregate autonomous factors ex ante. The disadvantage is that interbank market volumes will be
lower than in the symmetric corridor approach (which however does not imply in itself a lengthening
of the central bank balance sheet – see Q2.3). The extent to which interbank market activity suffers
depends on the size of the average recourse to the one standing facility. There is a trade-off: the
larger the average recourse (and hence the smaller the role of interbank markets), the more certain
is the control of the interest rate. There should be an inner optimum to this trade-off.
S4.3 Reichsbank 1900: one sided standing facility based system (systematic recourse to discount
window).
Reichsbank 1922: In principle the Reichsbank still implemented monetary policy through offering
recourse to the discount facility. However, liquidity conditions and interest rates were also
determined by the quasi- full funding facility offered to the Reich.
Bundesbank 1998: There is no mentioning of standing facilities in this balance sheet. This can reflect
that recourse was negligible, or that they did not exist. One can find out that the Bundesbank offered
a liquidity providing facility (called “Lombard facility”), but no deposit facility. Essentially the
Bundesbank controlled interest rates in an asymmetric corridor in which it controlled liquidity
through open market operations with allotment volumes set by the central bank.
Bank of Latvia, 2001: Again, it is not clear why standing facilities are not shown in this simplified
balance sheet. In any case, one can conclude without having more information that the Bank of
Latvia did not pursue a one-sided standing facility based system. (Note that the monetary policy
strategy of the Bank was to maintain a currency board with the euro).
S4.4
(a) With iD=0 and iB=1%, to achieve i=i* one needs to achieve: P(“short”)=P(OMO-50-μ < 0) = Φ((OMO-50- μ)/1) = i* => OMO = - Φ-1(i*) + 50. As Φ-1(0.5) = 0; Φ-1(0.25) = - 0.675 ; Φ-1(0.1) = 1.28, this implies that OMO will need to be 50, 50.675, 51.28, respectively.
(b) Solution: See excel spreadsheet. In the spreadsheet, 500 random draws (see rows 5 to 505) of μ1,
are simulated, using the excel randomizer (x=RAND()) and transforming the obtained draws of a
uniformly distributed random variable in [0,1] via the inverse of the cumulative normal
distribution (Norm.Inv(x, expected value, variance)) into a standard normal distributed random
variable). Result:
i*= 0.5 requires OMO* = 50; Implied stdev(i) = 0.28
i*= 0.25 requires OMO* = 51; Implied stdev(i) = 0.22
i* = 0.10 requires OMO* = 51.8; Implied stdev(i) = 0.14
The interest rate volatility is 28, 22, 14 basis points, respectively, i.e. the closer the rate is steered
towards one standing facility, the lower the volatility.
(c) One can easily verify that when the two autonomous factor shock volatilities develop
proportionally, the properties of overnight rates do not change. When the end day autonomous
factor shock volatility grows in relative terms, then for the OMO* evolves as follows:
μ1/ μ2 = 0.5 => OMO* =
50.8;
stdev(i) = 0.32
μ1/ μ2 = 1 => OMO* =
51.0;
stdev(i) = 0.22
μ1/ μ2 = 2 => OMO* =
51.5;
stdev(i) = 0.14
μ1/ μ2 = 4 => OMO* =
52.7;
stdev(i) = 0.08
54
In sum, if the autonomous factor volatility early in the day is relatively high, then the central bank
needs to increase the expected level of excess liquidity to achieve the desired expected level of
the overnight rate, and volatility of the overnight rate is relatively low.
S4.5 (a) These techniques rely on the idea that the less attractively priced of the two facilities is
accessible without binding limits in terms of counterparties and collateral (the latter relevant only for
liquidity providing operations), while the more attractively priced of the two facility must suffer from
some access limitations (only a limited set of counterparties, in the case of liquidity providing
operations also scarce collateral). Interbank rates will fluctuate between the two, and the position
within the corridor will depend on:
-
How strong are effectively the access constraints to the more attractively priced facility
(how limited is the number of counterparties, how constrained are they in arbitraging, in
case of a providing facility how scarce are eligible assets).
-
How big is the liquidity deficit or surplus that needs to be covered by the two facilities
(the lower the necessary recourse, the closer the interbank rate will be to the
constrained, more attractively priced facility).
In the case of the Reichsbank, mainly availability of discountable trade bills for the discount window
was a constraint that often pushed the interbank overnight rate to levels above the discount facility
rate. In the case of the Fed’s planned post-lift off, as Potter writes, “bank only access to IOER, credit
limits imposed by cash lenders, and other impediments to market competition, and the costs of
balance sheet expansion associated with arbitrage activity” all may let the fed funds rate deviate fall
below the IOER rate.
(b) Probably, control of the overnight rate will not be extremely precise, since access limitations will
vary in their effectiveness over time, and are not so well predictable as e.g. the factors affecting
interest rates in the classical symmetric corridor system.
55
S5: Several liquidity shocks, averaging, and the martingale property of overnight rates
S5.1 See page 66 of the book. The general definition of a martingale is a stochastic process for which
the conditional expected future values are equal to the latest available observation.
S5.2 An important impediment that only holds for reserve maintenance periods (i.e. not intra-day) is
the one identified by Peres-Quiros and Rodriguez (2006). It results from the asymmetry of the
corridor in the sense that unlimited over-fulfilment on any single day is possible but under-fulfilment
cannot exceed the level of required reserves because of the no-end of day overdraft constraint.
Moreover, banks may arbitrage only imperfectly because of cost, procedural or regulatory reasons.
S5.3 The following chart reflects the sequence of events.
Three subsequent independent
autonomous factor shocks
Morning
trading
Afternoon trading
End-day
recourse to
standing
facilities
OMO
The simulation tool used, which follows a similar logic as the one in Q4.4, is in the Excel workbook.
(a) The following table summarises the answer.
Q:
0.5
1.0
2.0
Morning
0.34
0.17
0.06
Volatility of interest rate in
afternoon
0.44
0.33
0.19
Day
0.37
0.23
0.11
Unsurprisingly, volatility of interest rates is higher when the autonomous factor volatility is
frontloaded during the day.
(b) The following table summarises the answer
q
0.25
0.50
1.00
2.00
4.00
8.00
OMO to
achieve
interest rate
of 0.25
13.0
11.5
11.3
11.8
13.0
16.0
Volatility of interest rate in
morning
0.37
0.29
0.15
0.06
0.02
0.00
afternoon
0.42
0.39
0.27
0.15
0.07
0.04
day
0.39
0.33
0.19
0.09
0.04
0.02
56
Volatility of interest rates again increases (decreases) with the frontloading (backloading) of
autonomous factor volatility. More remarkably, the OMO volume to achieve i=0.25 first decreases
and then increases again when q increases from 0.25 to 8. This provides an additional illustration of
the complexity of an asymmetric corridor model.
The following table provides plots of the morning and afternoon interest rates for three values of q.
In the strongly frontloaded autonomous factor volatility case, interest rates are mostly absorbed by
one of the corridor rates, and the OMO volume needs to determine the probability weights of being
absorbed by one or the other. In the strongly backloaded autonomous factor volatility case, interest
rates are in both sessions centred around their target value.
Note that the average interest rate is equal to 0.25 in all cases of q both in the morning and in the
afternoon session (and not only on average over the two sessions) although the target only referred
to the overall daily average rate. This must be the case because of the martingale property of interest
rates.
Interest rate morning
Interest rate afternoon
q=0.25
OMO=
13
q=1
OMO=
11.3
q=8
OMO=
16
57
S6: Standing facilities and the interest rate corridor
S6.1 In a discount window eligible short term bills are sold to the central bank, with the nominal
value of the bill being “discounted” using the discount rate. A Lombard (or advance) facility provides
collateralised central bank credit, with typically a broad list of eligible collateral. The two facilities coexisted in pre-WWI central banking with the Lombard facility rate typically 100 basis points above the
one of the discount facility. Therefore, recourse to the Lombard facility was typically the
consequence of scarcity of eligible bills for discounting, or a shorter time horizon of liquidity needs
(such as the pronounced end of months or end of quarter cash needs at that time).
S6.2 Out of habit. The US Fed’s discount window has been for many decades a Lombard facility.
S6.3 In the monetarists’ “verticalist” view of the world, control of quantities (e.g. of the monetary
base) is of the essence. Therefore, a by definition “horizontalist” tool like a standing facility must be
considered as undermining the effectiveness of monetary policy (we use once more the vocabulary
of Basil Moore here).
S6.4 The discount window was initially stigmatised in the US initially because the Fed blamed
excessive use of the discount window for the WWI inflation (instead of its deliberate lenient interest
rate policies to keep war financing cheap). It was then seen more and more as an exceptional
emergency tool (as open market operations took over the structural central bank liquidity supply to
banks), and the Fed and banks got used to this perception. Recourse to the discount window was
therefore considered as a sign of individual banks’ weakness, and the Continental Illinois case in 1983
reinforced this view.
S6.5 See section 6.2 of the book.
S6.6 The idea of a TARALAC facility is introduced in section 6.3 of the book. Its main advantages
compared to reserve requirements as tool to stabilise interest rates is that it is (i) symmetric (while
over- and under-fulfilling reserve requirements on a daily basis has asymmetric leeway), (ii) memory
free (i.e. every day the same buffers are provided, while in the case of reserve requirements, the use
of leeway on the previous days matter), and (iii) that it is invariant (while the buffers provided by
reserve requirements depend on where one stands within the reserve maintenance period).
S6.7 A key difference is that the US Fed discount window can be accessed against a much broader
collateral set than the Fed’s regular credit open market operations. The Eurosystem applies one pool
of collateral for both its marginal lending facility and regular Eurosystem credit operations. In so far,
the US Fed discount window goes a bit in the direction of what is called “emergency liquidity
assistance” (ELA) in the euro area (on ELA, see section 14.4 of the book). Apart from the collateral
dimension, the US Fed Discount window is however close to a monetary policy standing facility.
S6.8 The banks would have incurred somewhat higher costs from taking recourse to the facilities.
Over the period of the transitory measure, the average recourse to the marginal lending facility was
EUR 7.0 billion, and to the deposit facility EUR 2.7 billion (these figures can be found on the website
of the ECB). One (simple) way to calculate the cost difference would be: (EUR 7 billion * 75 bps + EUR
2.7 billion * 75 bps) * 21/360 = EUR 4 million. Banks might have been able to reduce this amount, as
the higher costs of the recourse to standing facilities could have provided extra incentives to avoid
such recourse. Beyond the cost reduction in the narrow sense, it could also be argued that the
narrow corridor helped to avoid stigmatisation of recourse to the marginal lending facility, and
generally fostered a relaxed and collaborative atmosphere during the first days of the euro area
money markets, setting it on the right path of an integrated and liquid market.
58
S7: Open market operations in normal times
S7.1 The view prevailed, in particular amongst monetarists, but also in the Fed at least as far as its
public communication is concerned, that open market operations were particularly effective in
initiating monetary impulses. Their effect, by injecting reserves and therefore creating leeway of
banks to create more bank money via the money multiplier would be more direct than effects of
interest rate changes. Monetarists were in addition enthusiastic because open market operations are
compatible with their “verticalist” view of monetary policy (to use again the term by Basil Moore).
S7.2 Open market operations were regarded as a tool to steer liquidity conditions in line with e.g. the
symmetric corridor approach. But in this role they were considered serving interest rate control, and
not having direct effects beyond that (i.e. the resulting short term interest rate was a sufficient
measure of monetary policy implementation). Today, a pragmatic view prevails on the role of the
two instruments in normal times. In the symmetric corridor approach, standing facilities are required
to establish the corridor, while open market operations have to achieve that the probability weights
of recourse to either facility are kept in balance, which means that they have to compensate for
autonomous factors. In an asymmetric approach in which the market rate is dominated by one
standing facility rate, the choice of the level of open market operations reflects a trade-off between
achieving extremely precise control of the interest rate versus reducing unduly money market
volumes.
S7.3 This question arises if one compares the pre-crisis Fed (very large part of open market
operations through outright holdings of securities) and the Eurosystem (no outright operations for
monetary policy purposes, i.e. all open market operations are credit operations). The two
approaches have different effects along a number of dimensions (see also pages 87-88 of the book):

Effects on market: both purchases and eligibility of a security as collateral have effects on
market liquidity and prices, but obviously not in an identical way. Some have argued that
acceptance as collateral interferes less with markets than outright purchases.

Risk taking and being exposed: outright purchases are a more direct risk exposure to the
securities issuer, as collateral is only in the second line of defence, the direct exposure being
to the bank obtaining the credit.

Duration: Outright securities holdings typically have longer average duration than credit
operations (average maturity of outstanding securities is in the order of magnitude of 4-6
years, while the average maturity of central bank credit operations in normal times is below
three months).

If outright positions are assumed to be in the form of Government securities (as it was the
case pre-2007 for the US Fed), then outright holdings are a way to achieve a lean
consolidated State balance sheet (as both the central bank and the Government are part of
the state sector). According to the German doctrine of central banking, the central bank
should however see itself as strictly separated from the Government, and the idea of
choosing an asset composition to have a lean consolidated state balance sheet would be
strongly rejected.
S7.4 See pages 90-92 of the book.
S7.5 Because thinking through the equilibrium between the central bank’s use of discretion and the
bidding behaviour of counterparties is extremely complex. Neither bidders nor the central bank are
likely able to solve this problem and to coordinate well on an equilibrium. See also page 92-93 of the
book.
59
S7.6 For longer maturities, it is obvious (in normal times) that variable rate tenders should be used,
as they avoid (i) giving guidance on long term rates and (ii) destabilising bidding behaviour and
liquidity conditions. For short maturities, central banks have used both variable and fixed rate
tenders. For example the US Fed has always used variable rate tenders (reflecting its more verticalist
thought traditions), while the Bank of England has always used fixed rate tenders (reflecting its more
horizontalist views). Indeed there are no general reasons why not use either one or the other
procedure for short term credit operations. “Short term” can generally be defined as the horizon up
to the next meeting of the monetary policy decision making committee.
60
S8: Reserve requirements
S8.1 To take the euro area as an example, the ECB specified a reserve maintenance which was from
1999 to 2014 around one month, with daily measurement points at day end. In other words, reserve
requirements need to be fulfilled on average over 30 measurement points. This raises the question
why no alternative frameworks with regard to the periodicity of reserve requirements are
considered, such as the various combinations suggested in the table below. The table shows the
possible combinations and the implied number of measurement points (assuming a 12 hours
business day and 5 business days per week).
Various combinations of length of reserve maintenance periods and number of measurement points,
with implied number of measurement points per reserve maintenance period
Length
or
reserve
maintenance period →
One day
One week
One month
One year
Hourly
12
60
264
3120
Daily
1
5
30
260
1
4
52
1
12
Periodicity
of
reserve
measurement points ↓
Weekly
Monthly
Yearly
1
In principle all these combinations, except those shaded grey, would be possible. Why have most
central banks ended in the one month maintenance period - daily measurement combination?
Consider first the frequency of reserve measurement points. Why not measuring reserve fulfilment
once every hour? Probably because there are no economic projects with a life cycle of less than a
day. If we believe into the Wicksellian arbitrage diagram as the foundation of monetary economics,
and there are no real projects with a shorter life cycle than daily, then we do not need to control the
scarcity of money intra-day. Doing so would only imply higher operational costs of technical systems
and data management. And indeed, most central banks consider intra-day liquidity as a free good,
i.e. do not impose an interest rate on intraday credit (but require collateralisation, as for overnight
credit). Why not measuring reserve fulfilment only once a month, and have a one month (i.e. no
averaging) or one year (averaging over 12 measurement points) maintenance periods? If there are
projects with a life-cycle of less than a months, this would lead to a strange and counterproductive
cyclicality of investment and economic activity, in which credit would be taken for the period within
one month, and then would be repaid before the measurement point, just to be taken again
afterwards. Obviously, this would not be efficient. The longer the period between measurement
points, the more obvious this problem would become (it is not entirely clear whether e.g. at a weekly
frequency of measurement points there would be a problem).
Also, a too low frequency of measurement points would not allow to adjust in time the stance of
monetary policy – even leaving aside the cyclicality problem. For instance, if there is only an annual
measurement point, then considerable monetary imbalances may build up in the meantime, and
there is not much scope for smoothing and fine tuning.
Now let us turn to the question of the optimal length of the reserve maintenance period for a given
frequency of measurement points (say daily). Why not e.g. a one year reserve maintenance period?
The reason is that maintenance periods should ideally not include in their middle a meeting of the
central bank’s decision making committee. Anticipated changes of interest rates within reserve
maintenance period destabilise reserve fulfilment and bidding behaviour of banks. And as central
banks should be transparent and rule based, their policy actions should also be in principle
61
predictable. This was one of the main insights by the ECB reflected in the changes to its reserve
maintenance period timing early 2004. Before that, policy meetings and reserve maintenance period
did not follow a clear joint rhythm and therefore often an unstable bidding behaviour of banks was
observed. Since the change, reserve maintenance periods exactly coincide with inter-meeting
periods. (See ECB press releases of 23 January 2003 and 1 August 2003).
Accepting this constraint means that lengthening the reserve maintenance period is only possible to
the extent that one can lower the number of occasions at which one may want to change interest
rates, which seems to depend on the intensity of possible news-flows on the economy and on
financial and monetary conditions. The majority view of central banks seems to be that one needs
monetary policy meetings at which the monetary policy stance can be changed at least 8 times a
year. Therefore, also reserve maintenance period should not exceed this length, and indeed the ECB
is currently with on average 6 weeks reserve maintenance periods the central bank which has
stretched their length to the maximum amongst major central banks.
S8.2 See section 8.2 of the book.
S8.3 See section 8.3 of the book.
S8.4 This may be subjective and dependent on circumstances. In advanced economies, the main
reason to have reserve requirements in the pre-2007 consensus was to have them specified with
averaging and hence to smooth short term interest rates. For emerging market economies with large
scale foreign reserves (exceeding banknotes), reserve requirements still play an important role to
absorb excess liquidity. Also, the increase of costs on bank money creation associated with nonremunerated excess reserves is often considered as useful in such economies.
S8.5 Monetarists tended to appreciate reserve requirements as they were considered to support the
stability of the money multiplier, the key transmission concept for monetarists between the
supposed operational target of monetary policy (the monetary base, or some reserve concept) and
the intermediate target, broad monetary aggregates. At the same time, more radical monetarist
statements like Friedman (1982) also seem to reject the usefulness of reserve requirements. In any
case, monetarists lobbied strongly for so-called “contemporaneous” reserve requirements, in which
the reference dates for calculating required reserves are within the reserve maintenance period.
Keynes in his “Treaties on Money” (1930) was enthusiastic on the power of reserve requirements –
much in a money multiplier logic. Today, rather little is left of this enthusiasm, and reserve
requirements are seen for industrialised countries to be of use essentially for averaging and
smoothing purposes.
S8.6 With hindsight, only the first function seems to have played a role in practice, and all ECB
publications on its reserve requirement system after 1999 refer only to the first function. The second
point seemed to reflect the fear of a possible downward trend in banknotes in circulation, and
therefore a tendency towards a structural liquidity surplus of banks vis-à-vis the central bank.
However (as also illustrated in figure 2-11 of the book, page 27), banknote demand continued to
increase rather steeply after the introduction of EUR banknotes, beyond growth of nominal income.
The third point seems more of an academic text book argument, and anyway it does not seem to
apply as long as reserve requirements are fully remunerated, as they were ever since 1999 in the
euro area.
S8.7 The benefits of lowering reserve requirements in the context of the sovereign debt crisis was
that this correspondingly reduced needs of banks to take recourse to central bank credit, and
therefore reduced collateral scarcity.
62
S9: Collateral
S9.1 See page 112 of the book.
S9.2 See page 112-113 of the book. The central bank should have more tolerance that the market
against lower liquidity of assets received as collateral, as it will itself never be liquidity stressed, and
therefore has more time to liquidate assets. More time is important as (i) asset values may be mean
reverting in a financial crisis, i.e. one may have legitimate hopes that their prices recover after a
while; (ii) it allows to avoid the fire sale discounts that one otherwise has to accept, which are
particularly relevant in a crisis situation. The two are linked. To address the lower liquidity, the
central bank can impose high haircuts, which banks will accept because the central bank is
considered a risk free counterparty (see also chapter 14).
S9.3 Losses in collateralised lending can arise in the following scenarios:

When there are legal challenges to the right and ability to liquidate collateral;

When after a counterparty default the collateral loses value before liquidation is possible,
and this loss of value exceeds the haircut;

In case of a double default, i.e. when both the counterparty and the entity that had issued
the security that was pledged as collateral default at the same time.
The last two cases should not be underestimated because of correlation between bad counterparty
and collateral developments. This correlation can be systemic, driven by economy-wide factors, or
specific, i.e. through some specific link or proximity of the counterparty and the issuer (collateral
frameworks of central banks tend to forbid the latter, at least as far as it can be formally established).
Risk control measures:

Haircuts

Daily margining (collateral calls, if necessary)

Concentration limits and exposure limits

Close link prohibitions between counterparty and issuer
None of these can protect perfectly against legal risks and systemic crisis. Also there is a trade-off:
extreme protection levels require very high haircuts, which would seem to reduce the central bank’s
ability to contribute its LOLR role to society.
S9.4 Assets with lower credit quality are more information intense, and therefore (i) valuation errors
are more likely; (ii) orderly liquidation time is longer (or fire sale discounts will have to be accepted);
(iii) the likelihood that in a systemic stress situation they will lose value or become less liquid is
higher than for high credit quality assets. All three factors imply a need for higher haircuts relative to
higher credit quality assets, if the same eventual risk protection is desired (even if the lower credit
quality is already factored in).
S9.5 Solution (see also in excel): It is easy to show that for independently identically distributed
shocks every day, the variance of the cumulative shock grows proportionally (and therefore the
standard deviation increases with the square root of time). Also, the variances of different types of
independent price shocks can be summed up to obtain the total price uncertainty.
Assume the total liquidation price risk x over three days should be N(0, σ2). To protect against losses
with a confidence level of 95%, we must ensure that only with 5% probability the liquidation price
risk x materialises such as to exceed the haircut, i.e. P(x+haircut<0) = 5%, i.e. Φ(-haircut/ σ) = 5% =>
haircut = - σ Φ-1(5%).
63
For asset 1, only market risk matters, and if daily market price risk is N(0,1%), then the total
liquidation price risk x over three days should be N(0, 3%), i.e. σ = sqrt(3%). The haircut will be sqrt(3%) * Φ-1(5%) = 1.732 * 1.645 = 2.85%. For asset 2, one obtains σ = sqrt(34%) and haircut =
9.59%.
S9.6 Solution: Assume that the bank has liquid and illiquid assets of 1 each. It will need equity for the
first type of 0.1 and for the second type of 0.3. The average funding costs of the bank will be (1.6*4%
+ 0.4*10%)/2 = 5.2%. The funding costs for liquid assets is (0.9*4% + 0.1*10%) = 4.6% and for illiquid
assets is (0.7*4% + 0.3*10%) =5.8%. Assuming that management/operating costs associated to the
two types of assets are equal, then also one should expect the spread between the interest rates of
the two types of bank credit to be 1.2%. The average funding costs of the real economy should be
equal to the bank funding costs plus a mark-up for the operating costs of the bank.
Haircut policy is a sort of monetary policy in this model since increasing (decreasing) haircuts means
tightening (loosening) funding conditions of the real economy. A tightening of the funding costs of
the real economy by one percentage point can be achieved by increasing the monetary policy rate by
one percentage point, or by increasing the average level of haircuts as follows:
((1.6-2x)*4% + (0.4+2x)*10%)/2 = 6.2% ((0.8-x)*4% + (0.2+x)*10%) = 6.2%  x*6% = 6.2% - 5.2%
 x= 1/6 = 16.4 percentage points.
In words: the central bank could increase its haircut vector from (10%; 30%) to around (26%; 46%). It
could also increase the haircuts in a more differentiated way across the two asset classes (e.g. only
increase one or the other haircut). Obviously the choice how to increase haircuts will determine the
relative costs of funding the two assets, and therefore also in the medium to long term the share of
the two types of assets in the economy.
S9.7 Consider the following two bank balance sheets, which include also cross issuance and cross
holdings of bank bonds. We denominate by X the scale of the cross issuance practice. We assume
that the cross-issuance practice is fully matched for these two banks.
Claims to corporates
Bonds issued by bank 2
Claims to corporates
Bonds issued by bank 1
D/2 + B/2
X
D/2 + B/2
X
Bank 1
Deposits
Central bank credit
Bonds issued
Bank 1
Deposits
Central bank credit
Bonds issued
D/2
B/2
X
D/2
B/2
X
Assuming that a haircut of h% applies to both claims to corporates and to bonds issued by bank 1,
the collateral constraint is (collateral value post haircuts must be at least as large as the recourse to
central bank credit):
(1-h)(D/2+B/2+X) ≥ B/2
As X is only on the left side of this equation, it can be confirmed that increasing X softens collateral
constraints. From a risk perspective, this technique by banks becomes dangerous in case it would be
done at large scales by stressed banks. Then, in case of a simultaneous default of the two banks, the
central bank finds itself with defaulted collateral to protect it against a defaulted counterparty.
64
S10: Optimal frameworks for monetary policy implementation in normal times
S10.1 Eight desirable properties are listed on pages 131 to 133 of the book (“design objectives”)
S10.2 The Australian framework seems simpler and from this perspective preferable (although it may
be an advantage of the Eurosystem framework that open market operations need to be conducted
only on a weekly basis. It is noteworthy that larger monetary areas (US, Eurosystem, Japan) seem to
have more complex frameworks than smaller ones (Australia). So maybe a larger, more competitive
banking system, or a lesser role of foreign exchange flows speaks in favour of a Eurosystem like
framework. But the reasons are not totally clear.
S10.3 See section 10.5 of the book.
S10.4 Key additional issues for emerging market economies’ central banks are typically those relating
to the fact that net autonomous factors in these countries tend to be strongly liquidity injecting, i.e.
that the banking system, has, before reserve requirements and before monetary policy operations, a
large liquidity surplus. The main reason for this is typically the accumulation of large foreign
exchange reserve, i.e. foreign exchange reserves by far exceeding banknotes in circulation.
Therefore, absent reserve requirements and monetary policy operations, the interbank interest rate
would be very close to zero (as all banks would have excess reserves). As this level of short term
interest rate would however be far too accommodative from the point of view of inflation control in
these countries (characterised by somewhat higher inflation rates and healthy growth rates), central
banks need to absorb these reserves, and the question arises what the ‘optimal’ way of absorption is
(through high reserve requirements, or through liquidity absorbing operations, and in the latter case,
what type of absorbing operations, maturity, repo or unsecured, tender procedure, etc.). A more
general challenge to these central banks is the one of profitability. Over the last 15 years, interest
rate in industrialised countries were low, i.e. foreign exchange reserves were poorly remunerated.
Moreover, the emerging market currencies were most of the time under appreciation pressures.
Finally, domestic excess reserves needed to be absorbed at higher interest rates (in line with the
appropriate stance of monetary policy). These three factors together obviously created profitability
issues, and finding an ‘optimal’ solution to these challenges was important from the perspective of
national wealth for these countries.
S10.5 This raises the question to what extent the differences between central banks’ monetary policy
implementation approaches, and their changes across time, are due to randomness, fashion and
history, and to what extent they are rational reflections of a changing environment. They are
probably both, but the first category of explanations seem to dominate, at least to explain the crosssectional and across-time evolution of the large industrialised country currency areas like the US;
Japan, and Germany (in the 1990s) and the euro area (1999-2007).
For emerging market central banks, it is more plausible that the changing environment explains to an
important extent the changes of operating procedures. Indeed, the large industrialised currency
areas have the enormous privilege that they have hardly to worry about the foreign exchange
dimension with its ever changing challenges. Therefore, central banking in large industrialised
monetary areas and outside crisis times can almost be characterised, in relative terms, by
Baudelaire’s verse “Là, tout n'est qu'ordre et beauté / Luxe, calme et volupté”. In this world,
specifying monetary policy implementation has relatively few problems and therefore degrees of
freedom that across the last 100 years were not always used totally convincingly.
65
S11: The nature of a liquidity crisis
S11.1
(a) The formula to be applied is PD = 1-Φ((20-5)/σ), with Φ being the cumulative standard
normal distribution. The resulting PDs are (i) 0.13%, (ii) 16%, and (iii) 27%.
(b) This depends on the damage done by the default and the implied “loss given default” (LGD).
Assume that the LGD is 50%. The expected loss is then PD*LGD, and a risk neutral investor
wants to be compensated exactly for this, i.e. the senior debt interest rate must be higher by
0.07%, 8%, 13.5%, respectively.
stdev(e)
P(Equity<0)
Eloss for LGD = 0.5
5
0,13%
0,07%
15
15,87%
7,93%
25
27,43%
13,71%
(c) Starting from a lower level of equity, PDs and Expected losses will obviously be higher.
stdev(e)
P(Equity<0)
Eloss for LGD = 0.5
5
15,9%
7,9%
15
36,9%
18,5%
25
42,1%
21,0%
(d) Volatility of asset prices could matter since the example above illustrated that a higher volatility
means a higher PD, which means higher funding costs for senior debt. Of course, one could argue
that higher volatility should be neutral when looking at equity and debt as a whole, as higher loss
rates on debt are compensated by higher expected returns on equity. However, such full
compensation does not apply if we assume, as suggested by the empirical corporate finance
literature, that default of companies is costly in itself. Above, we reflected the wealth destructive
effects of default in an LDG of 50%. Therefore, higher asset volatility eventually means higher total
funding costs and lower profitability.
S11.2
(a) “Financial needs” is the sum of all funding contributions by the Government to the banking
system, covering such diverse forms as in particular (i) guarantees for the issuance of bonds
(i.e. to allow banks to issue Government guaranteed bank bonds); (ii) capital injections. In
contrast, “Cumulated deficit effects” are what actually had to be booked, applying relevant
EU statistical rules, as real eventual costs by the Government. Indeed, guarantees may not be
called upon (and the Government then actually makes a profit as it gets a fee for granting the
guarantee) and Government positions in bank equity may be sold later on, possibly even with
a profit. Of course injecting capital is only likely to be non-loss making if the initial capital of
the bank was still positive or zero. Looking at the actual figures,
The differences between countries are obviously remarkable, with negligible costs in FR and
IT and very high costs in GR and in particular IE. In interpreting the figures, it is important to
recall that the ratios of the banking systems’ balance sheet lengths to GDP was
heterogeneous, ranking from below 3 (DE, IT and GR) to above 6 (IE). The differences in
losses (expressed in terms of GDP) are likely to reflect size of the banking system, quality of
banking supervision, pursued business models in the relevant countries, and the intensity anf
form of the financial crisis in the respective countries. For example, IE had the combination
of a laissez-faire banking supervision and real estate boom that went bust. ES also had a real
estate boom, but a somewhat more prudent banking supervision. DE had a number of banks
which entered unsound business practices, without this being spotted by supervision. For
example some banks were running large tail risk positions (Hypo Real Estate doing long term
66
public sector funding on the basis of optimistic assumptions on spread levels), setting up
SPVs buying subprime mortgage related US ABS and benefitting from liquidity guarantees of
the bank (Industrie Kreditbank, IKB), or generally running imprudent investment policies (a
number of Landesbanken). In the case of GR, the numbers are particularly high in relation to
the previous size of the banking system, and reflect the year-long deep recession of the
Greek economy.
What is also noteworthy in the data is the differences between the ratios of the figures in the
two columns, with the biggest difference in DE, and the smallest in ES. In principle one would
assume the two to be correlated, because banks typically have funding problems if they are
in poor capital and profitability conditions, but this also makes likely that capital injections
lead to losses. One possible interpretation of the moderate German cumulated loss figure
could be that because of the soundness of German Government finances, and the
Government’s unimpaired and cheap capital market access, Germany had a lot of time to
manage the stressed assets, which may be positive (as asset values may be mean-reverting in
a financial crisis) or negative (if it leads to a delay of the necessary asset sales and the
associated realisation of unavoidable losses).
(b) Also central bank credit played an important role in funding banks which had difficulties to
access their previous funding sources, and in particular in the cases of IE and GR, central
bank funding peaked at around 50% GDP. This is in addition to the funding support of
Governments shown in the tables (although not everything may have been simultaneous – in
particular in the case of DE, Government guarantees quickly substituted for central bank
LOLR credit). Central bank LOLR credit should be seen as being constrained in two respects: it
should be short term (after a while, Government guarantees on bank bonds should take
over) and it should only be granted to solvent banks. In for example GR, the value of
Government guarantees with regard to helping access to capital market was not very high
during some periods, which also explained the relative persistence of the role of central bank
LOLR to banks.
S11.3
(a) It is shown in the book (section 11.2, p. 149-150) that in order to make no losses, the bank
needs to demand an interest rate of: i*=(1- δ)(1-p)/(δp). The condition for the existence of a
credit market is that good companies (with good projects yielding returns of VG on one dollar
invested) can afford to pay this interest rate, i.e. i* < VG-1. For the given parameter values,
one obtains i*=16%, i.e. lower than the return of good projects which is 20%. Therefore a
credit market will exist.
(b) In a financial/economic crisis, the share of good projects, the quality of the monitoring
technology, and the returns of good projects, all likely deteriorate and therefore may lead to
a credit market breakdown. For example, any of the following three changes alone δ =0.3,
p=0.8, or VG=1.1 is sufficient to lead to a credit market stand still.
(c) The exact critical values can be calculated with the equation above. For example, the critical
value δ* can be derived as follows: (1- δ*)(1-0.9)/(δ*0.9)=0.2 => δ* = 0.357
S11.4 In a financial crisis: (i) volatility of asset prices go up; (ii) counterparty PDs go up; (iii) the capital
buffers of the cash provider will likely shrink; (iv) valuation uncertainty increases; (v) correlation
increases. All justify an increase of haircuts. Leverage has to decrease as a direct reflection of higher
haircuts. Collateral may become ineligible in interbank repo if its properties become too remote to
ideal collateral (i.e. it becomes illiquid, information intense, credit risky, etc). Then, the repo desks of
banks can no longer deal with it as they are not specialised in analysing the treatment of non-ideal
collateral types. Also, haircuts to protect the cash provider expose the collateral provider, implying
that haircuts are not a solution in case the two counterparties are similarly credit risky. Such
67
collateral can still be used for collateralised financing operations between a less risky cash provider (a
bank) and a more risky collateral provider (a hedge fund).
S11.5 More news hit the market and therefore also the potential for “insiders” or “information frontrunners” increases. In addition, capital of the market maker may become scarcer, constraining its
ability to take risk (and wider bid ask spreads are a protection against ending the day with a large
position in the asset).
S11.6
(a) The bank can generate in good times a total liquidity of L = Λ(D+1)+(1-h)(1- Λ)(D+1). It can be
shown that the condition for a unique no run Nash equilibrium is that L is at least equal to the
deposits of one of the two depositor, i.e. L ≥ D/2. The condition for financial stability in good times is
thus: Λ(D+1)+(1-h)(1- Λ)(D+1) ≥ D/2.
(b) Inserting the proposed values into the equilibrium condition shows that indeed it is fulfilled:
0.4*(2+1)+(1-0.8)(1-0.4)(2+1) ≥ 2/2  1.2 + 0.2*0.6*3 ≥ 1  1.56 ≥ 1
(c) For that we have to solve the condition for stable funding for the maximum level of D: Λ(D+1)+(1h)(1- Λ)(D+1) ≥ D/2  [-0.5 + Λ+ (1-h)(1- Λ)]D + [Λ+(1-h)(1- Λ)] ≥ 0  D ≤ -[Λ+(1-h)(1- Λ)] / [-0.5 +
Λ+ (1-h)(1- Λ)]  D ≤ -[1-h+hΛ] / [0.5-h+hΛ)]
(d) Now it is assumed that a crisis breaks out and Λ’=0. Therefore: L’= (1-h)(D+1). For h=0.8 and D=2,
we obtain L’=0.6, which is below D/2, and therefore financial stability is lost – unless the central bank
decreases its haircut sufficiently. We can calculate the maximum collateral haircut that restores
funding stability as follows: L’= (1-h)(D+1) ≥ D/2  (1-h)3 ≥ 1  h < 0.66
S11.7
(a) The general condition for a single no-run equilibrium is that the bank must be able to generate
sufficient liquidity to pay out one depositor, without the generation of this liquidity generating fire
sell losses exceeding the amount of available equity E. It seems clear that in an optimal strategy of
the bank, fully liquid assets will be sold (as fire sale losses are zero, while the central bank applies a
haircut h1), and that non-liquid assets will not be sold but pledged with the central bank (as fire sale
losses on those assets are 100%). What to do with the semi-liquid assets (fire sell of pledge) is less
clear (as f<h2). Let’s consider the two strategies to (I) fire sell also the semi-liquid assets vs. (II)
pledging them. The following table provides the maximum liquidity generation and the fire sale costs
for the two strategies.
Maximum liquidity generation: L
Implied fire sale losses: F
Strategy I: sell liquid and semiliquid, pledge with CB illiquid
Λ(2+E) + (1-f)Π(2+E)
+ (1-h3)(1-Π-Λ)(2+E)
fΠ(2+E)
Strategy II: sell liquid, pledge semiliquid and illiquid with CB illiquid
Λ(2+E) + (1-h2)Π(2+E)
+(1-h3)(1-Π-Λ)(2+E)
0
The condition for a no-run equilibrium is: [(LI ≥ 1 and FI ≤ E) or (LII ≥ 1)]
(b) Under strategy I, the central bank can generate enough liquidity with measures that do not
generate any fire sale losses, namely fire selling the most liquid (this generates a contribution to L of
0.25(2+E)) and pledging the least liquid (this generates a contribution to L of 0.5*0.5*(2+E). Together,
even with an equity of zero, this allows to generate liquidity of 1, i.e. sufficient to sustain a single no
run equilibrium. Obviously the same works under strategy II as these two liquidity generating
component are the same under both strategies.
(c) Under (b) it was shown that the bank could generate enough liquidity with zero equity and
without even touching the semi-liquid assets. Therefore, the increase of fire sale losses of the semi-
68
liquid category should not matter (still no equity is needed). Again, equity can be zero and still
funding will be stable.
(d) Liquidity generated with strategy I is now Λ(2+E)+(1-f)Π(2+E)+(1-h3)(1-Π-Λ)(2+E) = 0.5*0.25(2+E) +
0.2*0.75*(2+E) = 0.25+0.3 + (0.125+0.15)*E = 0.55 + 0.275*E. Therefore under strategy I, E needs to
be at the minimum 0.55 + 0.275*E ≥ 1  E ≥ 0.45/0.275 = 1.64. Fire sale losses will be: fΠ(2+E) =
0.5*0.25*3.64 = 0.455 which is below equity. Therefore the choice E=1.64 leads under strategy 1 to a
stable no-run equilibrium.
What about strategy II? Under II, liquidity generation is Λ(2+E) + (1-h2)Π(2+E) + (1-h3)(1-Π-Λ)(2+E), i.e.
0.8*0.25*(2+E) + 0.2*0.5*(2+E) = 0.6 + 0.3E. As this has to exceed 1, we can again identify the
minimum equity: 0.6 + 0.3E ≥ 1  E ≥ 1.33. Strategy requires less equity than strategy I will therefore
be chosen by the bank (as it allows for funding stability with lesser funding costs).
S11.8 Adding the liquidity and credit risk spread k to the non-accelerating interest rate, the neutral
rate definition becomes: it*=E(rt)+E(πt)-kt. Therefore increases of k add to the danger to hit the ZLB
and to end in a deflationary trap.
S11.9
(a) (i) ex ante: avoid excessive leverage through appropriate incentives and regulation such as to
avoid a violent increase of k in a crisis; (ii) ensure solid real growth rates to sustain r; (iii) do not
set the inflation target to zero (but to 2%, or even to 4% as e.g. Olivier Blanchard argued) so to
have an extra buffer relative to the ZLB; (iv) find technical solutions to overcome the ZLB (see e.g
W. Buiter, 2009, “Negative nominal interest rates: three ways to overcome the zero lower
bound”, NBER Working Paper No. 15118).
(b) (i) Lower nominal funding costs aggressively through conventional policies; (ii) use nonconventional measures before it is too late or before ever more extreme measures are needed;
(iii) be ready to act as LOLR such that liquidity problems in financial system that further drive up k
are contained; (iv) Support real growth perspectives through structural reforms, supporting r.
S11.10
(a) These German economists may have overlooked that financing conditions for the euro area real
economy were tight since the financial crisis and later on due to the euro area sovereign debt
crisis. Moreover, fundamental economic and political uncertainty creeped in after the debt crisis
spread to Spain and Italy in 2011. Also, banks were not only traumatized by their loss experiences
of 2007-2012 and the recession of 2009 and therefore tended to restrict lending, but also a wave
of new regulation to prevent a repeat of the 2007-2008 episode restricted banks in various ways
and supported deleveraging. Finally, the structural reforms in program countries strengthened
competition and lead to a positive supply side shock which tended to be dis-inflationary, and the
fiscal austerity contributed a negative demand shock. In sum: financing conditions remained
expensive and tight despite the significant and effective contributions of the central bank to ease
them (which at least prevented even more tightening) while economic developments were
subdue. This was not an inflationary environment at all and the ECB was right to worry about
rapid disinflation.
(b) That “countries with high debt levels tend to inflation” seems to have been invalidated as a
general statement by the Japanese experience. The statements of S. Homburg and R. Vaubel
which seem to focus on the monetary base and the money multiplier seem to rely on a reserve
position doctrine view of the world that for the reasons indicated in chapter 3 we would reject.
That “Financing of fiscal gaps by the central bank” always leads to high inflation seems to find
little empirical support from the cases of the US and Bank of England, in which indeed massive
purchases of Government debt took place in phases of high fiscal deficits (in 2009 and 2010).
Even in those countries inflationary pressures seem to remain low, years after the launch of
69
these very large programs. In contrast, in the euro area fiscal adjustment was frontloaded and
the purchases of sovereign bonds by the Eurosystem remained small compared to the US and UK
(at least until including 2014). The main legitimate worry on these programs may relate to the
challenges of exit and possible moral hazard issues when Governments have high debt-GDP
ratios and will also in the future be potentially vulnerable to impaired capital market access.
Reducing again the Central Bank’s stocks of sovereign bonds will contribute to increase capital
market yields and financing costs of Governments. Therefore it seems key that Government
address their structural and fiscal challenges so as to ensure that an orderly exit of the
Eurosystem from purchase programs and acquired sovereign debt stocks will be possible in the
future, so that the central bank is not stuck with very high Government bond exposures and
related possible pressures by the Government in the long term.
(c) It is always right to be also worried about inflation in the medium to long term. The fact that
inflation has been trending down for decades and that also recently, surprises of inflation in
major economies tended to be on the downside does not mean that this could not change again.
Also, as mentioned, it is true that large scale purchase programs may be difficult to exit and at
that stage could create undue political pressures and possible conflicts of interest.
S11.12 First, it seems that NFC funding costs (the black line) have varied only moderately during the
nine years covered by this figure. The biggest movements is the increase from 2005 to 2008
(reflecting first the increase of central bank rates, then effects of the tightening of credit supply
relating to the first year of the crisis), and then a decline 2008 and 2010 reflecting mainly monetary
policy easing. The amplitude of these changes in any case falls short of the amplitude of changes of
monetary policy rates. After 2010, the NFC funding costs have essentially moved sideward, and the
end 2014 level is only marginally below the 2005 level. Rates controlled by monetary policy (EONIA
monthly averages – the dotted line) exhibit one significant (2005-2009) tightening-easing cycle, and
one very small one (2011-2012). Finally, 5Y OIS rates (the grey line) follow to some extent the first
tightening-easing cycle, but then after 2009 follow the EONIA rate towards the zero level only with a
time lag.
Comparing the evolution of the three series, and considering NFC funding costs as being composed
of EONIA, the term spread, and a third component capturing liquidity and credit risks, it seems
remarkable that he latter component would seem to have persistently increased during the period
under review, so that the decline in the other components was not really “transmitted” to funding
costs of the real economy. In this sense, the transmission mechanism of monetary policy could only
be partially improved through non-conventional measures. This of course does not mean that the
ECB non-conventional measures were not successful. Absent these measures, NFC funding costs
would certainly have significantly increased (instead of remaining more or less constant). Which
would have created significant disinflationary pressures. Main factors that explain the increase of
liquidity and credit spreads: (i) fact that this is a euro area NFC cost index, and that perceptions of
risks in the formally stressed countries remain elevated compared to pre-crisis (pre-crisis, the pricing
of credit and liquidity risk was levelled out in the euro area to a possibly excessive extent); (ii)
generally higher prudence of banks in extending and pricing loans; (iii) higher regulatory
requirements (more capital, more liquid assets) which reduce leveraging abilities of bank and
therefore likely make the bank liability structure more expensive (and puts higher minimum return
burdens on non-HQLA assets); (iv) profitability challenges of banks due to higher NPLs (in some
countries) and a lower absolute level of interest rate (in the entire euro area; reducing the
profitability of deposits as a cheap funding source relative to the general interest rate level) – the
profitability challenges imply a reduced willingness to provide credit at very low rates as lending to
NFCs needs to provide a significant contribution to overall profitability; (v) it appears that the shadow
cost of equity component remained rather elevated across the crisis years and thereby was a
relevant factor in preventing a stronger drop in overall NFC funding costs.
70
S11.13 Unconventional measures may address the ZLB problem, but they may also be related to the
LOLR function of the central bank, which is at least partially independent from the monetary
policy/ZLB problem. Indeed, defaults of solvent and sound companies due to a systemic liquidity
crisis are economically inefficient: they destroy value (as a default event typically leads to significant
losses of value of the company). For example the Bindseil and Jablecki (2013) model (“Central bank
liquidity provision, risk taking and economic efficiency”, ECB WPS No 1542) is a LOLR model in which
the central bank optimizes the specification of its LOLR function in view of a trade-off between
letting default too many sound firm versus letting survive too many weak firms (i.e. allowing for
zombification). Moreover, when interpreting the chart above, one needs to take into account that
probably views have changed were the effective ZLB is. In 2010 and 2011, it was probably believed
that 25 basis points is more or less the ZLB (or that going further does not really make a difference),
while in 2013 the perceived ZLB was seen at a deposit facility rate of zero. Finally, in 2014, the
deposit facility rate was pushed into negative territory without this causing yet any major distortions.
71
S12: Collateral availability and monetary policy
S12.1 Various reasons can be identified:

Larger needs for central bank credit (in the case autonomous factors increase, such as
banknotes or Government deposits, which is the case if the respective parties, i.e.
households and Governments, fear to be exposed to the banking system)

At the individual bank level, a higher variance of liquidity shocks, and therefore an increase
of the likelihood of a high needed recourse to the central bank

Collateral values drop (as central banks today tend to apply mark-to-market valuation)

Collateral can lose eligibility due to rating downgrades

Volatility increases and would justify an increase of haircuts (although central banks normally
apply the inertia principle vis-à-vis higher volatility of collateral values)

Collateral may be consumed more than normally for other uses (e.g. if market participants
and infrastructures increase haircuts, etc.)
S12.2 Increased collateral scarcity can affect monetary policy transmission in various ways:

Overnight interest rate control: Recourse to the marginal lending facility becomes effectively
more expensive due to higher collateral value and danger to run out of collateral =>
overnight rate will be above mid of the corridor for neutral liquidity conditions

Higher expected medium term bank funding costs in view of the assignment of a higher
probability of ELA needed

Financial instability if previous stable funding equilibria no longer apply. Banks need to move
to more expensive (but stable) funding sources. This will also lead to an increased banking
intermediation spread.
All these effects would imply a tightening of financial (or “monetary”) conditions. Therefore, the
central bank needs to reduce its policy interest rate as compensation (unless it cannot, because it has
already reached the ZLB).
S12.3 To reduce collateral scarcity, the central bank can:

Apply “inertia” to the collateral framework despite the worsening of the environment
(increased volatility of values, more uncertainty on true values, etc).

Make previously ineligible collateral eligible (e.g. collateral that is less convenient to handle,
so that it is not worth having it eligible in normal times).

Reduce haircuts (as modelled in the stylised models Bindseil, 2013, and Bindseil and Jablecki,
2013 – in reality, the central bank is more likely to extend collateral eligibility, which should
increase risk taking lesser)

Offer a securities lending programme (provide liquid, take illiquid securities)

Purchase illiquid assets from banks.
72
S12.4 (a) What is the maximum sustainable level of d in normal times? Let us summarise first in a
table the fire sale discounts and the haircuts on the two types of bank assets.
Credit claims
Corporate bonds
Fire sale discounts in
good times: f
100%
25%
Fire sale discounts in bad
times: f’
100%
50%
Central bank collateral
haircuts h
100%
50%
Consider two liquidity strategies of the bank, first to fire sell corporate bonds (strategy I) and second
to pledge them (strategy II). Starting with strategy I, the condition that liquidity generated is at least
equal to the deposits of one depositor means that: 0.75(d+2)/2 ≥ d/2  0.75(d+2) ≥ d  d ≤ 8.
We also have to verify that with this strategy, fire sale losses to not exceed equity. If d=8, then
deposits of one depositor are 4, and to generate liquidity of 4 the bank will incur fire sales losses of
4*0.25 = 1. This exactly eats up equity, so this strategy just allows for a no-run equilibrium.
The alternative strategy (strategy 2), to pledge the corporate bonds, obviously allows to generate
less liquidity as the liquidity condition is 0.5(d+2)/2 ≥ d/2  0.25d + 0.5 ≥ 0.5d  d ≤ 2, i.e. the
maximum sustainable amount of deposits is only 2. Therefore the answer to question (a) is 8.
(b) If haircuts are 50%, then the banks have no advantage in fire selling corporate bonds relative to
lending from the central bank. Therefore, they will borrow from the central bank, but that under the
prevailing haircut scheme allows only to sustain a level of deposits of 2, i.e. much less than the actual
8. Therefore, the only way to restore funding stability of banks is to lower the haircut on corporate
bonds to 25%, implying that the deposits of 8 can exactly be supported.
S12.5 Obviously, the ECB is tightening the treatment of ABS as collateral – just a week before the
collapse of Lehman. It should however be noted that 4 September 2008 was only the announcement
day of these measures, while they were implemented only with the beginning of 2009. The
tightening of the treatment of ABS as central bank collateral in the middle of a financial crisis in
which ABS played a key role reflected that also the ECB revised its assessment of ABS somewhat as a
consequence of the practices discovered. In some sense the ECB move can therefore be considered
“pro-cyclical”. Still, it seems defendable as (i) ABS were not only the victims of a general liquidity
crisis, but malpractices in the use of this instrument was one of the key origins of it; (ii) The ECB took
other counter-cyclical collateral measures, and overall it broadened collateral availability. In so far,
the 4 September 2008 announcements of the ECB do not seem incompatible with Bagehot (one may
also note that on 4 September, in addition to the quotation above, the ECB announced it would no
longer accept multiple layer ABS and certain close links with the counterparty submitting the ABS as
collateral. All these measures were validated in the subsequent weeks as Lehman Brothers,
Frankfurt, and Icelandic banks had taken more than EUR 10 billion of central bank credit from the
Eurosystem, collateralised with ABS that mostly would not have been eligible if the announcements
of 4 September 2008 would already have been implemented).
S12.6 Lowering the credit rating threshold can be viewed both as a measure to increase actively
collateral availability, and as measure to reduce pro-cyclicality if the central bank witnesses or
expects that important amounts of collateral will suffer, in the context of a crisis, from a
deterioration of their credit quality to below the previous levels. On first sight, a lowering of the
credit threshold seems to lead to higher risk taking. However, the dictum of Bagehot that “only the
brave plan is the safe plan” should also cover in principle this measure, i.e. the measure does not
necessarily lead to more risk taking because of positive systemic effects. Finally it is an interesting
philosophical question whether the lowering of the rating threshold can also be seen as a reflection
of Bagehot’s other dictum, namely to lend against what “is in ordinary time good collateral”.
Deterioration of credit quality in a crisis might not only reflect the liquidity component in the crisis,
but often will reflect persistent reductions of equity levels.
73
S13: Open market operations and standing facilities in a financial crisis
S13.1 (i) The central bank can conduct fixed rate full allotment instead of “auctions” to remove
allotment uncertainty; (ii) It can add further maturities of credit operations (e.g. additional long term
operations); (iii) It can offer credit open market operations more frequently; (iv) It can make its
corridor narrower, such that recourse to the marginal lending facility / discount window becomes
cheaper (and the former less stigmatised); (v) it can widen the set of eligible counterparties, so that
more liquidity stressed entities that normally have no access to the central bank can directly benefit
from the central bank.
S13.2 The answer to this question can be found in the book on pages 219-220 (in short) and in more
detail pages 220-227.
S13.3 Also in the case of outright purchase programmes, it is desirable to have well-defined
operational targets, as these provide clarity on what has been decided, and on what the market
operation experts in the central bank are supposed to achieve. The operational targets should be
clear and simple, and can be either quantity or rate related:

Achieve a certain purchase volume over a certain period of time (e.g. EUR 60 billion market
value per month, as in the case of the ECB’s PSPP launched in March 2015)

Purchase a certain duration (e.g. “EUR 10 billion 10 years duration equivalent”, which could
also be “EUR 20 billion of 5 year duration paper”)

Achieve a certain (maximum) yield at some maturity (“keep the 10 year bonds sovereign
debt yield at up to 100 basis points”)

Achieve a certain (maximum) spread level (“keep the spread between covered bonds and
Government bonds at 100 basis points maximum”)
An example for purchase programmes with not so well defined operational targets are the ECB’s SMP
and the OMT. In contrast, the EAPP/PSPP had a very clearly defined operational target (EUR 60 billion
per day).
S13.4 Of course the answer to this question has to depend on the purpose of the programme. Also
one needs to distinguish the achievement of operational targets (e.g. achieve the monthly purchase
volume that has been announced; see the previous question), intermediary targets (e.g. compress
long term risk free yields) and ultimate objectives (e.g. restore price stability). General measurement
problems are:

Intermediary and even more ultimate targets will of course also be affected by other factors
than the programme, and attribution may not be easy. This is also the case since significant
time lags and uncertainty on those apply between the achievement of the operational target
and the intermediate and in particular ultimate targets.

Role of announcement effects, vs implementation / flow effects. First, it is not generally clear
to what extent to expect all the effects on intermediary targets such as longer term yields /
spreads as of the announcement, or whether the implementation / flows are themselves
important. This will depend on market circumstances. Moreover, often programmes are
gradually pre-announced, like in the case of the ECB’s PSPP (which was supposed to have
been priced in to a significant extent before having been formally decided and announced).
This is particularly a problem for identifying the impact on intermediate targets, such as the
level of the yield curve.
In sum, only the success in terms of achieving the operational target can really be measured well.
Measuring the rest is very difficult, as the relevant academic literature also confirms.
74
S13.5 Below we illustrate the two cases in financial account systems, namely (I) that the securities
purchased by the central bank come from banks, vs. (II) that they come from households / nonbanks.
(I) If Households / non-bank financials do not change their financial allocation and therefore QE
assets come only from banks (it is assumed here that households have no securities holdings at all).
Real Assets
Deposits Bank
Banknotes
Bank capital
Households / Investors
E – D - B -C
Household Equity
D
B
C
Corporate / Government
Credits from banks
D+B+C
Debt
Real assets
Claims to Gvt / corp
Excess deposits with CB
Debt securities
D+C+B-SCB
SCB –B
SCB
E
D+C+B-SCB
SCB
Bank
Household deposits
Bank capital
D
C
Central Bank
Banknotes
Excess deposits of banks
B
SCB -B
(II) If QE securities come from Households / non-bank financials (we assume that households have an initial
securities position of SHH)
Households / Investors
Real Assets
E – D – SHH - B -C
Household Equity
E
Deposits Bank
D + SCB
Claims to Gvt/corporates
SHH - SCB
Banknotes
B
Bank capital
C
Corporate / Government
Credits from banks
D+B+C+ SHH
Debt
Real assets
Credit to Gvt / corp
Excess deposits with CB
Debt securities
D+C+B
SCB -B
SCB
D+B+C
SHH
Bank
Household deposits
Bank capital
D + SCB
C
Central Bank
Banknotes
Excess deposits of banks
B
SCB -B
In the first case, the length of the banks’ balance sheet does not increase, while in the second it does.
This will make a difference if leverage constraints are important to banks, i.e. then it may be better
that the securities purchased come from banks. The central bank can influence this to some extent
by selecting the type of securities. Ideally, the securities purchased:
-
Are held by banks, and preferred securities of banks are different than those of
households and non-bank investors, so that indeed the CB can make this choice;
-
The demand of banks is not too elastic, so that interest effects are strong
75
S13.6 The advantages and possible disadvantages of this procedure are described on pages 216-217
of the book. In the concrete context of October 2008, fixed rate full allotment procedures made
particular sense as they contributed to give certainty on central bank funding availability to banks
(subject to collateral availability – on which the ECB also took measures). Also, bidding behaviour of
banks would have been very aggressive in variable rate tenders at that time, with corresponding high
levels and volatility of spreads.
S13.7 Normally, fixed rate tenders do not make sense if they go beyond the next meeting of
monetary policy decision making bodies – they may create arbitrage opportunities leading to very
aggressive or insufficient bidding, and they thereby also destabilise liquidity conditions. In December
2011, this was not an issue as the ECB wanted to underline its commitment to keep rates low for
long, and was not worried about aggressive bidding behaviour and the implied large excess liquidity,
as this outcome would be compatible with the intention to ease monetary conditions significantly.
S13.8 LSAPS are useful when the central bank has exhausted conventional monetary policies because
it reached the ZLB at the short end of the interest rate curve. LSAPS can then reduce the term spread
and thereby lower actual interest rate for long term credit, i.e. ease monetary conditions further. The
lowering of term spreads can be viewed as the result of a flow effect (reflecting the increase of
demand in the daily clearing of markets) and/or of a stock effect, i.e. an equilibrium price effect of
the reduced stock available to private investors and other users. The flow effect should stop once
purchases stop, but the stock effect should prevail for as long as the central bank holds the acquired
stock. (See also Stefania D’Amico and Thomas B. King, “Flow and Stock Effects of Large-Scale Treasury
Purchases”, Finance and Economics Discussion Series, Divisions of Research & Statistics and
Monetary Affairs, Federal Reserve Board, Washington, D.C., 2010-52)
Once an LSAP is considered to be effective and successful, it should of course also lead to a pricing in
of the higher inflation expectations resulting from it. If the program is fully credible from the first
second on, all corrections could take place immediately. If however the effects take some time to
convince market participants, then a correction may take place in the market only after a while, and
interest rates may then go up despite the continued purchasing activities of the central bank. Even if
such a correction sets in, this does not mean that the purchase programme is ineffective, as, for
given inflation expectations, the LSAPs still leads to a downward effect on interest rates, which eases
monetary conditions.
S13.9 In a financial crisis, fire sales may depress prices unduly, i.e. may distort them to the downside.
In this case, a central bank purchase programme of a credit easing time which purchases the
securities suffering from fire sales will actually reduce distortions, and not contribute any. In contrast,
outside an acute crisis, compressing credit and liquidity spreads through a purchase programme of
illiquid and credit risky assets is likely to distort the pricing of these assets, i.e. the pricing of liquidity
and credit risk. This does not necessarily imply that such programmes should not be done, as their
advantages may outweigh the drawbacks of these distortions. The fact that many LSAPs put all or
almost all weight on Government assets suggests that central banks consider the distortive effects of
credit easing programmes in times outside acute crises as relevant (partially, this may however also
be explained by the operational costs of large scale purchases of credit risky and less liquid assets).
S13.10
(a) The “stance of monetary policy” seems to be used in the sense of “intended monetary
conditions” or e.g. “intended funding conditions of the economy”. Obviously the program
aims at changing (easing) actual monetary conditions, as it aims at changing the transmission
mechanism, which, with given conventional policy rates, should mean an easing of monetary
conditions.
(b) In particular in Germany, a significant part of the public (including conservative academics
and media – see also question Q11.10), believed that a sovereign bond purchase programme
76
meant significant inflation dangers. Since at the same time, this group of observers often also
tend to have a monetarist understanding of monetary policy implementation in mind (i.e.
that the monetary base is a key target variable of monetary policy implementation), the
announcement of sterilisation seemed to be a signal to these observers that they should not
fear inflation as a consequence of the announced programme. At the same time the
sterilisation was not believed to weaken the effectiveness of the programme in the eyes of
the rest of the observers (and the central banking community), which neither had
inflationary fears, nor did it believe into the relevance of the monetary base. The sterilisation
announcement of the ECB should have raised problems with observers who combined these
two dimensions differently. Believers in the monetary base who were worried about
deflation risks should have argued that sterilisation is counterproductive and is selfdefeating. Non-believers in the monetary base who were worried about an inflationary
impact of the SMP should have remained worried by inflation. The first type seemed to have
been rare, the second type existed, as exemplified by some of the statements in question
Q11.10.
(c) In the legal challenges to the OMT brought by plaintiffs to the German Constitutional Court,
it was argued inter alia that it is problematic that a link to Government policies is made in the
SMP, as this would undermine the independence of the ECB (similar issues were raised when
the OMT was taken to court later on). However, it can be argued that the reference to
Government policies simply underlines that effectiveness of the SMP as a monetary policy
tool (to provide necessary monetary easing) can only be expected to be successful if
Governments do not undermine it by e.g. irresponsible fiscal and economic policies. The ECB
must not undertake non-conventional measures if preconditions for their effectiveness are
not met.
(d) The announcement of the SMP is not clear on the operational target, i.e. in contrast to the
PSPP announcement in spring 2015, no monthly volume target (or alternatively, interest rate
target) is announcement. This makes day-to-day implementation of a programme more
challenging, as every day some policy judgements need to be made. The intermediate target
of the SMP was probably to reduce long term interest rates, as these are crucial for
monetary conditions. The ultimate target of the SMP was certainly to maintain price stability,
as this is the mandate of the ECB with regard to monetary policy (and SMP is a monetary
policy tool). At the same time, it is nothing totally exceptional to have central bank market
operations without quantified operational target: by definition, a managed float regime for
the exchange rate is managed in a flexible and even deliberately non-predictable way.
77
S14: The lender of last resort (LOLR) role of the central bank
S14.1 See section 14.2 of the book (pages 236-240).
S14.2 See the beginning of section 14.3 of the book (pages 240-241).
S14.3 See the second half of section 14.3 of the book (pages 241-242), and the six points listed there.
S14.4 See the comparative table 14.1 on page 244 of the book. Generally accepted principles of ELA
are in particular (i) constructive ambiguity (although note that a number of central banks seem to
move towards transparency of ELA frameworks – e.g. HKMA as described in section 14.4 of the
book); (ii) penalty rate (going back to Bagehot); (iii) only to solvent banks (to limit moral hazard and
risk taking, and as providing ELA to an insolvent bank does not stop a bank run); (iv) in ambiguous
cases only when the will of the democratically elected sovereign is documented in the form of a
guarantee provided to the central bank (to ensure that risk, if any, is taken consciously by the elected
Government; to protect further the central bank; in view of the fact that in some cases financial
stability considerations argue in favor to also have ELA provision to banks that are of ambiguous
solvency).
S14.5: Constructive ambiguity seems useful if it prevents that banks factor in ELA ex ante and
therefore leverage to an extent which is only sustainable if one can be sure that the central bank will
provide ELA with certainty. Anyway banks tend to be myopic in terms of factoring in in good times a
possible future crisis related deterioration of liquidity (also competition may force banks to not be
overly prudent with leveraging). Therefore, ideally, ELA is not factored in by banks, but nevertheless
available once asset liquidity conditions deteriorate and the previous equilibrium balance sheet
structure of banks becomes unstable, unless additional liquidity support by the central bank becomes
“suddenly” available. In more moralistic words, the idea is that constructive ambiguity prevents
“moral hazard”.
What one may find doubtful with constructive ambiguity is that even if ELA is not clearly announced
by the central bank and in this sense “ambiguous”, it may be factored in. Only if it would really be
excluded it would for sure not be factored in. Therefore, it could seem naïve to believe that by
adding uncertainty, one can improve the overall outcome. Maybe one will only add noise. Also,
critical voices could argue that “constructive ambiguity” is a “constructive excuse” for not being clear
ex ante. According to this view, ambiguity would reflect the lack of ability to be clear because of a
limited understanding of the overall problem and its best, rule-based solution.
One response to such criticism, in defense of constructive ambiguity, has been that there are
strategic games in which mixed strategies are optimal for society, i.e. strategies in which the players
randomize in a certain way the choice of their actions. Constructive ambiguity could be nothing else
than such a mixed strategy in a strategic game which is optimal for society.
S14.6 (a) See excel spreadsheet. The DTI can be calculated by comparing CVPH to the actual recourse
to the central bank. If x is the total household deposit withdrawal shock, then PI = P(x > DTI). The
shock x has an expected value of 0 and a variance that can be calculated for each bank out of the
presence of the two independent shocks and their coefficients (applying that for independent
random variables y, z, and constants a and b, Var(ay+bz)=a2Var(y)+b2Var(z)).
78
Haircut
Assets
Gvt
bonds
0%
Corp
bonds
20%
Corp
loan
100%
Bank 1
CVPH
80
80
20
16
100
0
96
Bank 2
CVPH
20
20
80
64
100
0
84
total
CVPH
Liabilities
HH
CB
Equity
deposits credit
Buffer Probability
CB credit of liquidity
(DTI)
(PL)
100
70
30
26
99,80%
100
70
30
14
99,39%
(b) Solution: After this, the balance sheets of the two banks look as follows:
Government bonds
Corporate bonds
Loans to corporates
Deposits with CB
80
20 14
100
0
Government bonds
Corporate bonds
Loans to corporates
Deposits with CB
20
80 56
100
0
Bank 1
Deposits of HH
Borrowing from CB
Equity
100 - 0.75η + μ
70 +0.75η - μ
30 24
Bank 2
Deposits of HH
Borrowing from CB
Equity
100 - 0.25η - μ
70 + 0.25η + μ
30 6
For bank 1 a DTI of 21.2 is obtained and PI = 99.07%. However, bank 2 has a DTI of -5.2, i.e. it has
become illiquid. The central bank will request the bank to provide more collateral but the bank will
be unable to do so. Therefore, the bank will default unless the central bank allows for “emergency
liquidity assistance”.
(c) The balance sheet now takes the following form:
Government bonds
Corporate bonds
Loans to corporates
Deposits with CB
80
20 10
100
0
Government bonds
Corporate bonds
Loans to corporates
Deposits with CB
20
80 40
100
0
Government bonds
Corporate bonds
Lending to banks
50
50 100
140 90 +η
Bank 1
Deposits of HH
Borrowing from CB
Equity
100 - 0.75η + μ
70 60 +0.75η - μ
30
Bank 2
Deposits of HH
Borrowing from CB
Equity
100 - 0.25η – μ
70 30 + 0.25η + μ
30
Central bank
Banknotes
Deposits of banks
Equity
200 +η
0
40
For bank 1 we obtain now a DTI of 28 and PL = 99.91%. For bank 2 we obtain a DTI of 22 and a PL of
99.996%. The liquidity situation of the banks has improved as the central bank has purchased an
asset from banks to which it applied a positive haircut when accepting it in its central bank credit
operations.
(d) DTI increases to 76 and 64, for bank 1 and bank 2, respectively, and PI gets to far below one basis
point.
(e) The DTI of both banks is now 30, and PL is 99.96% for bank 1, and above 99.99% for bank 2,
respectively.
79
(f) The central bank is involved in absolute intermediation of the banking system if one bank is made
over-liquid due to inflows of bank deposits, i.e. that even if the bank reduces its recourse to the
central bank to zero, it still has excess reserves with the central bank. In the example here it may be
assumed that there is no interbank market, so that the excess reserves cannot be channeled to the
bank that still depends on central bank credit.
In fact in the present example such a case is unlikely as both banks heavily depend on central bank
credit. Also, collateral constraints could be hit before this happens.
Central bank intermediation would occur for example in the unlikely case that η = -100 and μ = 35.
In this case the system of accounts will look as follows, whereby the initial haircuts applied by the
central bank do not need to be changed (however Bank 2 has almost exhausted its collateral buffer):
Government bonds
Corporate bonds
Loans to corporates
Deposits with CB
80
20
100
0 40
Government bonds
Corporate bonds
Loans to corporates
Deposits with CB
20
80
100
0
Government bonds
Corporate bonds
Lending to banks
50
50
140 +η 80
Bank 1
Deposits of HH
Borrowing from CB
Equity
100 - 0.75η + μ 210
70 +0.75η – μ 0
30
Bank 2
Deposits of HH
Borrowing from CB
Equity
100 - 0.25η – μ 90
70 + 0.25η + μ 80
30
Central bank
Banknotes
Deposits of banks
Equity
200 +η 100
0 40
40
S14.7 AIG was no bank, but an insurance group. Therefore, providing LOLR to it was unconventional.
Normally, the Fed is not supposed to provide credit to non-banks, but Art 13.3 of the Federal Reserve
Act allows to go beyond credit institutions under certain circumstances: “In unusual and exigent
circumstances, the Board of Governors of the Federal Reserve System, by the affirmative vote of not
less than five members, may authorize any Federal reserve bank, … to discount for any participant in
any program or facility with broad-based eligibility, notes, drafts, and bills of exchange when such
notes, drafts, and bills of exchange are indorsed or otherwise secured to the satisfaction of the
Federal Reserve bank: Provided, that before discounting any such note, draft, or bill of exchange, the
Federal reserve bank shall obtain evidence that such participant in any program or facility with
broad-based eligibility is unable to secure adequate credit accommodations from other banking
institutions.” The philosophy that first it needs to be established that the entity could not get credit
from another banking institutions is probably not always unambiguous to put in practice.
S14.8 Depositors seems to have feared that Northern Rock was insolvent, and that therefore despite
LOLR support, the depositors which will remain in the bank could eventually suffer losses to close the
capital gap (the case of Cyprus Popular Bank in 2013 seems to have validated that such fears are not
necessarily wrong). This supports also the central bankers’ dictum that LOLR should be provided only
to solvent banks, as otherwise the run does not need to stop.
S14.9 In H2 2007 and H1 2008, there is little to see in the aggregate balance sheet, but significant
relative intermediation of the banking system by the central bank was already taking place. As of
Lehman (15 September 2008), the readiness of central banks to act as LOLR for a banking system in a
full liquidity crisis lead to an expansion of central bank balance sheets, as liquidity rich banks
preferred to deposit excess reserves with the central bank, instead of lending to their fellow banks in
liquidity stress, who therefore needed to extend their central bank borrowing. In the US and the UK,
QE took over as driver of balance sheet extension from LOLR in the second half of 2009 (as the acute
liquidity crisis receded, while however deflation fears and the ZLB problem did not). Only in case of
80
the Eurosystem, the LOLR phase seems to continue with some oscillation until end H1 2015. QE takes
over as main driver of the central bank balance sheet gradually in the course of 2015.
S14.10 First we have to define relative and absolute central bank intermediation (call it RCBI and
ACBI). Absolute intermediation could be defined as the lengthening of the central bank balance
sheet:
ACBI = 1 – (minimum length of CB balance sheet for given autonomous factors and reserve
requirements / actual length of central bank balance sheet)
If ACBI = 0, then the minimum length of the central bank balance sheet prevails; If ACBI tends to 1
then the actual balance sheet length moves to infinity (which is hardly possible because of collateral
constraints of banks).
We can define RCBI in the case of two banks as follows. Call “AvCBC” the average central bank credit
to individual banks and “MinCBC” the central bank credit given to the bank with less recourse to
central bank credit. Then we may define RCBI as:
RCBI = 1- MinCBC / AvCBC
Again it is a variable that takes the value 0 if there is no RCBI, namely if both banks take the same
amount of central bank credit, while it can reach as maximum a value of 1, namely if one bank
reaches zero recourse to central bank credit.
Assume that Bank 2 is the weaker bank, i.e. the deposit shift shock μ is positive. Then:
RCBI = 1- (1- μ+η/2-P/2) / ((2+η-P)/2)
ACBI = 1 – (minimum length of CB balance sheet / actual length of central bank balance sheet) = 1 –
(3+ η)/(3+ η+max(0,-( 1- μ + η /2 –P/2)).
(b) We focus on illiquidity of the weaker bank. If we define MaxCBC as the larger of the two banks’
borrowings from the central bank, then Illiquidity is reached when MaxCBC = CVPH.
CVPH = (1-0.2)*(1-P/2)+(1-0.4)*1 = 1.4 – 0.4*P.
MaxCBC = 1 + μ + η/2 – P/2
DTI = CVPH – MaxCBC = 0.4 + 0.1P – (μ + η/2)
S14.11 Assume first banks rely on asset fire sales. Then each can generate liquidity: L = 0.4 ((D+B+FP)/2) and this needs to be enough to cover the deposits of one depositor and to pay back the central
bank, i.e.: L = 0.4 ((D+B+F-P)/2) ≥ D/4 + (B-P)/2  0.4 ((D+B+F-P)) ≥ 0.5D + (B-P)  -0.1 D ≥ 0.6 (B-P)
-0.4F  D ≤ -6 (B-P) + 4F . The maximum sustainable length of the balance sheet is thus, from the
liquidity perspective: D* = -6 (B-P) + 4F. In the case of a run one needs to fire sale (1/(1-f))D*/4,
which generates fire sale losses of (f/(1-f))D*/4 = (0.6/0.4)D*/4 = 1.5D*/4 = (3/8)(-6(B-P)+4F) = (9/4)(B-P)+1.5F. If e.g. B=P, then fire sale losses exceed obviously the equity of the single bank, i.e.
this degree of leveraging is often not possible from the equity /cost of fire sales perspective. If we
derive the maximum amount of deposits from the fire sale loss and equity perspective, we have to
start from (f/(1-f))(D/4+(B-P)/2) ≤ F/2  D ≤ 2F((1-f)/f)-2(B-P)=1.33F-2(B-P). If P=B, then D*=1.33F.
One can verify that this also fulfils the liquidity constraint.
What if banks instead seek to only rely on the central bank and leverage according to this constraint?
Then the constraint is: L = 0.125(D+B+F-P) ≥ 0.25 D + 0.5(B-P) …  D ≤ F – 3(B – P). Compared to
the fire sale strategy, this allows a slightly higher leverage, and therefore allows cheaper stable bank
funding.
81
S15: LOLR and central bank risk taking
S15.1 Central bank risk taking increases automatically in a financial crisis – due to the four reasons
listed on pages 240-241 of the book ((i) increased default probabilities and default correlations
during financial crisis; (ii) Increased asset price volatility and decline of liquidity, increasing the
probability of losses in collateral liquidation; (iii) deterioration of average credit quality of
counterparties and increase in concentration of exposures to (weak) counterparties; (iv) lengthening
of central bank balance sheets).
S15.2 There are four views on that (see pages 248-249 in the book: “inertia”; “active additional risk
taking”; “only the brave plan is the safe plan”; “credit protection above all”). Overall, Bagehot’s “only
the brave plan is the safe plan” reasoning seems convincing. Well-designed extra liquidity support
measures should help to overcome the liquidity crisis such that actual financial risks of the central
bank decrease thanks to this measure.
S15.3 This result is obtained if we believe that the central bank is special. It owns the “widow’s cruse”
in the sense that it can never become illiquid itself, and it can therefore be considered credit risk free
by its counterparties, who are therefore willing to accept high haircuts making liquidity provision
against non-liquid assets workable. Taking these unique features and considering its systemic
relevance, the central bank can in some cases with additional readiness to enter credit-risky
exposures improve the stability of the system by so much that eventually this reduces risks, instead
of increasing risks (as it would be normal for a small non-systemic market participant).
S15.4
(a) To verify stability, it should be checked that the withdrawal of deposits by one of the two
depositors can be sustained through sufficient liquidity and capital buffers. First we check if
the cheapest solution in terms of capital, namely recourse to the central bank, is sufficient.
Liquidity provision by taking recourse to the central bank is at the maximum L = (1-0%)*10 +
(1-20%)*20 + (1-50%)*70 = 10 + 16 + 35 = 61. The initial recourse to the central bank is 10, so
remaining buffers are 51. This exceeds the deposits of one depositor, and is therefore
sufficient.
(b) First, one may remark that decreasing haircuts should not change the zero-probability of
losses in the base case since the stability of the financial system is assured. On increasing
haircuts, it needs to be checked what happens once lending from the central bank is no
longer sufficient to ensure that one depositor can be paid out. From that point on, fire sales
become relevant for the stability of the financial system. What is the level of a scaling factor s
for haircuts at which central bank funding becomes insufficient? The critical level can be
calculated as the solution to the equation: (1-s*0%)*10 + (1-s*20%)*20 + (1-s*50%)*70 -10 =
40  s = 1.29. The haircut vector is then {0, 26%, 64%}. Now one can check whether the
pure fire sales approach is powerful enough beyond that level to support funding stability.
Fire sales allow to generate a liquidity of: (1-0%)*10 + (1-10%)*20 + (1-50%)*70 = 63. If we
assume that the bank would also need to pay back the 10 central bank credit to be able to
fire sale all assets, still there would be enough liquidity to pay out one depositor. Still, we
need to check if bank solvency is also ensured. Losses to generate 40 of extra liquidity would
amount to (assuming that the 10 central bank funding are maintained and collateralized with
credit claims) 0%*10 + 10%*20 + 40%*20 = 10. (fire selling 20 of loans is necessary to
generate a contribution from this source of 12 to the total additional liquidity of 40). This just
consumes capital buffers, and therefore also the remaining depositor does not have to fear
immediate losses. Therefore, financial stability is still maintained (but sharply).
(c) With this new fire sale loss vector, still sufficient liquidity can be generated, but now losses
under the pure fire sale approach to generating liquidity buffers, amount to 0%*10 + 10%*20
+ 50%*24 = 14, implying negative capital of 4. Therefore, funding stability is no longer
82
maintained and with probability of 50% a bank run occurs. Assume that if a bank run occurs,
the bank is immediately liquidated. As the liquidation losses in the crisis exceed for one asset
class the haircut of the central bank (while they are equal for the two other assets), central
bank losses can occur. (It could however also be argued that the central bank has the
privilege to not be in a hurry with liquidation of collateral, and thus that the fire sale losses in
crisis times do not need to apply to it).
S15.5 The central bank risk curve is upward sloping in central bank haircuts if at the moment the
increase of haircuts destabilises deposits, the damages of liquidation of the bank are so large that the
central bank does not recover its asset value, i.e. the haircuts were too low relative to the losses of
asset value that will occur under default and liquidation. One reason for this result may be that the
central bank underestimated the “systemic” component of collateral value losses in a liquidation
scenario. Maybe the central bank calibrated the haircuts looking at asset price volatility under
“normal” circumstances, and not in the more likely case that collateral needs to be sold exactly when
there are significant problems in the relevant markets because also others need to liquidate. (As
mentioned in the previous question, it could be argued that the central bank never needs to hurry
when liquidating seized collateral).
Consider now the concrete example of Q15.5. Assume that the central bank calibrated its haircuts,
observing normal times volatility, to be h% and that h% is higher than the “normal” fire sales
discount f. The banks choose a liability structure such that (1-h)(D+d)>= d/2 => d = ((1-h)/h)D. For
example, if h = 0.5, then d=D, and if h=0.25, then d=3D, and if h = 0.1, then d = 9D. Assume that the
central bank indeed did the latter, i.e. h=0.1.
Now assume however that in crisis times, f jumps to 0.5. What are now the losses as a function of
haircuts? If the central bank keeps haircuts unchanged at h=0.1, nothing happens. If however it now
increases haircuts to 0.11, a run occurs with ½ probability, and in this case the bank is liquidated and
the central bank will face a loss.
In sum, the condition for an upward sloping risk curve is that the central bank calibrated its haircuts
such as to be too low for addressing fire sale losses in crisis times. Solutions are:

Set higher haircuts already in normal times, namely at the level of fire sale losses in crisis
times.

Do not increase haircuts in crisis times so that funding stability continues to be assured.

Take time to liquidate assets (and have the capability to manage assets to preserve their
value before liquidation)
The second approach seems to have the advantage to allow banks to perform more maturity
transformation services to society.
S15.6 The following key lessons can be identified from this episode. First, from the negative
experience of ending up with the need to build a large provision:

Sophisticated banks are likely, before they collapse under liquidity stress, try to access
central bank credit to the maximum limit, including with regard to the use of eligible
collateral, i.e. by stretching eligibility criteria to the limit and possibly by submitting a
collateral pool which is both special, concentrated, and correlated with the counterparty
itself.

Therefore, central banks must always monitor the evolution of their exposure to individual
counterparties, and be vigilant with regard to emerging large size exposures and
concentration risks.

This may be particularly true for foreign counterparties, which may try to use a host central
bank for curing the funding gaps that appear at the international group level, and for which
the host central bank may have relatively limited supervisory information.
83

The haircuts applied on ABSs, and the relatively liberal eligibility criteria, may have been
insufficiently restrictive for an as flexible instrument as ABS.
Second, from the positive fact that at the end the provision was not needed and all claims were
recovered:

Central banks have an enormous privilege from not being liquidity constrained in a liquidity
crisis, and thereby to be able to undertake liquidation without any time pressure. Indeed, the
Eurosystem would have realised large losses (even beyond the provisions) if it would have
had to sell the assets in a short time horizon, such as e.g. a few weeks or months.

Despite the fact that the Lehman ABS were stretched structures in many respects (multiple
layer, with close links to Lehman, designed essentially for use as collateral with the
Eurosystem only and considering the relatively liberal pre-September 2008 eligibility criteria,
etc), they eventually contained significant value which allowed the Eurosystem to realise the
exposure without eventual losses. This speaks in favour of the soundness of ABS as financial
instrument in general (in particular if one would have paid more attention to ensure the
simplicity of the submitted structures and the absence of close links from the collateral
provider).
84
S16: LOLR, moral hazard and liquidity regulation
S16.1 First it may be noted that the discussion on whether maturity and liquidity transformation by
banks is primarily a legitimate, core activity of banking, and is actually a key service to society, or
whether it is essentially an undue risk taking creating risks to society dates back to the mid of the 19th
century. Taking the German literature as an example, the contribution of Schmalenbach (1933) still
seems to be particularly valid in discussing this question (E. Schmalenbach, 1933, Kapital, Kredit und
Zins, Leipzig). Potential central bank reliance in bad times allows banks to deliver more maturity and
liquidity (ML) transformation in good times. In so far, the readiness to act as LOLR supports ML
transformation and for those who believe that ML transformation is good, the LOLR would be
positive even if its possibility is anticipated. According to this view, the related effects on bank
behaviour should not be classified as “moral hazard”. Key arguments against this view should be
based on identifying actual drawbacks of reliance of banks in stressed times on central banks. What
could these drawbacks consist in:

The LOLR does not work well for non-solvent institutions, as it likely does not stop a bank run
in this case. At the contrary, the LOLR at the end may appear counterproductive and unfair,
as it allows the more sophisticated depositors to withdraw, while those who leave their
deposits in the bank will face a higher eventual haircut on their exposure (loss-given-default),
as the central bank’s exposure is typically well protected with collateral. In other words, the
LOLR allows for a partial flight of “bail-inable” assets. Therefore, it is essential that banks to
which LOLR is provided are solvent. However, solvency is not always easy to establish in a
crisis situation, and restoring solvency needs some time as various procedurally steps are
typically foreseen by legislation. Therefore, ambiguous situations will arise, in which the
problem described above may be unavoidable to some extent.

Generally, it is not the central bank’s comparative advantage to act as manager of exposures
to stressed financial entities. This diverts the central bank’s attention from its core task,
achieving price stability through monetary policy, which is demanding enough.

Most central banks consider that the LOLR should be provided under “constructive
ambiguity” to reduce ex ante reliance on it. However, constructive ambiguity seems to imply
discretionary elements, and those are never easy to administrate and inconsistencies may be
difficult to avoid.
S16.2 See page 264 of the book. Moral Hazard seems to be associated with a negative externality of
a decision. Substantial maturity and liquidity transformation could be considered as moral hazard if it
allows to enrich those who decide upon it, but created at the same time an expected cost to society
in the form of likely later bail outs of banks with costs to the taxpayer. Such costs do not seem to
arise directly from LOLR activities (but see caveats in the answer to the previous question), but when
recapitalisation is needed, starting from a negative capital level, or if there are not enough bail-inable
liabilities to close a gap and the Government considers that the smallest damage is achieved by
injecting taxpayers money.
S16.3 Key challenges in liquidity regulation:

It is difficult to take reliable assumptions on the stability of funding sources and roll over
rates, and in particular with regard to crisis times.

It is very difficult to take assumptions on the liquidity properties of assets, again in particular
with regard to crisis times.

Imposing certain holdings of liquid assets means to block these liquid assets in some sense
instead of really making them available as buffers. In principle, one could allow to run down
85
liquidity buffers in a crisis, but the declaration of a crisis case by supervisors is not easy, in
particular not if it concerns a single bank.

A recent study by the CGFS (2013, “Regulatory change and monetary policy”) suggests that
post crisis regulation, including liquidity regulation, has a number of effects on markets
which may also be regarded as negative (e.g. lower market liquidity, lower turnover, higher
volatility)

Bindseil and Lamoot (2011) have shown that Basel III liquidity regulation may make weak
banks take more structural recourse to central bank funding, instead of less.
S16.4
(a) There are a number of analogies – and differences - between the failed rescue of Lehman in
September 2008, and the discussions on Danat Bank in July 1931. In both cases (i) there was
a failed attempt to find a convincing solution over a weekend for a systemically important
bank that had run out of liquidity and that would default after the weekend if no new
funding sources could be identified; (ii) in both cases no bank volunteered to take over the
stressed bank over the weekend, due to the large uncertainties relating to the valuation of
the stressed bank; (iii) in both cases also the central bank refused to unlimitedly solve the
issue with LOLR credit; (iv) in the case of Lehman, the Fed NY would have been ready to
provide funding to a bank that would take over Lehman, while according to Priester, the
Reichsbank would have refused in the meeting on 13 July 1931 to be part of the solution; (v)
The Lehman rescue weekend ended with the default of Lehman, while Danat Bank was, after
being closed for some days, taken over by Dresdner Bank.
(b) Collective private solutions brokered by the central bank seem to be nice solutions, as they
address private sector problems with private sector solutions, and thereby reduce moral
hazard and the involvement of taxpayer money. Also, it is plausible that co-ordination and
soft pressure by a public agent with authority, such as the central bank, can overcome coordination problems between the individual private banks. Finally, it could be argued that if
deposits flow from one bank to the other banks, then these other banks should be cash rich
and could lend the same money exactly back to the stressed bank. On the other side, it has
to be acknowledged that this sort of solution finds its limits exactly where the specific
reasons for central bank LOLR can be found (see the list of reasons provided in section 14.2
of the book): for example, the banks that are supposed to rescue collectively their fellow are
likely to be liquidity stressed themselves (as in a liquidity crisis, deposit flows are not a zero
sum game, but all private players have acute liquidity worries); also, the bank to be rescued
may find unfair the collateral and haircuts requested by its rescuers in view of the fact that
the rescuers themselves are not credit risk free, etc.
(c) The answer to this question probably needs to be case-dependent. The question whether to
follow rues mechanically or flexibly in practice is also a very general almost philosophical
question applicable to many other areas beyond central banking.
In the case of central banking, rules are typically set in the central banks’ statutes (such as
e.g. the ECB/ESCB Statute) or in a key legal act (such as the Federal Reserve Act, or the
Reichsbank Law mentioned by Luther). Moreover, the central bank establishes in more detail
how it operates (e.g. in the case of the ECB, details of monetary policy operations are
specified in its Guideline (EU) 2015/510 of the ECB of 19 December 2014 on the
implementation of the Eurosystem monetary policy framework; ECB/2014/60). The hurdle to
change the latter types of rules is obviously lower. Important constraining rules that some
might argue require flexible interpretation in a financial crisis include in particular (i)
collateral rules; (ii) counterparty eligibility rules; (ii) rules on gold coverage of banknotes in
86
circulation (in case of the gold standard, i.e. in history); (iii) rules prohibiting “monetary
financing” of the Government.
Obviously, ignoring rules, or interpreting them flexibly, should always require as precondition
that one is deeply convinced that from an economic perspective, a strict interpretation of
rules does not make sense in the relevant exceptional environment, and that those who
established the rules did not anticipate the possibility of the prevailing conditions.
Second, the following issues need to be carefully checked in case a flexible interpretation is
considered: (i) Is there a risk of being taken to court by political adversaries, or by parties
who feel damaged by the measures taken by the central bank? If so, what would be the
consequences of losing the case in terms of damage to credibility, future flexibility and
possible payments? (ii) Can possible reputational damage be contained, in particular if a noncompliance with rules is exploited by political adversaries in the media? (iii) Is a perceived
flexibility in interpreting rules harmful to the future credibility of the central bank and its
ability to overcome time-inconsistency problems through reputation? (iv) Can the rule not be
changed by the one who has formal responsibility to change them? (v) Can the measures not
be amended such that they preserve their effectiveness, but become compliant with the
rules?
In the case of the Reichsbank on 13 July 1931, the real constraint seems to have been that
the Reichsbank was running out of gold, and that foreign central banks who could have acted
as LOLR to the Reichsbank (notably Banque de France) demanded as a precondition a
restrictive credit policy by the Reichsbank, and a strict adherence to all rules.
(d) Whether Luther was right in arguing that Reichsbank LOLR to Danat Bank would have been a
“misuse” of the Reichsbank, seems to relate to the more fundamental question whether
LOLR is fundamentally good (as it helps bank to provide maturity and liquidity transformation
services to society, by protecting this activity against systemic liquidity shocks) or bad (as it
invites excessive liquidity risk taking with negative externalities). Today (and probably ever
since Bagehot 1873) one should conclude that the LOLR function makes economic sense,
even if there is a potential issue with “moral hazard”, and therefore the term “misuse”
seemed clearly wrong in the middle of the 1931 German liquidity crisis.
(e) The gold standard and the constraints associated with it were a key issue here, as the
Reichsbank was actually running out of gold reserves and was close to violating the related
constraints on banknote coverage as also imposed by its statutes. These statutes were part
of international agreements (namely the treaties associated with the Dawes and Youngplans] and could not be changed easily. Therefore, the legal hurdles to abolish the gold
standard were higher in Germany than elsewhere. Many have argued that the Reichsbank
could have managed the situation better than it did. For example, it could have aimed at
restoring confidence by lending freely, hoping that this would make money flow back,
eventually allowing the Reichsbank to comply with all constraints. Others argued that the
Reichsbank should have asked more forcefully to be allowed to not respect constraints (as
anyway all rules were given up subsequently in the months and years after 13 July 1931,
when the damage had already been done.
S16.5: At least two links can be identified between central bank credit risk taking and the solvency of
the bank receiving LOLR credit: first, if a bank receiving LOLR is not solvent despite getting LOLR, and
if depositors know about it, then the run will not stop despite the LOLR, and central bank exposure to
the bank will correspondingly grow further and further. Therefore, also potential credit risks will end
to be rather large - and there is always a possibility that the assets that were accepted as collateral
eventually do not protect the exposure of the central bank.
87
The second link between central bank credit risk taking in LOLR and the solvency of the bank
obtaining LOLR is that only a bank that is solvent can in principle pledge enough assets as LOLR
collateral to eventually finance its entire balance sheet with LOLR without this implying for the
central bank to have an under-collateralised exposure. Indeed, “solvency” means that the value of
assets exceeds the nominal value of debt, i.e. what might potentially be replaced by LOLR lending. In
practice the central bank also needs some collateral value buffers, i.e. it needs to be able to impose
significant haircuts on LOLR collateral, to protect against (i) negative surprises in true collateral value
at the moment of bank default, and (ii) the possibility of collateral value deterioration during the
liquidation period. But obviously, the higher the solvency of the bank, and the higher the share of
long term funding of the bank that cannot run away in the relevant period in which LOLR is needed,
the more comfortable will be the collateral availability and hence the possible credit risk protection
for the central bank.
88
S17: The international lender of last resort
S17.1 (a) Country A is a smaller country than country B in terms of size of the financial system. More
interestingly, in country A, the banking system has provided relatively more loans to the real
economy, and finances a part of these through interbank credit from country B. In other words,
capital imports from country B to country A took place. This probably reflected that there was a
belief that capital productivity in country A was larger than in country B, and it was therefore
considered welfare improving (for all) to export some capital from country B to country A.
(b) We represent the following five shocks in the system of financial accounts – they can be traced
thanks to the different amounts (and they are shown in the order of appearance). For (ii), to allow
easy identification we underline the related changes:
i. Households shift deposits of 5 from A to B banks. What is important to note in this case is
that the net Eurosystem claims change sign, and therefore shift the side in the national
central banks’ balance sheet (which is not explicitly shown in the financial accounts)
ii. Household shift deposits from B to A bank amounting to 32 – all changes underlined. We
assume here that the deposit shift leads to a closing of the interbank position, as the Abank becomes thanks to the capital inflow very cash rich now and it would be
counterintuitive that still they receive interbank credit from bank B. Therefore, the
central bank credit provision does not need to be adjusted by the same amount as the
deposit shift, but by 10 less, and also the effect on intra-central bank claims is only 22.
iii. Decline of interbank lending to A bank to zero (i.e. by 10). Again in this case intra-system
claims switch sign.
iv. Households withdraw banknotes from A bank for 6 (we assume that each central bank
accounts for its banknotes separately)
v. NCB A injects reserves into the A bank by purchases of corporate claims of 4
Euro area households
Deposits with A banks
Deposits with B bans
Banknotes
Real assets
10 -6
Equity
100
40
10 +6
40
A country banking system
Loans
20
-4
HH Deposits
10-5 +32 -6
Deposits with NCB A (RR=5)
5 +17
Eurosystem refinancing 5 +5 -5 +10 +6 -4*
Net interbank liability 10 -10 -10
B country banking system
Loans
40
HH Deposits
40+5 -32
Net interbank claims
10-10 -10
Eurosystem refinancing
20 -5 +22 -10
Deposits with NCB B (RR=10)
10
NCB A
Eurosystem credit
5 +5 -5 +10 +6 -4
Banknotes
3 +6
Claims on corporates
+4
Deposits of banks
5 +17
Intrasystem claims
3 -5* +22 -10*
NCB B
Eurosystem credit
20 -5 +22 -10
Banknotes
7
Deposits of banks
10
Intrasystem liabilities
3-5*+22 -10*
*position shifts side in balance sheet
89
(c) This is the system of financial accounts after we split the household accounts into two parts. The accounts
below show the current account transaction.
Deposits with A banks
Deposits with B banks
Banknotes
Real assets
10
-10
3
17
+10
Deposits with B banks
Banknotes
Real assets
40
7
23
Loans
Deposits with NCB A (RR)
20
5
Loans
Net interbank claims
Deposits with NCB B (RR
40
10
10
+10
30
B households
Equity
70
-10
A country banking system
HH Deposits
Eurosystem refinancing
Net interbank liability
B country banking system
HH Deposits
Eurosystem refinancining
Eurosystem credit
5 +10
Intrasystem claims
3 -10*
Eurosystem credit
A households
Equity
NCB A
Banknotes
Deposits of banks
NCB B
Banknotes
Current accounts of banks
Intrasystem liabilities
* Position switches side of balance sheet.
20 -10
10
5
10
-10
+10
40 +10
20 - 10
3
5
7
10
3 -10*
S17.2 (a)
Deposits with Greek banks
Deposits with German banks
Banknotes
Real assets
Deposits with Greek banks
Deposits with German banks
Banknotes
Real assets
Real assets
Loans
Deposits with NCB A (RR=5)
Loans
Deposits with NCB B (RR=5)
Eurosystem credit
Intrasystem claims
Eurosystem credit
Intrasystem claims
“Greek” households
6
Equity
12
5
27
“German” households
8
Equity
14
5
23
Euro area corporate sector
50
Real assets
“Greek” banking system
25
HH Deposits
5
Eurosystem refinancing
“German” banking system
25
HH Deposits
5
Eurosystem refinancing
“Bank of Greece”
16
Banknotes
Deposits of banks
0
Intrasystem liabilities
“Deutsche Bundesbank”
4
Banknotes
Deposits of banks
6
Intrasystem liabilities
50
50
50
14
16
26
4
5
5
6
5
5
0
90
(b) Eurosystem credit of 16 needs to be collateralised with collateral value after haircuts of (1-h)25. The critical
value of h can therefore be calculated by equating 16 = (1-h)25 => h = 1 – 16/25
(c) The German banking system will be in excess liquidity (relative to required reserves) after further inflows of
4. If annual inflows are 6 and they are spread regularly over time, then after the first 8 months of 2011, the
Eurosystem balance sheet starts to lengthen (i.e. it starts to lengthen on 1 September 2011). The Bundesbank
balance sheet on 31 December 2011 should look as follows:
Eurosystem credit
Intrasystem claims
“Deutsche Bundesbank” at end December 2011
0
Banknotes
Deposits of banks
12
Intrasystem liabilities
5
7
0
S17.3 This proposal would make monetary union more similar to a fixed exchange rate system. In a
fixed exchange rate system, the central bank from the country suffering a negative balance of
payment uses its foreign reserves to balance foreign exchange markets. When however foreign
reserves are exhausted (despite whatever measures were taken), the central bank may have to give
up the exchange rate peg and devalue. In a monetary union, markets could factor in similar
developments if TARGET balances would be limited, which could accelerate capital flight. Also, the
break-up of a monetary union is more dramatic and destructive then giving up an exchange rate peg.
S17.4 (a) To establish the conditions under which this state has stable access to international capital
markets, we can apply the two conditions for a single Nash no-run equilibrium (see section 11.3 of
the book). First, the state has to be able to generate sufficient liquidity to satisfy the desired
withdrawal of cash by one depositor, i.e. 1-F(1)≥d/2. Second, the solvency damage from the liquidity
generation needed for satisfying one depositor must not exceed equity. The fire sale damage
associated with the necessary liquidity generation of d/2 can be calculated as follows: The total
amount of assets to be liquidated is x with: x-F(x)=d/2. Call x* the solution to this equation. Total fire
sales damage is thus F(x*). This must not exceed the equity of the state, i.e. F(x*)≤(1-d).
(b) Both concepts are not exactly comparable to the case of a company (and they are probably less
well defined). “Assets” can include both classical assets such as a state-owned railway, electricity
production and distribution networks, road networks, state owned broadcasting, etc. However, if we
consider it, in line with question (a) as whatever is able to generate money by taking recourse to it,
then it also includes measures relating to the general productive capacity of the economy, the
political stability and willingness and awareness or voters as basis to impose for some time higher
taxes, etc. The meaning of “equity” for states follows directly from this broader concept of assets (i.e.
if we define as equity the difference between “assets” and debt).
(c) Again, one could imagine classical asset value shocks on physical assets (e.g. destruction of a
country’s infrastructure trough WWII; more recently and at a lower scale, the destruction of the
largest electricity power plant of Cyprus on 11 July 2011 as a consequence of an explosion of a
nearby depot of confiscated arms from the middle-east, etc.). Moreover, anything that damages the
ability of the Government to generate liquidity in the short term in the sense of the model above can
be seen as analogous to an asset value shock. For example, if a charismatic political contender of the
ruling Government appears on stage, who promises that “austerity” is not needed and in any case a
mistake, this limits the actual ability of a Government to generate liquidity, and thereby may be
pivotal to the Government having funding access or not (for given debt level).
(d) Now it is assumed that the liquidity generation cost function f(x) has the functional form f(x) = xα.
As also reminded in the book on page 110, The integrated function of a power function f(x) = xα is
F(x) = x(α+1) /(α+1). Therefore the maximum liquidity that the Government can generate to face the
run by one depositor is 1-1/(α+1) = α/(α+1) and fire sale costs of generating this are 1/(α+1).
Therefore the first condition for a no-run equilibrium are: α/(α+1) ≥ d/2 => d ≤ 2α/(α+1). The second
91
condition is that equity exceeds fire sale losses in case there is a need to liquidate assets to pay out
one depositor. The amount of assets liquidated is x as determined by x-F(x)=d/2  x - x(α+1) /(α+1)
=d/2. Call x* the solution to this equation and as mentioned under (a), the total fire sales damage
F(x*) must not exceed the equity of the state, i.e. x*(α+1)/(α+1)≤(1-d).
(e) The following table summarises the relevant results. It has been generated in excel (see the excel
workbook). Note that the identification of x*, the amount of assets that needs to be sold in order to
generate the liquidity necessary to pay out one depositor, is foreseen in this spreadsheet to take
place via trial and error (the alternative is to use the excel “Solver” function, which is not complicated
either). Note that cases which were obvious and implicitly covered by what is shown have been
omitted. For example, in the case of d=0, even with the highest fire sale costs (α=0.1), liquidity and
solvency conditions are fulfilled, so there is no point to show in the table that this is also the case for
more favourable asset liquidity conditions.
In the case d=0.25, only with the worst asset liquidity (α=0.1) the Government’s funding is unstable,
while for the better asset liquidity conditions, both the liquidity and solvency conditions are fulfilled.
For example, for the case d=0.25 and α=0.5: the liquidity condition is fulfilled as total liquidity that
can be generated via asset fire sales is α/(α+1) = 0.333, versus deposits of one depositor of
0.25/2=0.125. To generate liquidity of 0.125, assets need to be sold for an initial book value of 0.173
(i.e. 17.3% of the state’s assets need to be liquidated to pay out the one depositor who finances
12.5% of the state’s balance sheet), and implied fire sale losses are 0.05 (i.e. 5% of the total state
balance sheet value). This is obviously less than the equity of the state, which is in this case 0.75.
For d=0.75, the minimum asset liquidity parameter α that ensures that the liquidity condition can be
fulfilled is α=1. Again, as in the previous cases (with d=0.25 and d=0.5), whenever the liquidity
condition is fulfilled, then also the capital condition is violated.
This is no longer the case for d=1. The liquidity condition is still fulfilled for α=1 and α=5, but the
solvency condition is no longer fulfilled in either of these cases. For α=5, the fire sale losses needed
to generate the necessary liquidity are low (0.003), but this too high if equity is zero,.
Given
Liquidity
Assets to be sold to generate d/2
fire
Capital
parameters condition?
Proposed x Checking that x is right
sale Equity condition?
x-x (α+1) /(α+1) d/2
x(α+1)/(α+1)≤(1-d)
d
α
d/2 ≤ α/(α+1)
x
Δ loss
0,00 0,10
yes
0,000
0
0
0,00 0,00
1
yes
0,25 0,10
no
0,25 0,50
yes
0,173
0,125
0,125 0,00 0,05 0,75
yes
0,25 1,00
yes
0,134
0,125
0,125 0,00 0,01 0,75
yes
0,25 5,00
yes
0,125
0,125
0,125 0,00 0,00 0,75
yes
0,50 0,10
no
0,50 0,50
yes
0,454
0,250
0,250 0,00 0,20
0,5
yes
0,50 1,00
yes
0,293
0,250
0,250 0,00 0,04
0,5
yes
0,50 5,00
yes
0,250
0,250
0,250 0,00 0,00
0,5
yes
0,75 0,10
no
0,75 0,50
no
0,75 1,00
yes
0,500
0,375
0,375 0,00 0,13 0,25
yes
0,75 5,00
yes
0,376
0,376
0,375 0,00 0,00 0,25
yes
1,00 0,10
no
1,00 0,50
no
1,00 1,00
yes
1,000
0,500
0,500 0,00 0,50
0
no
1,00 5,00
yes
0,503
0,500
0,500 0,00 0,003
0
no
S17.5 Generally, state asset fire sales to counter a balance of payment crisis is unfortunate and has
more weaknesses than strength. It is a costly emergency solution and normally ex ante it should be
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ensured that the probability of ending in this state is kept minimal. The following “advantages” of
state asset sales in a BoP crisis may be identified:
-
The need to generate some cash
-
That it shows willingness of the Government of the stressed country to contribute to the
solution by taking painful measures, and not only ask for external funding support.
-
That privatisations may also be a form of supply side reform, i.e. may strengthen growth
dynamics.
However also the following disadvantage appears to be relevant: As long as question marks on
political stability, the success of an adjustment programme, of debt sustainability prevail, private
investors will not trust in the rule of the law and private property rights in the stressed countries, nor
will they believe that the country’s development will support the future price development of the
asset they consider purchasing. This implies that the timing of privatisations should be such that they
come when a positive perspective has emerged. Commitment to do them can of course be taken in
the context of the design and agreement of an adjustment programme, when still large uncertainty
prevails.
S17.6 The figure below captures three possible sources of intra-Eurosystem claims and liabilities.
TARGET2 balances are driven by current account transactions (“CUR”) and capital transactions
(“CAP”). Remittances (e.g. payments from Greek residents to relatives abroad) can be understood to
have identical effects to capital outflows and are therefore captured by CAP. The household sector
has been split up into a “Rest of euro area (REA)” and Greek (GR) household. Both households
undertake capital flight (i.e. both the “REA” household and the “Greek” household transfer deposits
from the “Greek” banking system to the REA banking system). In addition, the REA household sells a
good (say a used car) to the GR household, reflecting a current account transaction. The impact of
both transactions on household deposits, central bank credit taking by the two banking systems, and
TARGET2 balances within the Eurosystem are of identical nature, implying that it is not possible to
identify the nature of TARGET2 balances in terms of type of balance of payment transaction from any
position in the financial system (i.e. in the banking system or central banks). Only the balance of
payment statistics is able to provide an answer to the question whether a change of TARGET2
balances is driven by current accounts of capital accounts transactions. (The case of a Greek exporter
or tourist service provider who keeps his income on an account outside Greece can be interpreted in
the financial accounts as a simultaneous Current account inflow and Capital export).
In addition, the financial accounts below capture that Greek households withdraw additional
banknotes (“ATM”). We assume that, in line with Eurosystem accounting rules, banknotes are shown
in balance sheet proportional to capital key, with the compensating position being intra-Eurosystem
claims and liabilities. The ECB capital share owned by Band of Greece is captured in the parameter g.
The financial accounts also demonstrate the domestic money creation - Greek banks providing fresh
loans (“FL”) to Greek corporates who add to the deposits of Greek corporates – in themselves do not
create additional needs for central bank credit or T2 balances (in fact the banking and central
banking sector are not affected at all). In the accounts representation below, it is assumed that the
REA banking system remains dependent of central bank funding. In case CUR+CAP exceeds the initial
reliance of the REA banking system on central bank credit, the REA banking system will end in excess
liquidity and hold a deposit with the NCBs of REA. Note that for the sake of simplicity it has been
assumed that REA and GR are ex ante identical.
In sum, it appears that the need to increase recourse to central bank funding by Greek banks is
driven by the sum CAP+CUR+ATM. This means that in case of a ceiling, Greek authorities need to
manage the sum of these three factors such that they remain close to zero or preferably are
negative, so that liquidity buffers of Greek banks increase again. Positive contributions of a current
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account surplus of course depends on the assumption that the payments of exports of goods and
services (including tourism) is made on domestic bank accounts (otherwise. It is like the combination
of a current account inflow and an immediate compensating capita export). Greek authorities need
to impose on importers the repatriation of proceeds.
System of financial accounts to present the summer 2015 situation Greece vs. rest of euro area
REAL SECTORS
Deposits A-bank
Deposits B-bank
Banknotes
Real assets
Household REA
D/2+CAP/2+CUR
Equity
D/2 -CAP/2
B/2
(E-D-B)/2 - CUR
Household GR
Deposits A-bank
D/2+CAP/2+CUR
Equity
Deposits B-bank
D/2 -CAP/2
Banknotes
B/2
Real assets
(E-D-B)/2 - CUR
Euro area corporate sector
Real assets
D+B
Credit from banks
Deposits (with Greek banks)
FL
BANKING SYSTEM
Corp loans
Corp loans
(D+B)/2
(D+B)/2+ FL
CENTRAL BANKING SYSTEM
Credit to bank
B/2-CAP-CUR
Intrasystem claims
CAP+CUR+(1-g)ATM
Credit to bank
B/2+CAP+CUR+ATM
Intrasystem credit
CAP+CUR + (1-g)ATM
REA bank
Deposits
CB credit
GR bank
Deposits
CB credit
NCB REA
Banknotes
Bank of Greece
Banknotes
Intrasystem liab.
E/2
E/2
B+FL
D/2+CAP+CUR
B/2-CAP–CUR
D/2-CAP-CUR-ATM+FL
B/2+CAP+CUR+ ATM
B/2+(1-g)ATM
B/2 + g.ATM
CAP+CUR+(1-g).ATM
ECB
Eurosystem credit
Intrasystem liab.
CAP+CUR+ (1-g)ATM
For information: consolidated Eurosystem = ECB + NCB REA + BoG
B + ATM
Banknotes
B + ATM
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