Banking
Tutorial 8 and 9 – Credit risk,
Market risk
Magda Pečená
Institute of Economic Studies, Faculty of Social Science,
Charles University in Prague, Czech Republic
November 28, 2012
Excursus (related to Tutorial 6 – capital
structure
Tier 1 capital
–
„the capital“
Slide 2
Credit risk (in terms of capital requirement) –
recap
Source: CNB, Financial market supervision report, 2010
Slide 3
Credit risk management models
Credit risk assessment
Scoring
Altman Z-score
Rating
Credit risk models
,
Credit Monitor Model (KMV Moody´s)
Credit Margin Models
CreditMetrics (based on VaR methodology)
RAROC
Slide 4
Credit scoring
Original Altman Z-score:
Z  0,012 X 1  0,014 X 2  0,033 X 3  0,006 X 4  0,999 X 5
where
X1
X2
X3
X4
X5
Working capital/Total assets
Retained earnings/Total assets
EBIT/Total assets
Market value of equity/Book value of total liabilities
Sales/Total assets
Revised several times, but the ratios used
are more or less the same/similar
Slide 5
Credit risk – KMV model
  2 

VT  V0 exp  r  V  T   V T ZT 
2 


E (VT )  V0 erT
Market value of assets (V)
Possible path of the asset value
Distribution of the
asset value at time T
V0
Distance to default (DD)
The expected rate of growth in the
asset value

Default Point
F
Probability of default
T
Time
Slide 6
Loss distribution of credit risk with
certain weight of fat tails
Slide 7
Loss distribution of market risk with
zero weight of fat tails ?
probability of state
expected value of the exchange rate, bond, stock
- one standard
deviation from
the mean
+ one standard
deviation from
the mean
losses
profits
Slide 8
Credit risk – CreditMetrics
Example of a migration matrix
AAA
AA
A
BBB
BB
B
CCC
AAA
90.81%
0.70%
0.09%
0.02%
0.03%
0.00%
0.22%
AA
8.33%
90.65%
2.27%
0.33%
0.14%
0.11%
0.00%
A
0.68%
7.79%
91.05%
5.95%
0.67%
0.24%
0.22%
BBB
0.06%
0.64%
5.52%
86.93%
7.73%
0.43%
1.30%
BB
0.12%
0.06%
0.74%
5.30%
80.53%
6.48%
2.38%
B
0.00%
0.14%
0.26%
1.17%
8.84%
83.46%
11.24%
CCC
0.00%
0.02%
0.01%
0.12%
1.00%
4.07%
64.86%
D
0.00%
0.00%
0.06%
0.18%
1.06%
5.20%
19.79%
N.R.
0.00%
0.00%
0.00%
0.00%
0.00%
0.01%
-0.01%
Slide 9
Credit risk – CreditMetrics
Loan information
Spreads
Rating/ Issuer rating
A
AAA
0%
Maturity
3 years
AA
0.00%
Coupon
10.2072%
A
0.20721%
Principal value
100
BBB
0.46081%
AAA-yield
10%
BB
0.96801%
B
1.98241%
CCC
4.01121%
Recovery rate
50.00%
Year-end
rating
AAA
AA
A
BBB
BB
B
CCC
D
Probability
of state
Bond price +
coupon
Yield
0.09%
2.27%
91.05%
5.52%
0.74%
0.26%
0.01%
10%
10.00%
10.21%
10.46%
10.97%
11.98%
14.01%
recovery
0.06% rate
110.567
110.567
110.207
109.770
108.904
107.206
103.944
Confidence level
99.90%
Difference
from the
mean
0.09951
2.50987
100.34367
6.05929
0.80589
0.27874
0.01039
0.429
0.429
0.070
-0.368
-1.234
-2.931
-6.193
0.03000
-60.137
50.000
Mean =
99.00%
99.50%
Probability
weighted
value
110.13735
Difference
from the
mean
(absolute)
Probability
weighted
difference
squared
0.42948
0.42948
0.06986
0.36757
1.23358
2.93101
6.19314
0.0002
0.0042
0.0044
0.0075
0.0113
0.0223
0.0038
60.13735
2.1699
Variance =
St. dev. =
2.2236
1.4912
Normal distribution assumed
2.326 Var
2.576 Var
3.090 Var
3.4690
3.8413
4.6081
Slide 10
Loan princing
Traditional approach (Cost-plus-profit approach)
RAROC (Risk-adjusted return on capital (risk
adjusted profitability measure where the volatility of
losses is taken into account)
,
Slide 11
Loan pricing – traditional approach,
example
Market data
Rating
Historical 5-Year
default rate (%)
AAA
AA
A
BBB
BB
B
…
0,01
0,6
1,22
2,5
8,69
18,63
Maturity (years)
1
2
3
4
5
10
…
Cost of funds (% p.a.)
2
2,75
3,5
4
4,5
7
Slide 12
Loan pricing
Item
Calculation
Result
Assumptions
Borrower rating
A
Loan maturity
5
Default rate
1.22%
Capital ratio (capital
adequacy)
Hurdle rate
Loan amount
8%
10%
1000000
Calculation
Capital required
Annual capital charge
Annual funds costs
Annual loan loss allowance
Break-even annual interest
income
Loan Interest Rate (with no
funding risk)
Minimal spread
1,000,000 * 0,08
80,000 * 0.1
920,000 * 0.045
80,000
8,000
41,400
1,000,000 * 0.0122 / 5
2,440
8,000 + 41,400 + 2,440
51,840
51,840 / 1,000,000
0.05184
5,184 5.84 % - 4.5 %
68.4 bps
Overhead and other costs not included.
We also assume that capital (capital adequcy requirement) is equal to equity
Slide 13
Value at risk
- Interpretation
VaR = CZK 1 million at a confidence level of 99% over a 1-day
holding period. (VaR is expressed in absolute numbers,
amounts).
Interpretation:
•In 99% of cases, i.e. on an average of 99 out of 100 trading
days, a maximum loss of CZK 1 million is expected.
•The second largest loss to occur in 100 trading days is
expected to be a maximum of CZK 1 million.
•The CZK 1 million is the minimum loss to be expected for the
worst 1% of days.
Slide 14
Value at risk
Historical simulation
Monte Carlo simulation
Variance-covariance method (analytical method, delta normal
method)
VaR = (z-value)* σ *P
VaRt-days=t1/2 *VaR1-day
Portfolio VaR
VaRP  VaR1  VaR2  2 *  * VaR1 * VaR2
2
2
! Risk factors vs. positions weights !
Numbers to be remembered:
95 % confidence level – 1,65 standard deviations
99 % confidence level – 2,33 standard deviations
Slide 15
VaR - example
A US investor is holding a position of CZK 1 million
(which translates into USD 40 000 at the exchange
rate of 25 CZK/1USD). The standard deviation (daily
volatility) of the CZK/USD exchange rate is 0.7%.
a) What is the daily VaR at a 95% confidence level?
b) Determine the 10-day VaR on the same confidence
level.
Slide 16
VaR – example (solution)




σ = 0,7 %
t = 1 day
P = 40 000
95 % confidence level → 1,65 standard deviations
a) 1 day VaR = 40 000 * 0,007 * 1,65 = USD 462 nebo/ or CZK 11 550
or equivalently
the value of the position will not fall with a probability of 95% under USD 39 538
(P - 1,65*σ)
b) 10 day VaR = CZK 11 550 * 101/2 = CZK 36 524
Slide 17
Value at risk - examples
1. We have a position worth CZK 15 mil in ČEZ shares. Calculate the VaR
at a confidence level of 99 %, the holding period is 10 days. The daily
volatility of ČEZ shares is 0,5 %.
2. Now, determine the VaR from the point of view of an German investor
(so VaR in EUR). The CZK/EUR expected FX rate is 24,6, the daily
volatility of the FX rate is 0,8 % and the correlation between FX risk and
Czech equity risk is 0,2.
3. Assume, the German investor made a portfolio of his ČEZ shares (in
CZK) and EUR 2 mil of German government bonds, with a daily
volatility of 0,2 %. Determine (all on the confidence level of 99 %) the
total VaR his portfolio is exposed to. The correlation between the i.r. of
the government bond and his position in Czech shares is -0,1.
Slide 18
VaR – interest rate risk
Present value of a basis point - Unlike the modified duration, the PVBP
measures the absolute – and not the percentage – change in the current
market price of a fixed-yield security when the market interest rate has
changed by one basis point (0.01%), so the size and value of the position
is already taken into account.
PV
PVBP 
Dmod
* PV
100 * 100
PV(r)
PV(r+0,01%)
Spot rate
r
r + 0,01 %
r
+
PVBP( r )  PV ( r )  PV ( r  0,01%)
Slide 19
VaR – interest rate risk
There is a zero coupon bond with a PVBP of EUR 47,500
and a 1-day volatility estimate of 0.02% (2 bps). Calculate
the daily VaR at a confidence level of 95%.
VaR = 47 500 * 2 * 1,65 = EUR 156 750
Slide 20
RAROC
Risk adjusted return on capital (RAROC ) is the risk-adjusted
profitability measure where the volatility of losses is taken into account.
RAROC provides a consistent view of profitability across businesses
(business units, divisions). It allows the comparison of two
businesses with different risk profiles, and with different volatility
of returns.
The pricing of a loan/product is derived from the fact that the
manager must meet certain RAROC requirements (benchmark
RAROC).
RAROC is based on Value at risk methodology
Slide 21
RAROC
Net __ Expected _ Income
RAROC 
Economic _ Capital
Net Expected Income = interest income + fee income
Economic capital =
Change in a loan value when the interest rate changes by 1% / credit
quality decreases (this is only an arbitrary setting, other institutions may
model a 2% increase in interest rates as the corresponding economic
capital requirement).
The capital requirement may be calculated as follows:
L
dL   D
di
1 i
dL
D
L
i
di
–change in a loan value
–duration of the loan
–the face (par) value of the loan
–interest rate
–change in the interest rate
Slide 22