Liquidity risk in
Fixed Income Markets
Valuation adjustment, risk assessment,
stress testing and portfolio construction
Research paper #3
Publishing Director:
Ibrahima Kobar
Co-chief Investment Officer,
in charge of Fixed income investment division
Written by Quantitative Research and Analysis - Fixed income:
Nathalie Pistre, PhD, Head of the team,
Deputy Head of Fixed income investment division
Chafic Merhy, PhD
Matthieu Garcin
With the contribution of:
Philippe Berthelot, Head of Credit - Fixed income
Elisabeth Breaden, Head of Product Specialists - Fixed income
NATIXIS ASSET MANAGEMENT
Fixed income investment division
With assets under management of € 294 billion and 633 employees1,
Natixis Asset Management ranks among the leading European asset
managers.
Natixis Asset Management offers its clients (institutional investors,
companies, private banks, retail banks and other distribution networks)
tailored, innovative and efficient solutions organised into 6 expertises:
Fixed income, European equities, Investment and client solutions,
Structured and volatility (developed by Seeyond2), Global emerging
and Responsible investing (developed by Mirova3).
Natixis Asset Management’s offer is distributed through the global
distribution platform of Natixis Global Asset Management, which offers
access to the expertise of more than twenty management companies
in the United States, Asia and Europe.
The Fixed income investment division implements an active
fundamental management, where risk is taken into account at every
stage of the investment process. It offers a collegial approach with
sector teams specialised by market segment.
The Fixed income investment division is supported by close to
one hundred specialists, including asset managers, credit analysts,
strategists, financial engineers and economists.
With € 214.6 bn under management1 and a track record of more than
30 years, this investment division has proven experience.
The Quantitative Research and Analysis team supports Natixis Asset
Management’s fixed income investment teams by providing portfolio
construction tools, quantitative model outputs, and valuation models
for structured credit and derivatives. They help to calibrate the portfolio
management process and the risk budgeting approach.
1- Source: Natixis Asset Management – 31/12/2013.
2- Seeyond is a brand of Natixis Asset Management.
3- Mirova is a subsidiary of Natixis Asset Management.
Liquidity risk in Fixed Income Markets
TABLE OF CONTENTS
EXECUTIVE SUMMARY
1 /// DEFINING AND MEASURING LIQUIDITY RISK
I. LIQUIDITY: AN HETEROGENEOUS CONCEPT
6
II. ASSET LIQUIDITY RISK
6
III. MEASURING LIQUIDITY RISK IN FIXED INCOME MARKETS
8
2 /// THE LIQUIDITY FACTOR
10
I. WHAT FACTORS DRIVE LIQUIDITY?
10
II. THE LIQUIDITY PREMIUM
12
III. THE ROLE OF LIQUIDITY IN CRISIS
13
3 /// IMPACT OF LIQUIDITY ON PRICING, RISK MEASURES
AND PORTFOLIO CONSTRUCTION
I. PRICING ILLIQUID SECURITIES: MTMARKET VS MTMODEL
II. CONTROLLING LIQUIDITY RISK: L-VAR VS VAR
III. PORTFOLIO CONSTRUCTION AND STRESS TESTING:
THE LIQUIDITY EFFICIENCY SCORE
6
4 /// APPENDIX
15
15
17
18
21
REFERENCES22
3
Liquidity risk in Fixed Income Markets
EXECUTIVE SUMMARY
Market risk and liquidity risk are by far the main
sources of uncertainty affecting a portfolio’s future
P&L. While the former can be explained by uncertainty regarding price fluctuations, the latter is incurred
when trading assets. Illiquidity increases with the size
of the position. It occurs over some short term but
vanishes over a longer horizon. Typically a security
held to maturity has no liquidity cost.
However, unlike other risk factors, liquidity risk cannot
be diversified. For example, one cannot offset a given
level of liquidity “exposure” by going short an illiquid
security. More generally, no known liquidity-based
derivatives could hedge this particular risk. Indeed, in
stressed markets, bid rather than mid prices prevail.
In this paper, after a brief survey of the financial theory
on liquidity risk, we examine its main characteristics,
its measures and drivers as well as its preeminent
role in the development of crisis and the burst of
bubbles. Liquidity thus appears as a risk factor that
signals returns ex ante and explains performance ex
post, at least partially. According to the existing literature, liquidity risk premium would be around 0.6%
for investment grade bonds and 1.5% for speculative
bonds.
Extending equity liquidity measures to bond market is
not henceforward as they depend on bond’s intrinsic
characteristics. Unlike stocks, bonds redeem. The
liquidity of 10 years bond is not the same as 3 months
one even for the same issuer. A traded volume based
liquidity measure can be quite misleading as a traded
bond is not necessary a liquid one e.g. forced selling
and falling angels and vice versa bonds not traded
are not necessary illiquid. We use Barclays’ Liquidity
Cost Scores (LCS) as a measure for liquidity in credit
markets. Liquidity cost typically falls as issue size
and volume increase, option adjusted spread (OAS),
duration times spread (DTS) and age decreases.
Notably, we find that omitting liquidity risk can underestimate credit portfolio VaR (99%) by up to 22%.
We also discuss appropriate techniques for recovering
liquidity premiums and extracting fair prices, depending on the degree of market liquidity. We broaden our
analysis to present a general framework that encompasses both market and liquidity risk, and measure the
impact of both at the security and portfolio levels. In
short, we highlight the importance of explicitly taking
liquidity into account in portfolio construction, and
propose a methodology to do so.
4
Liquidity risk in Fixed Income Markets
U
ntil recently, the market paradigm encapsulated in the financial theory did
not explicitly account for liquidity risk, and rather assumed that investors
could buy and sell significant position sizes without affecting market prices.
As a consequence, securities are priced, and their risk measured, at the mid price
irrespective of any friction stemming from liquidity. However, in nervous markets,
liquidity recedes and the bid price becomes the only relevant value. Such circumstances call into question the notion of mark to market, as it no longer reflects a
“fair” price.
Financial history is replete with liquidity crises. During the 1998 LTCM crisis, hedge
fund positions had grown so large that it was impossible to liquidate them without
significant price impact. More recently, in the 2007-2008 financial crisis, widespread
liquidity shortage forced banks to reduce exposures by liquidating assets. Many
asset managers became forced sellers to meet outflows and margin calls. Prices
dropped as liquidity melted.
The over the counter (OTC) nature of fixed income markets makes tracking liquidity
risk much more challenging than in equity markets which are more centralized and
use a single price. For example, whereas the 2007-2008 crisis forced European
Fixed income markets to shut down temporarily, the “Trace” system (unavailable
in Europe) enabled US market operators to track which bonds had traded and at
what price. This enabled US markets to remain open despite minimal volume. This
led to Barclays transposing their Liquidity Cost Score (LCS) methodology in Europe
mid 2010 following its existence in the US since October 2009.
Following the financial crisis, policymakers and regulators have sought to impose
tougher rules and standards on banks to prevent future systemic crises. Basel III
introduced new liquidity standards, namely new liquidity ratios and higher-quality
liquid assets. Notwithstanding, the very issue such standards seek to address can
be taken by some market participants as a damper to liquidity and thus dissuasive
to active management. Indeed, in Europe and the US alike, higher restrictions on
RWAs1 impose higher costs for market making activities. The subsequently diminished risk “envelope” for such activities compromises available market liquidity for
secondary trading. The direct consequence, illustrated below, is that US broker/
dealer corporate bond inventories have substantially diminished since 2007.
One could be frightened up when discovering the evolution of dealer’s inventory
of corporate bonds in the US: it has impressively diminished since 2007!
Although the corporate bond market has doubled in size since 2001, the available
inventories remain largely unchanged!
Outstanding US Corporate Bonds (LHS)
10,000
250
US Dealer’s Inventory of Corporate Bonds (RHS)
9,000
8,000
200
7,000
6,000
150
5,000
100
4,000
3,000
50
2,000
1,000
0
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
0
Source: DB, SIMFA, Federal bank of New York
1 RWA: Risk Weighted Assets.
5
Liquidity risk in Fixed Income Markets
Amihud et al. (1991) posited that a change in investor perception of liquidity risk
would push them to price securities at lower levels which could result in a crash akin
to October 1987. The root of liquidity risk lies in information asymmetries and the
existence of incomplete markets which lead to adverse selection and moral hazard
situations. It follows that in order to reduce systematic liquidity risk, transparency
and information flow should be enhanced. Nonetheless, this could be a very costly
strategy that requires a long time before being fully operational.
1
DEFINING AND MEASURING LIQUIDITY RISK
I. LIQUIDITY: AN HETEROGENEOUS CONCEPT
When talking about liquidity, some caution is required as the nature of risk is not
the same when analyzed on a global macro economical level, on a corporate level
or on a specific asset level.
From a broad economical perspective, liquidity risk is the ability of economic agents
to exchange their wealth into goods2. Liquidity is thus a flow notion (in opposition
to the notion of stock). Illiquidity arises in case of inability of exchanging. When
money lacks in the overall economy, transactions and thus activity slow down.
Banks finance the economy through lending operations. By doing so, they boost
the economical activity by supporting investment and consumption. However,
banks have to meet some legal obligations in terms of reserve requirements which
create a global deficit in liquidity. Banks rely on central bank to offset this liquidity
deficit and to get refinanced.
Central bank can improve (or sterilize) global liquidity of the economy by acting on
the monetary base through open markets operations in a way to keep the interbank
lending rates close to its target rate. The latter is a tool to monitor the overall liquidity
with respect to certain objectives e.g. inflation and/or growth.
From a theoretical perspective, asymmetrical information hinders exchanges leading to illiquidity and market incompleteness. Central bank plays an important role
in managing a liquidity crisis. “It can act as an immediate but temporary buffer to
liquidity shocks, thereby allowing time for supervision and regulation to confront
the causes of liquidity risk.”3
From a corporate perspective, liquidity denotes the solvability of the firm e.g. the net
liquidity of assets and liabilities. When assets’ cash flows are no longer sufficient
to cover liabilities, the firm is facing a credit event that may lead to bankruptcy.
Default risk varies from one country to another according to the economical cycle.
It depends also on the sector and other factors.
From a market perspective, investors are concerned with asset liquidity issues
generally defined as the ease of trading the asset4. In the following sections we
will focus our attention on this specific risk.
II. ASSET LIQUIDITY RISK
Liquidity is an elusive notion, not only because it applies to different levels of the
economy with complex linkages but also because it is a multi dimension concept
difficult to capture in a single measure and thus to model. Even on a single asset
level, liquidity appears as a heterogeneous concept.
2 Williamson (2008) cited in Nikolaou (2009) p.10.
3 Nikolaou (2009).
4 Amihud and Mendelson (2006).
6
Liquidity risk in Fixed Income Markets
The term liquidity risk has a negative connotation as it occasions costs and losses5. The
cost of liquidity when trading an asset is typically captured by the bid-ask spread. This
spread, at least from the market maker perspective, can be broken into two components: the effective spread which compensates market maker for insuring the liquidity
of the market and corresponds to the technology and inventory costs incurred by the
market maker, the information spread that compensate market makers for potential
loses they may incur when taking an uninformed bet. Since they cannot distinguish
informed from uninformed bets, they might well be “the opposite side” of an informed
order in their role of insuring market liquidity.
Amihud and Mendelson (2006) split liquidity costs into three components:
➜➜Direct trading costs: deterministic transaction costs encompassing brokerage
commissions, transaction taxes and exchange fees.
➜➜Price impact costs correspond to the difference between the executed price
and the mid one. It is limited to (half) the bid-ask spread for small orders but
can exceed this spread for higher positions. When trading a small position,
a single counterparty is sufficient to execute the order at the best price. As
the size of the position increases, many counterparties are required to absorb
the order, each with different beliefs about the fair value of the asset, which
leads to a lower price.
➜➜Search and delay costs incurred when traders delay the execution and search
for a better execution price than the one “displayed” by the bid-ask spread.
By doing so, traders undertake the risk of seeing the market move by the time
they decide to execute their order. This tradeoff between price impact costs
and seeing the market move is particularly relevant for block orders.
By denoting a liquid market as one in which every agent can buy and sell at any time
a large quantity rapidly at low cost, Harris (1990) distinguishes four interrelated dimensions for liquidity:
➜➜Width, that measures the cost incurred by a round trip transaction e.g. by
instantaneously buying and selling a position. The costs incurred will thus
correspond to the price impact costs and direct trading costs.
➜➜Depth, which is the number of shares that can be traded at a given price without
incurring additional costs above the bid-ask spread. According to Bangia et al.
(1999), up to the quote spread, liquidity costs are exogenous as the market
is able of absorbing the position. The quote applies to all market participants
irrespective to their characteristics. For higher position, liquidity costs are
assumed endogenous6 as they are supposed to be specific to the individual
trade position. Chart 1 shows bid-ask spread as a function of the quote depth.
Chart 1 : Effect of position size on liquidation value
Above a cut-off size, illiquidity becomes endogenous and its burden higher
Source: Bangia et al. (1999)
Point of endogenous
illiquity
Security Price
Ask
Bid
Quote Depth
Position size
5 Negative basis strategy, e.g. when a CDS is lower than the underlying bond’s spread; is a typical counterexample where liquidity offers very attractive risk reward opportunity for investors.
6 The distinction between exogenous and endogenous liquidity is challenged by Stange and Kaserer (2009) who argue that whole
price impact curve is exogenous because it is determined by the market.
7
Liquidity risk in Fixed Income Markets
➜➜Immediacy,
which captures how quickly positions can be traded and
corresponds to time between placing the order and its settlement.
➜➜Resiliency that indicates the ability of the market to absorb random shocks
e.g. uninformative orders.
Stange and Kaserer (2009) argue that liquidity is a continuous characteristic and
distinguish 4 degrees of liquidity (reproduced in Chart 2) according to the liquidity
costs they occur:
➜➜Costless trading when any position can be traded without any cost.
➜➜Continuous trading when most of the orders are executed at a certain cost.
➜➜Interrupted trading when some orders are executed from time to time.
➜➜No trading when the market is completely illiquid, prices are not available
and should be recovered by suitable techniques.
Those degrees of liquidity depend on the asset type, the size of the position
and the liquidation horizon. Exchanging cash is a costless trading as it does not
require any value adjustment. Exotic securities are traded interruptedly while some
structured credit products like CDO and ABS were typical illiquid assets during
the 2008 financial crisis. Illiquidity increases with the size of the position as
explained before. It occurs over some short term but vanishes over a longer
horizon. Typically a security held to maturity has no liquidity cost.
This differentiation will be useful later on for selecting an appropriate method to
incorporate liquidity adjustment and determine the fair value prices according to
the degree of liquidity of the market.
Chart 2: Degrees of market liquidity
The cost of liquidity increases with illiquidity in a non linear way.
4 different degrees of liquidity can be distinguished
Source: Stange and Kaserer (2009)
Relative
liquidity costs
illiquidity
liquidity
Costless
trading
Continuous
trading
Interrupted
trading
Degree of
illiquidity
No
trading
Almgren and Chriss (2000) stressed the importance of distinguishing temporary
price impact from permanent one when determining the optimal execution of
portfolio transactions in a dynamical liquidity framework. Temporary price impact
is due to transitory imbalances in supply and demand caused by one’s trading and
leading to an actual price lower than the equilibrium/mid one. It vanishes rapidly
according to market’s resiliency. Permanent price impact entails a change in the
equilibrium/mid price caused by one’s informed trade at least until the end of the
liquidation horizon. The trade contains “real” information that affects the equilibrium price.
III. M
EASURING LIQUIDITY RISK IN FIXED INCOME MARKETS
As mentioned in Chacko (2005), existing studies have focused on US equities
due to data limitation and the sparse nature of bond market. Extending equity
liquidity measures to bond market is not henceforward as they depend on
8
Liquidity risk in Fixed Income Markets
bond’s intrinsic characteristics. Unlike stocks, bonds redeem. The liquidity
of a 10-year bond is not the same as a 3-month one even for the same issuer.
A traded-volume-based liquidity measure can be quite misleading as a traded
bond is not necessary a liquid one e.g. forced selling and falling angels and
vice versa bonds not traded are not necessary illiquid.
At some point, one has to come back to reality: what liquidity can be expected
from typical issuance sizes of €M 500 (corporate benchmark size) vs. dozens of
billions issued for a typical government bond benchmark?
What liquidity can be expected when such issuances are 3 to 5 times oversubscribed
and kept until maturity in buy-and-hold portfolios (Life insurers have become the
dominant player in corporate bonds in the last 7 years): only 20-30% of free float
is available. It cannot be improved without an active Repo market on such assets.
Dastidar and Phelps (2009) introduced the liquidity cost score (LCS) to measure
bond level liquidity. LCS are computed by Barclays Capital© on a monthly basis
over a wide range of fixed income securities (IG, HY, Covered, MBS) and regions
(US, Euro).
Price the round-trip
Price cost, as a percent of the bond’s price,
A bond’s LCS, represents
.
of immediately executingPrice
a standard institutional transaction. So according to
this definition, a lower LCS value denotes better liquidity. More formally, LCS is
computed as follows:
LCS =
{
(Bid - Ask)Spread x OASD
if bond is spread - quoted
Ask Price - Bid Price
Bid Price
if bond is price - quoted.
“
A corporate
bond is only liquid
during its life time
when it is issued in
primary markets!”
(trader’s joke)
For non-quoted bonds, LCS is estimated given bonds characteristics. Liquidity
cost typically falls as issue size increases, volume increases, option adjusted
spread (OAS) decreases, duration times spread (DTS) decreases, or age
decreases.
see boxed text
Table 1: Cross sectional correlation of bond’s LCS
with the corresponding bond’s attributes
Illiquid securities have lower prices and higher DTS
Source: Natixis Asset Management
Yield
Issue
Price Maturity
to Mat
Size
July 12 - June 13 -0.25
-0.27
0.32
0.59
L-OAS
Mod Dur
DTS
to Mat
0.50
0.32
0.62
These findings suggest that liquidity risk is priced by the credit market, at
least partially.
On Chart 3, we can check that LCS varies among and within sectors7 and seniority.
Subordinated securities have a higher LCS. These findings are consistent with
the high correlation of LCS with DTS.
7 The sector partition is the one used by the credit investment team in NAM’s Fixed Income department.
9
Given the Barclays Euro
Aggregate Corp Index
(BEAC) constituents observed
from July 2012 till June 2013,
we noticed that liquidity on
a security by security level
improves with the issue size
and the price and that higher
LCS were concomitant to
higher maturity issues, higher
yield to maturity (YTM),
Libor option adjusted spread
(LOAS), duration and DTS as
reproduced in the Table 1.
Liquidity risk in Fixed Income Markets
Chart 3: LCS boxplot for each sector
On average, subordinated securities have a higher LCS than senior ones.
This holds also for Financials securities relative to Non Financials ones
Source: Natixis Asset Management
LCS by BEAC sector July 2012
Other Financials
InsuranceSub
InsuranceSen
BankingSub
BankingSen
Utilities
Telecommunications
Energy
Consumer Non Cyclical
MNCT
Transportation
Consumer Cyclical
Capital Goods
Basic Industry
0
1
2
3
4
6
5
7
8
9
The tops and bottoms of
each blue box are the 25th and
75th percentiles of the sectors,
respectively. The red line in the
middle of each box is the sector
median LCS. Black dotted whiskers are drawn from the ends
of the interquartile ranges to
the furthest observations within
the whisker length. Outliers are
displayed with a red + sign.
10
LCS
LCS by BEAC sector June 2013
Other Financials
InsuranceSub
InsuranceSen
BankingSub
BankingSen
Utilities
Telecommunications
Energy
Consumer Non Cyclical
MNCT
Transportation
Consumer Cyclical
Capital Goods
Basic Industry
0
1
2
3
4
5
LCS
6
see boxed text
One can notice that, on average, the higher the Beta of the sector (i.e. Subordinated Insurance), the larger the LCS. It reached a paroxystic level during 2008 end
and the beginning of 2009 (crisis times) when perpetual bonds reached distressed
prices ca 20-30% of par: at that time it was not unfrequent to suffer from 4%-5%
bid-ask spread!
2
THE LIQUIDITY FACTOR
I. WHAT FACTORS DRIVE LIQUIDITY?
Theory and empirical studies suggest that liquidity risk is priced by the market
e.g. higher illiquidity implies lower prices and higher expected returns. However,
unlike other risk factors liquidity risk cannot be diversified. One cannot offset
a liquidity exposure by going short an illiquid security. More generally there
is no liquidity based derivatives to hedge this particular risk.
However, liquidity can be managed. Portfolio managers for instance may choose
their liquidation policy with respect to the illiquidity cost profile of underlying securities keeping illiquid assets for a longer time and trading more frequently liquid
securities. It is not a free lunch, and liquidity management may cause some
performance drawdown.
10
Liquidity risk in Fixed Income Markets
Every active portfolio manager has realized that alpha generation was excessively
impacted nor to say shrunk to a certain degree by large bid ask spreads: being
active is required in order to beat any benchmarks but it gets impossible to reach
this aim if one cannot implement its active strategies.
see boxed text
Table 2: Summary table for monitoring liquidity costs in PACT
Credit portfolio managers would have been better off not rebalancing
their October 2013 model portfolio if spreads were to tighten less then 1.41%
(Source: Natixis Asset Management)
Turnover
Benchmark Portfolio Breakeven relative
Turnover
cost
LCS*
LCS
spread movement
Date
October 13
42bp
50bp
-1.41%
7.2%
2.8bp
*The benchmark is the Barclays Euro Aggregate Corporate.
The trade off between performance, risk and liquidity is a key element in managing
public funds subject to inflows and outflows of cash. Besides the usefulness of
keeping a liquid basket to face outflows without burdening a prohibitive liquidity
cost, it is convenient to monitor overall liquidity of the market as it seems to be
related to other market factors like implied volatility, Libor-overnight indexed swap
(LOIS) spread, etc. However the correlation is far from being perfect (61% with
V2X and 79% with the difference between LOIS over the period June 2010 - June
2013). Moreover a hedge using V2X may be difficult to implement for Fixed Income
managers.
We can check on Chart 4 that correlation between LCS and V2X and LOIS reaches
its maximum when lagging the latter up to 4-7 weeks, suggesting that V2X and
LOIS impact on liquidity attains its maximum with some delay. However advanced
causality tests, based on Independent Component Analysis for example, do not
corroborate the leading predictive capacity of V2X and LOIS on LCS. Moreover, we
can check on Chart 5 and on Chart 6 the difficulty of estimating a robust relationship
with or without lags.
Chart 4: Correlation between LCS and lagged V2X and LOIS
Correlation reaches its max with a 4-7 weeks delay
Source: Natixis Asset Management
Correlation level
Correlation between LCS and lagged market variables
1.00
0.95
0.90
0.85
0.80
0.75
0.70
0.65
0.60
0
2
4
V2X Index
Lag (in weeks)
LOIS
6
8
LCS
11
10
Liquidity risk is closely
monitored by the Credit investment team at Natixis Asset
Management’s Fixed Income
department. Funds are kept
inside a range of leeway with
respect to a model portfolio.
Portfolio managers express
their views regarding future
relative spread movements for
both top down (directional and
sector) and bottom up (security
selection) strategies. Mixing
all of these inputs in a single
framework is the key for generating a robust and repeatable
alpha while addressing liquidity costs incurred by active
trading. A dedicated proprietary tool, Portfolio Allocation
and Construction Tool (PACT),
has been developed to address
this issue.
When building the next period
model portfolio using PACT,
liquidity risk ranks high among
other risk factors. The expected
excess returns stemming from
portfolio managers’ views are
put in balance with the cost
of implementing these views.
Breakeven relative spreads
are derived for each aggregate
bucket. If the expected gain of
implementing a view is offset
by the liquidity cost generated by turnover, the strategy
is challenged. In general, the
credit model portfolio construction is conducted under the objective of minimising liquidity
costs and thus turnover on an
issue by issue level.
For instance, in order to rebalance the credit model portfolio
as of October 2013 a minimum
turnover of 7.2% is required.
This turnover would have cost
less than 3bp. Portfolio managers would have been better
off not adjusting their exposure
if spreads were to tighten less
than 1.4% over the investment
horizon as we can check on
Table 2.
Liquidity risk in Fixed Income Markets
Chart 5: LCS dynamics vs V2X and LOIS
No clear robust correlation whether lagged or instantaneous can be depicted
Source: Natixis Asset Management
1.00
80
0.80
60
0.60
40
0.40
LOIS
21-jun-13
8-mar-13
3-may-13
18-jan-13
12-oct-12
30-nov-12
6-jul-12
24-aug-12
18-may-12
3-feb-12
23-mar-12
16-dec-11
9-sep-11
V2X Index
28-oct-11
3-jun-11
22-jul-11
8-apr-11
18-feb-11
29-oct-10
17-dec-10
0.00
10-sep-10
0.20
0
4-jun-10
20
LCS
1.20
100
23-jul-10
V2X, LOIS
LCS and market distress indicators (V2X and LOIS)
120
LCS
Chart 6: Scatterplot of V2X x LCS and LOIS x LCS
The relation is not obvious for higher values of V2X and LOIS
Source: Natixis Asset Management
LCS market distress indicators (V2X and LOIS)
1.2
1.0
LCS
0.8
0.6
0.4
0.2
0.0
0
20
40
80
60
100
120
V2X, LOIS
V2X x LCS
LOIS x LCS
II. THE LIQUIDITY PREMIUM
Amihud (2002) shows that expected market illiquidity positively affects ex ante
stock excess return, suggesting that expected stock excess return partly
represents an illiquidity premium. This complements the cross-sectional positive
return–illiquidity relationship. This increasing relation between illiquidity and return
still holds after controlling for risk and some other characteristics.
Amihud and Mendelson (1986, 1988) show that the relation between asset returns
and illiquidity is upward sloping and concave. Returns increase less for highly
illiquid assets. This pattern holds for stocks and bonds as advocated in Amihud
and Mendelson (1991). For corporate bonds, Chen et al. (2007) found that illiquidity
costs increase as rating deteriorates and that change in bonds illiquidity costs
lead to changes in bonds yield.
Jong and Driessen (2012) show that corporate bond returns have significant exposures to liquidity fluctuations. Liquidity risk premium would be around 0.6% for
investment grade bonds and 1.5% for speculative bonds. Further, this liquidity
risk is a priced factor for the expected returns. Since liquidity is a risk factor, investors ask for higher return to get compensated for bearing this risk.
Looking at LCS dynamics for the Barclays Euro Aggregate Corp Index (BEAC)
sectors, we also found a positive dependency with YTM especially when YTM are
tightening e.g. since 2012 as highlighted in Chart 7.
12
Liquidity risk in Fixed Income Markets
Chart 7: BEAC YTM and LCS dynamics
LCS follows similar trend to YTM as least since 2012
Source: Natixis Asset Management
1.2
5
1.0
4
0.8
3
0.6
2
0.4
1
0.2
0
0.0
YTM
LCS
LCS
6
4-jun-10
23-jul-10
10-sep-10
29-oct-10
17-dec-10
4-feb-11
25-mar-11
13-may-11
1-jul-11
19-aug-11
7-oct-11
25-nov-11
13-jan-12
2-mar-12
20-apr-12
8-jun-12
27-jul-12
14-sep-12
2-nov-12
21-dec-12
8-feb-13
29-mar-13
17-may-13
5-jun-13
YTM
YTM vs LCS dynamics for BEAC
One could be amazed at
seeing the graph below: the
LCS lagged to react to the
Sovereign crisis in 2011, when,
as usual, liquidity totally dried
up in August - September 2011
when lots of market operators
began to lighten exposure
to their financial allocations
(correlation between banks
and sovereigns was very high
without a Bail in directive): this
is another proof statement of
the funnel syndroma.
see boxed text
Chart 8: Scatterplot YTM x LCS for BEAC
The concave relationship: YTM increases less than illiquidity
Source: Natixis Asset Management
June 2010 - June 2013
6
5
The upward sloping
relation is concave as depicted
in Chart 8. Yields increase less
for illiquid assets. This concave
shape particularly holds for
Subordinated issues bucket.
4
3
2
1
0
0
0.2
0.4
0.6
0.8
1.0
LCS
1.2
see boxed text
III. THE ROLE OF LIQUIDITY IN CRISIS
The role of market liquidity in crisis is mainly twofold: the liquidity of an asset
grows with bubbles until a critical state where it may suddenly fall in illiquidity and precipitate a crash.
First, speculative bubbles often arise in a frame of a huge turnover of transactions.
Cochrane (2003) observes indeed that prices higher than the fundamental value of
an asset are associated with high trading volumes and low supply: therefore, the
market seems very liquid for buyers, who do not face much difficulty to buy the
asset at an increasing price. Baker and Stein (2004) also explain that phenomenon
by a model in which a big liquidity is generated by the big number of irrational
traders who overestimate the value of the asset. In short, bubbles and liquidity
grow concomitantly.
When bubbles have grown a lot, they may burst and the role of liquidity may be
determinant. We underlined that when the bubble arises, the volume is high but
the supply is low. This means that the situation is quite unstable and can reverse
dramatically. The mechanism of crisis involving the market liquidity is also linked
with the funding liquidity8 of the investors. That is the downward liquidity spiral,
8 For Perdersen (2008), the funding liquidity risk is the risk that the investor is unable to fund his position on an asset from its
own capital and is forced to unwind: for example, leveraged investments of hedge funds are possible if banks lend them money,
but if banks raise their margins the funding costs increase a lot to such investors and they must deleverage their positions.
13
Liquidity risk in Fixed Income Markets
as detailed by Pedersen (2008) or Brunnermeier (2009): when the market liquidity
begins to be reduced, then prices become lower and the risk management, fearing
the upcoming crisis, tightens9. Therefore, the funding is more complicated and
this implies less transactions. The mechanism loops here, as the diminution of the
number of transactions reduces again the market liquidity and worsens the crisis.
Chart 9: Liquidity spiral
The downward liquidity spiral, in that schema, is initiated by funding problems, but,
as it is a circle, it can also be initiated by market liquidity problems (reduced positions)
Source: Pedersen (2008)
initial losses e.g.
due to credit
reduced positions
prices move away from
fundementals
funding problems
Higher margins
(margin spiral)
Losses on existing
positions
Tighter risk
management
(risk management spiral)
Beside these descriptive analyses, an increasing number of papers propose methods
to predict the time at which the bubble will burst, like Kaizoji et al. (2002). Most of
them describe the behaviour of traders and rely on the assumption that some
traders know the fundamental value of the traded asset. This allows these articles
to link the price to the supply and demand (which is a consequence of the behavioural mechanism invoked) through the hypothetical knowledge of that fundamental price. Tóth et al. (2011) allow to get rid of such an assumption by taking into
account the market liquidity and more precisely the resilience. They describe indeed
the price impact of any volume traded. Such a model coupled with this type of
bubble model would allow a more realistic description of bubbles and a more accurate prediction of crashes.
In the description of the role of the liquidity in a bubble, we mainly dealt with the
liquidity of an asset. However, such a liquidity risk can be spread to the whole market.
For instance, the contagion to other asset classes can be led by the funding risk:
when margins of the banks raise or even when a bank goes to bankruptcy because
of one asset type, investors have difficulties to fund other kinds of investments as
explains Pedersen (2008) about the wide bursting of the housing bubble.
9 For instance, risk indicators, such as the VaR, which are calibrated on recent historical price evolutions, are more pessimistic at
the first signs of bear market and imply a more conservative attitude.
14
Liquidity risk in Fixed Income Markets
IMPACT OF LIQUIDITY ON PRICING,
RISK MEASURES AND PORTFOLIO
CONSTRUCTION
3
I. PRICING ILLIQUID SECURITIES: MTMARKET VS MTMODEL
In the previously defined interrupted and illiquid markets10, the price of the securities is affected by frictions. Moreover, when the illiquidity is particularly strong,
the market price of a security may no longer be available. In both cases, getting a
fair price, that is a price that reflects all risks except liquidity, is then a useful and
challenging purpose.
On the one hand, when a market price is available but is affected by illiquidity,
some methods allow estimating the fair price. Among them, Guégan and Merhy
(2010), propose to filter optimally, with a Kalman filter, the observed price in order
to infer the fundamental price and the related liquidity premium, which is the difference between the observed price and the fundamental one. Their definition of
liquidity is similar to that of Chacko and Stafford (2004), who define liquidity as
the gap between the fundamental value of a security and the price at which the
security is actually transacted ; high liquidity means this gap is small and vice versa.
In Guégan and Merhy (2010) method, we must define a fairly general dynamic for
the fundamental price. In the aforementioned paper, the fundamental price at time
t is defined as a noisy weighted average of the fundamental price at time t – 1 and
the long run price (mainly the par value for fixed income securities). With such a
fundamental price model, many situations are taken into account, such as a very
erratic random fair price, or a random walk, or a mean-reverting fair price. Chart 9
and Chart 10 illustrate the functioning of their method.
Chart 10: Fair prices and liquidity premium
Market price of a Mortgage Backed Security tranche in the aftermath of august 2007
(on a long period between 2006 and 2009 and on two sub-periods), compared
with the fundamental price filtered by a Kalman filter for a mean reverting model.
The difference between both prices stands for the liquidity premium
Source: Guégan and Merhy (2010)
STORM 2006 1C - Mean Reverting Fair Price 09 - Mar - 2006 till 14 - Aug - 2009
105
100
95
90
85
80
75
70
65
60
Jan06 Apr06
(a)
Forecasted Price St l t-1
Filtered faire Price Zt l t
Market Price St
Jul06
Oct06
Jan07
Apr07
Jul07
Oct07
STORM 2006 1C - Mean Reverting Fair Price
09 - Mar - 2006 till 26 - Jul - 2007
100.2
Jan08
Jul08
Oct08
Jan09
Apr09
Jul09
Oct09
STORM 2006 1C - Mean Reverting Fair Price
09 - Mar - 2006 till 14 - Aug - 2009
100
100.15
95
100.1
100.05
90
100
85
99.95
80
99.9
75
99.85
Forecasted Price St l t-1
Filtered faire Price Zt l t
Market Price St
99.8
99.75
99.7
Apr08
Jan06
Apr06
(b)
Jul06
Oct06
70
Forecasted Price St l t-1
Filtered faire Price Zt l t
Market Price St
65
Jan07
Apr07
Jul07
Oct07
60
Jul07
(c)
Jan10
10 Refer to Chart 2.
15
Liquidity risk in Fixed Income Markets
Chart 11: Liquidity premium dynamics
Liquidity premium switches regime in July 2007 and continues to increase
till July 2009 where it begins to ease
Source: Guégan and Merhy (2010)
Liquidity Premium 09 - Mar - 2006 till 26 - Jul - 2007
14
12
10
8
6
4
2
0
Jan06
Apr06
Jul06
Oct06
Jan07
Apr07
Jul07
Oct07
Jan08
Liquidity Premium 09 - Mar - 2006 till 26 - Jul - 2007
Apr08
Jul08
Oct08
Jan09
Apr09
Jul09
Oct09
Liquidity Premium 26 - jul - 2007 till 14 - Aug- 2009
14
0.9
0.8
12
0.7
10
0.6
0.5
8
0.4
6
0.3
4
0.2
2
0.1
0
Jan06
Apr06
Jul06
Oct06
Jan07
Apr07
Jul07
0
Oct07Jul07
Jul10
On the other hand, when illiquidity is such that no market price is available, the
only possible thing to do is to refer to liquid markets and find a shrewd proxy. Of
course, in that case, as no market price is observable, trying to define a liquidity
premium is meaningless. We highlight here two methods which both rely on the
same idea that it is necessary to refer to an observable liquid universe of securities.
In the following development, we are particularly interested in bonds.
In the first method, we build buckets of bonds reputed to be liquid. Each bucket
stands for a particular currency, a sector, a seniority and a credit rating. Then, using
a classical bootstrap and a rate curve model such as Svensson model, we build a
generic rate curve for such a liquid bucket. Then, when we want to price a particular
illiquid bond, we discount its cashflows with the curve of the bucket with the same
currency, sector, seniority and credit rating.
Chart 12: Calibrating a model yield curve
Svensson model (in blue) calculated on a bucket of liquid defensive senior bonds
of rating A-, as of 5 December 2013. The bootstrapped curve is in pink.
The illiquid bonds are then priced with that blue curve
Source: Natixis Asset Management
Generic Yield Curve: EUR Credit NonFin NonFinDef Senior >=A- <=A4.5%
4.0%
3.5%
3.0%
2.5%
2.0%
1.5%
1.0%
0.5%
Empirical rate
2/
20
33
03
/0
5/
20
30
10
/0
8/
20
27
14
/0
20
24
11
/
17
/
2/
20
22
21
/0
5/
20
19
28
/0
8/
20
16
31
/0
05
/1
2/
20
13
0.0%
Rate
16
Liquidity risk in Fixed Income Markets
In the second method, we also build buckets of liquid bonds, but, instead of modeling a generic rate curve, we determine the risk aversion on such a bucket, using the
theory of indifference price, following Arrow (1965) and Pratt (1964). Then, similarly
to the previous method, we can discount the cashflows of any particular illiquid
bond taking into account the risk aversion calibrated on the corresponding bucket.
Chart 13: Risk aversion function
Probability density function of the risk aversion calibrated on a bucket of liquid
BBB bonds as of September 2009
Source: Natixis Asset Management
0
0.01
0.02
0.03
0.04
II. CONTROLLING LIQUIDITY RISK: L-VAR VS VAR
From a risk perspective, ignoring liquidity risk tends to underestimate the overall
risk of a position. Bangia et al. (1999) found that ignoring the liquidity effect
leads to underestimating of market risk in emerging markets by more than
25%. More recently, Stange and Kaserer (2008) proposed a weighted spread to
improve on previous liquidity measures by taking into account the price impact
costs into their VaR framework. They found that liquidity factor increases the
10 days VaR@99% by 25% for liquid DAX stocks.
Ernst et al. (2008) distinguish 3 types of models including market liquidity:
➜➜Models based on bid-ask spread data: liquidity costs are captured from
observable bid-ask spreads and subtracted from prices. Bangia et al. (1999)
and Ernst et al. (2008) developed a liquidity augmented VaR model. This
class of models offers the advantage of simplicity. However, only exogenous liquidity costs are taken into account as the price impact is explicitly
not modeled.
➜➜Models based on volume or transaction data: this class of models attempt
to correct Bangia et al. (1999) drawbacks by estimating the price impact
function. For instance, Berkowitz (2000) estimated it from past trades in
regression wise approach.
➜➜Models based on limit order book or weighted spread data as in FrançoisHeude and Van Wynendaele (2001) or Stange and Kaserer (2008).
Bangia et al. (1999) included liquidity into a parametric VaR framework. Based on
observed bid-ask spreads time series they derived their liquidity augmented VaR
model.
Denote by rt+1 = 1nPmid,t+1 -1nPmid,t
the logarithmic return of the mid price
at time over one period of time. Assuming centered Gaussian returns, Bangia et
al. (1999) exploit information embedded in the distribution of normalized spreads
to incorporate the effect of liquidity risk into a parametric VaR framework. Prices
dynamic is given by the following equation:
17
,
Liquidity risk in Fixed Income Markets
Pmid,t+1= Pmid,t e rt+1
-
Next Period Price Projection
1 P S
mid,t t+1
2
.
,
Cost of liquidity
where St denotes the normalized price spread at time t, namely:
St =
Pask,t - Pbid,t
Pmid,t
.
Given these assumptions, Bangia et al. (1999) derived a close form expression for
the liquidity adjusted VaR11. Though their approach relies on restrictive assumptions, its main advantage relies in the low data set required to include liquidity into
a risk framework.
III. PORTFOLIO CONSTRUCTION AND STRESS TESTING:
THE LIQUIDITY EFFICIENCY SCORE
The ex ante future distribution of P&L of the portfolio is the relevant objective
function that a portfolio manager looks at and insure that it has the adequate properties especially from a risk perspective. Tracking Error Volatility (TEV) or Value at
Risk (VaR) are synthetic risk statistics commonly used to measure the risk of yet
to come P&L distribution.
Even if the investor is absolutely certain about the outperformance of a specific
strategy in the near future, would he go long this strategy if transaction costs are
prohibitive? The answer requires a general framework that explicitly takes into
account liquidity risk for portfolio construction.
To account for liquidity risk, conventional VaRs are computed over longer horizon in
an ad hoc fashion. The Basel Committee on Banking Supervision (2009) extended
from 10 days to 3 months the liquidity time horizon in the calculation of VaR@99%.
The Basel Committee on Banking Supervision (2009) acknowledged that the liquidity
of traded assets varies substantially over time and that banks’ exposures to market
risk and credit risk vary with liquidity conditions in the market.
Bangia et al. (1999) addressed the problem of computing liquidity VaR for a portfolio. They recommend to compute the average portfolio spread and to apply their
abovementioned technique in order to avoid computing correlation among bid-ask
spreads between securities12.
Meucci (2012) presented a framework for modeling jointly market risk and liquidity
risk. Liquidity is not just a deterministic bid-ask but modeled as a risk factor per se
whose impact on the P&L of the portfolio is state dependent. Thus when volatility
is high and market is down the negative impact of liquidity is more important. The
framework takes also into account endogenous liquidity risk stemming from forced
selling in adverse market scenarios. The impact of liquidity risk on the portfolio P&L
will depend also on the liquidation scheme or the turnover, in a take profit case or
a stop loss one.
11 Reader may refer to appendix for a full presentation of Bangia et al. (1999) approach.
12 More recently Brigo and Nordio (2010) accounted for liquidity by introducing randomness into the holding period. The operational time over which assets should be liquidated may differ from the one retained for computing risk measures for instance
VaR. More generally, a portfolio manager who rebalances his portfolio on regular basis e.g. monthly may not be able to fully
adjust his portfolio to his new set of views if liquidity conditions are degraded and a longer horizon is required. Their stochastic holding period (SHP) shifts the P&L distribution downward and increases VaR.
18
Liquidity risk in Fixed Income Markets
The choice of a liquidity model in Fixed Income markets will ultimately depend on
available data e.g. LCS in our case. Though LCS does not account directly for price
impact for large trades, Dastidar and Phelps (2009) argued that it is highly correlated
with price impact. It is found to be persistent on average: bonds with low LCS are
likely to remain liquid according to the LCS measure for a while.
Our approach differs from that of Bangia et al. (1999) in 3 ways as it departures from
the normality assumption, it models the liquidity for each security and aggregate
positions holdings into the portfolio and it takes into account dependency structure
between traditional risk factors and liquidity ones. Moreover, our non parametric
approach allows for stress testing and scenario analysis.
For each security, we define the achieved return in h steps forward, as a function
of the carry, the market return and the liquidity cost. Carry is proportional to the
mid YTM and the market return is proxied by the product of the modified duration
by the sum of h variations of the mid YTM. Liquidity at the liquidation horizon is
x
assumed as in Bangia et al. (1999) equal to half of LCS13 prevailing at the end of
the period e.g. t+h.
x
L Rett→t+h=YTMmid,t xCoveraget→t+h - ModDurmid,t x ∆YTMt→t+h Projected Return over h Periods
1
2
(LCSt+∆LCSt→t+h )
Projected Costs of Liquidity over h Periods
At the beginning of the period e.g. at time t, the carry and the coverage are known.
We need to project YTM and LCS to the end of the period. We do that by jointly
modeling the variations of YTM and those of LCS. For the sake of simplicity we
consider a portfolio of equally weighted generic securities corresponding to the
14 credit sectors14 presented in section I-C. The joint distribution of YTM and LCS
weekly15 changes is calibrated over the period June 2010 till June 2013.
see boxed text
Chart 14: The LVaR@99% over different horizons
The red sticks correspond to the difference between the LVaR and the traditional VaR (in blue)
Source: Natixis Asset Management
Liquidity augmented VaR@99% at various horizons for an equally weighted portfolio
0
LVaR add-on
VaR
-0.5
-1
V@R-99%
-1.5
-2
-2.5
-3
-3.5
-4
-4.5
0
5
10
15
20
25
30
Projected Time Horizon (weeks)
The framework allows for stress testing liquidity risk. It allows us to examine the
impact on VaR of higher correlation between YTM and LCS, of larger LCS volatility
or both.
13 In Bangia et al (1999) bid-ask spread is normalized to the mid price, LCS is normalized to the bid price and hence is more
conservative.
14 The sector partition is the one used by the credit investment team in NAM’s Fixed Income department.
15 LCS are computed by Barclays according to a monthly frequency. Weekly changes are recovered by interpolation and bootstrapping techniques.
19
Omitting liquidity, underestimates VaR@99% by
22% over the short run. The
underestimation decreases
with the projection horizon as
market risk would take over
liquidity as depicted in Chart
14. At a 6 month horizon, the
ratio of LVaR@99% to traditional VaR@99% would converge
around 10% suggesting that
usual market risk factors will
take over liquidity risk factor
over longer horizons.
Liquidity risk in Fixed Income Markets
In Table 3 we reproduce figures we obtain when increasing16 the correlation
between LCS and YTM everything else being equal.
Table 3: VaR, LVaR and stressed LVaR@99% over 1 week horizon
The stressed 1 week LVaR is higher than the LVaR
(Source: Natixis Asset Management)
VaR@99%
LVaR@99%
Stressed LVaR@99%
-1.26
-1.54
-1.80
Portfolios can be ordered according to their liquidity profile. For instance, portfolios
with lower LCS are preferred over less liquid ones. Meucci (2012) proposed the
liquidity efficiency score as a criterion for assessing portfolio’s liquidity risk. Since
the liquidity adjustment always hits the P&L downward, he defined the liquidity
efficiency score as the percentage of deterioration of the left tail e.g. as the ratio
of traditional expected shortfall17 to the liquidity augmented one. This ratio is larger
than 0 and lesser than 1. The closer to 1, the lower the risk of liquidity. The fourweek efficiency score of our sample portfolio is equal to 91%.
CONCLUSION
Portfolio managers need to take into account the effect of liquidity on pricing, the
cost of transactions etc in the decisions they make. When modelling the liquidity
premium, we obtain different results in terms of VaR or expected returns. This implies that very often the concrete decisions portfolio managers make are different
from theoretical optimal decisions, precisely because of the lack of liquidity. One
of the difficulties is that the lack of liquidity often increases when financial risk or
risk aversion increase. This is not a diversifiable risk or a risk that it is possible to
hedge. On the other hand, the absence of liquidity can also offer a surplus of return
for long-term investors who do not need liquidity from day to day.
16 The stressed correlation matrix is a linear combination of the original one and a panic matrix with cells 1 for correlation
between LCS and YTM.
17 Expected shortfall (ES99%) is defined as the average loss exceeding VaR99%.
20
Liquidity risk in Fixed Income Markets
4
APPENDIX
Bangia et al. (1999) included liquidity into a parametric VaR framework. Based on
observed bid-ask spreads time series they derived their liquidity augmented VaR
model.
Denote by rt+1 = 1nPmid,t+1 -1nPmid,t the logarithmic return of the mid price at
time t over one period of time e.g. from t till t+1. Assuming centered Gaussian
returns, Bangia et al. (1999) exploit information embedded in the distribution of
normalized spreads to incorporate the effect of liquidity risk into a, parametric VaR
framework. Price dynamics are given by the following equation:
Pmid,t+1= Pmid,t e rt+1
-
Next Period Price Projection
1 P S
mid,t t+1
2
,
Cost of liquidity
.
where St denotes the normalized price spread at time t, namely:
St =
Pask,t - Pbid,t
Pmid,t
.
Under perfect correlation between liquidity and return they derived the following
formula for the liquidity adjusted VaR:
LiquidityAdjustedVaR99%,t+1= Pmid,t (1-e-2.33.θ.σ)+
1
Pmid,t (μs+K.σs ),
2
where  denotes the volatility of returns and  is a scaling factor. =1 for Gaussian
distribution and >1 to account for fat tailed returns. ms and s are the mean and
the standard deviation of the bid-ask spreads and k the 99% empirical percentile.
They found that it ranges between 2 and 4.5 as compared to 2.33 for the 99%
percentile of the Gaussian distribution.
The main advantage of this approach relies in the low data set required to include
liquidity into a risk framework. The historical spread series are sufficient. The
drawdowns are the additive nature of liquidity risk irrespective to correlation issues
especially in the tail dependence. It also fails to take into account the price impact
function which leads to underestimation of higher positions.
Ernst et al. (2008) departure from the Bangia et al. (1999) Gaussian assumption for
prices and use a Cornish-Fisher approximation to develop their liquidity adjusted
total risk VaR. Although their specification yields a more precise risk forecast, it
fails to capture the price impact as the liquidation occurs on the bid-ask spread
cost and correlation among risk factors is assumed perfect. The advantage is still
the same with the additive add on scheme.
21
Liquidity risk in Fixed Income Markets
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Liquidity risk in Fixed Income Markets
ADDITIONAL NOTES
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Natixis Asset Management
Limited Liability Company
Share Capital: 50 434 604,76 e
RCS Paris 329 450 738
Regulated by AMF: GP 90-009
21 quai d’Austerlitz 75634 Paris Cedex 13 - France
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In order to face the new challenges in financial markets, Natixis
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Natixis Asset Management - French Société Anonyme (joint stock company) with a share capital of € 50,434,604.76 - RCS Paris 329 450 378 - Authorised by the AMF under no. GP 90-009
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