Incorporating Liquidity Risk in VaR Models

Incorporating Liquidity Risk in VaR Models

First Version: September 2000This Version: June 2002

LE SAOUT ERWAN♣

Abstract

Conventional Value at Risk models lack a treatment of liquidity risk. Neglectingliquidity risk leads to an underestimation of overall risk and misapplication ofcapital for the safety of financial institutions. Standard Value at Risk model assumesthat any quantity of securities can be traded without influencing market prices. Inreality, most markets are less than perfectly liquid. Recent financial turbulences, asthe collapse of LCTM, prove that liquidity is a significant risk for market players.

The main aim of this article is to demonstrate the importance of the liquidity riskcomponent in financial markets. First, we make a survey of literature explaininghow the liquidity risk can be incorporated into one single measure of market risk.Then, we apply the Liquidity Adjusted Value at Risk model provided by Bangia,Diebold, Schuermann et Stroughair (1999) on the French stock market: our resultsindicate that the exogenous liquidity risk defined by Bangia, Diebold, Schuermannet Stroughair (1999) can represent more than an half of market risk for illiquidstocks. We extend this model to show that endogenous liquidity risk, which refers toliquidity fluctuations driven by individual action such as the size of the investors’position, is also a very important component of overall risk.

Key-words : Liquidity Risk, Value at Risk, Depth, Bid-Ask Spread, WeightAverage Spread.

♣ Paris 1 University - CREFIB & CREREG. Correspondance :[email protected] document is available through internet: http://www.market-microstructure.orgI want to thank Professors Patrick Navatte, Patrice Fontaine, Jean-Pierre Gourlaouen, Jacques Hamon, MichelLevasseur, and Charles-André Vailhen. I also received many helpful comments from participants in presentations atthe 2000 IAE Meeting (Biarritz), the 2001 AFFI Meeting (Namur) and IRG Workshop. All remaining errors aremine.

Incorporating Liquidity Risk in Value at Risk Models

1

Introduction

The Russian financial crisis, which took place in July 1998 and the distribution of the

effects that followed it on all the world financial places, was at the origin of numerous

debates. Many wondered about the components of this systematic crisis. If the

underestimate of credit risks is at the origin of the Russian monetary crisis, one of the

factors prevailing in certainly due to the correlation of the risks. According to the IMF,

the factor, which started this process of interdependance of the risks, is exchange market

illiquidity. In times of crisis, liquidity tends to dry up suddenly; we can observe a

decline of the liquidity’s offer and the increase of assets ’correlation, what has the

consequence of making ineffective the diversification.

This liquidity risk is with difficulty predictable in spite of numerous models including

the value at risk models because it’s very difficult to measure liquidity.

This paper is organised as follows: in a first part, we examine the literature dealing with

the consideration of the liquidity risk in the evaluation of market risk. In a second part,

we adapt the VaR model adjusted by the liquidity proposed by Bangia, Diebold,

Shuermann and Stroughair (1999) on the French stocks market.

1. Liquidity Risk Management

Liquidity becomes a major stake for stock exchange authorities as shown by the

numerous current reorganisation projects. Liquidity is the ability to transact quickly at

low cost a large size position. However, no agreement exits on the proper measurement

of liquidity. Terms such as “large” and “quickly” tend to be subjective. Hence,

following BIS Report (1999), we may define asset liquidity according to at least one of

three dimensions: depth, tightness and resiliency. Tightness, measured by bid-ask

spread, indicates how far transaction price diverges from the mid-price. Depth defines

the maximum number of shares that can be traded without affecting prevailing quoted

market prices. Finally1, resiliency denotes the speed with which price fluctuations

resulting from trades are dissipated or how quickly markets clear order imbalances.

1 Another uses concept is immediacy, which refers to the time between the order placement and its execution. Thisdimension incorporates element of tightness, depth and resiliency.


2

1.1 Liquidity risk: a definition

Liquidity risk is the risk of loss arising from the cost of liquidating a position. Liquidity

risk increases when markets are not liquid. Typically, market illiquidity manifests itself

in the form of important costs of trade, a weak number of trades and wide bid-ask

spread2. These factors mean that investors who wish to settle a position are going to

have to pay significant costs to do it: they have to bear important cost of trade, relatively

long period of wait because of the absence of counterpart or still sell quickly to an

unfavourable price. It is obvious that most of the market know liquidity troubles. There

are only few markets that can offer an adequate level of liquidity to investors. However,

liquidity of these markets cannot be guaranteed all the trading day or during crisis where

liquidity dries out. So, liquidity risk is an important factor, at least potentially, which is

often ignored by investors.

According to Dowd (1998), it’s possible to distinguish two types of liquidity risk. The

first one is the “normal” liquidity risk which increase according to the exchanges on

markets considered as little liquid. The second type is more insidious. It’s about the

liquidity risk arising during stock market crises where the market loses its current

liquidity level: investors who settles its positions registers so a loss more important than

during normal circumstances.

Consequently, we should modify our conception of the value at risk and take into

account of liquidity. The relation between liquidity costs and the value at risk is

indicated by the figure 1 below. It indicates situation of liquid and illiquid positions. We

can settle our liquid position quickly and to obtain the market price without significant

liquidity cost. On the other hand, we can settle our illiquid position only by paying

conversely proportional costs of liquidation to the period when it was necessary to close

its position: the more the period the investor will have agreed to liquidate his positions

is long, the less the costs will be high. However, it is necessary to be careful in the fact

which during the wait, the price can vary in a very unfavourable way. So, ceteris

paribus, an illiquid asset a most important value at risk if we take into account liquidity

cost.

2 As defined by Dowd (1998).


3

Now we have demonstrated clearly the necessity of taking into account the liquidity

costs in the estimation of value at risk models, we have to know how to do it.

[INSERT FIGURE 1]

1.2 Modelling liquidity risk: a survey

The last few years have witnessed increasing interest in the measurement and

management of liquidity risk. Liquidity risk has been investigated in several ways.

Chordia, Roll and Subrahmanyam (2001), Hasbrouck and Seppi (2001) and Huberman

and Halka (2001) investigate commonalities in liquidity. Authors consider the existence

of a systematic and a specific liquidity risk. Amihud and Mendelson (1986), Brennan

and Subrahmanyam (1996), and Jacoby, Fowler and Gottesman (2000) develop a

CAPM model and examine the relationship between expected return and the liquidity

level. Finally, the last but not the least way, different answers have been proposed to

consider liquidity costs in Value at Risk models.

Prior research investigated the optimal execution strategy for liquidating portfolios.

Jarrow and Subramanian (1997) consider optimal liquidation of an investment portfolio

over a fixed horizon. They derive the optimal execution strategy by determining the

sales schedule that will maximise the expected total sales values. In the same way,

Bertsimas and Lo (1998) derive dynamic optimal trading strategies that minimize the

expected cost of execution over an exogenous time horizon. Then, they obtain an

optimal sequence of trades as a function of market conditions. Almgren and Chriss

(1998) consider the problem of portfolio liquidation with the aim of minimizing a

combination of volatility risk and transaction costs arising from permanent and

temporary market impact. From a simple linear cost model, they build an efficient

frontier in the space of time-dependant probability. They consider the risk-reward trade-

off both from the point of view of classic mean-variance optimization, and the

standpoint of Value at Risk. This analysis leads to general insights into optimal

portfolio trading, and to several applications including a definition of liquidity-adjusted

Value at Risk. Hisata and Yamai (2000) propose a Liquidity Adjusted Value at Risk

model based on the framework presented by Almgren and Chriss (1998). Unlike

Almgren and Chriss (1998), Hisata and Yamai (2000) turn the sales period into an

endogenous variable. This model incorporates the mechanism of the market impact


4

caused by the investor’s own dealings through adjusting Value at Risk according to the

level of market liquidity and the scale of the investor’s position.

According to Lawrence and Robinson (1995), the best way to capture liquidity issues

within the VaR would be to match the VaR time horizon with the time investor believes

it could take to exit the portfolio. For example, if investors believe liquidity is a problem

for the given portfolio, he could estimate the time needed to exit the positions and use

this as his VaR time horizon. As this time horizon is increased (due to the illiquidity of

the portfolio), his reported VaR would also increase to reflect higher risk. Lawrence and

Robinson (1995) appear among the first ones to wonder about the fact that conventional

VaR models often exclude asset liquidity risk. From an example of estimation of Value

at Risk, the authors find that the largest amount of money a position could lose, with a

given degree of confidence, over a one day time horizon is underestimated. Indeed,

according to Lawrence and Robinson (1995), the liquidation of a portfolio during a

trading day generate an additional liquidity cost. The more the time horizon is weak, the

more we underestimate liquidity risk and this, especially the investor’s position is

important. The act to settle a position, in itself, will have a consequence, unfavourable

for the investor, on the price range. So, on the illiquid markets, consequent volume of

assets should bear a high liquidity risk that current Value at Risk models don’t take into

account. From this report, to Lawrence and Robinson (1995) provide a generic model of

Value at Risk by deriving the optimal execution strategy incorporating the market risk

using a mean-standard deviation approach. In the same way, Haberle and Persson

(2000) provide a modelling with easier calculation. The authors propose a method based

on the notion of orderly liquidation3. This method assumes that single investor can

liquidate a fraction of the daily trading volume without significant impact on the market

price.

Le Saout (2000) distinguishes interday and intraday Value at Risk. The author proposes

a new intraday measure of liquidity risk, which is constructed from the return during a

market event defined by a volume movement. His results indicate that we can

distinguish an exogenous liquidity risk, which refers to liquidity fluctuation driven by

factors beyond individual investors’ control, from an endogenous liquidity risk, which

3 The liquidation doesn’t impact the market price.


5

refers to liquidity fluctuations driven by individual actions such as the investors’

position.

Bangia, Diebold, Schuermann and Stroughair (1999) approach the liquidity risk from

another point of view. The summer of 1998 was exceptionally turbulent times for

financial markets. During this period, The authors noticed that losses have been

amplified by the increase of liquidity risk. Bangia, Diebold, Schuermann and Stroughair

(1999) develop a Value at Risk model, which take into account bid-ask spreads. Thus

model allows an increase of the Value at Risk when investors decide to liquidate in the

same time their portfolio. According to Bangia, Diebold, Schuermann and Stroughair

(1999) and Shamroukh (2000), Value at Risk models mustn’t ignore the volatility of the

bid-ask spread even if it is likely to be of at least one order of magnitude than the

volatility of prices. Value at Risk models, which adjust the holding period upward in

line with the inherent liquidity of the position, imply that the liquidation takes place

throughout the holding. Shamroukh (2000) argues that scaling the holding period to

account for orderly liquidation can only be justified if we allow the portfolio to be

liquidated throughout the holding period.

Before any modelling, Bangia, Diebold, Schuermann and Stroughair (1999) study the

nature of the concept that is liquidity. They make the distinction between an

endogenous liquidity and an exogenous liquidity. Exogenous liquidity is the result of

market characteristics; it affects all market players without attribute the responsibility of

the degradation of the liquidity level to one investor rather than another one. This

degradation is the result of a collective action. In contrast, endogenous liquidity is

specific to one’s position in the market. Concretely, the exhibition at the liquidity risk of

an investor is determined by its position: the more the size is important, and the more

the endogenous liquidity risk increases. Figure 2 describes this relationship.

[INSERT FIGURE 2]

Market risk is characterised by the uncertainty of the prices or returns due to market

movements. In a market without friction, risk management deals exclusively with the

distribution of returns. A more rigorous management implies so the consideration of the

“frictions” such as the assets liquidity especially when important positions have to be

liquidated quickly. In this case, investors won’t get the mid-price. Bangia, Diebold,


6

Schuermann and Stroughair (1999) argue that the deviation of this liquidation price

from the mid-price is important components to model in order to capture the overall

risk.

So, the authors estimate the Value at Risk in two stages: uncertainty that increases from

asset returns and uncertainty due to liquidity risk. Figure 3 summarizes their market

taxonomy.

[INSERT FIGURE 3]

2. An empirical analyse on the French Stock Market

In this section, we apply the Liquidity adjusted Value at Risk model provided by

Bangia, Diebold, Schuermann and Stroughair (1999) on the French stock market. First,

we describe briefly the organisation of the French stock market and the database that

were used. Then, we proceed to the estimation of the BDSS’ model. In a third time, we

comment our results. Finally; we extend the modelling of the bid-ask spread to weight

average spread which allows us to show the importance of the endogenous liquidity

component in the Liquidity adjusted Value at Risk model.

2.1. Data

The Paris Bourse is a computerized limit order market in which trading occurs

continuously from 9 a.m. to 5.35 p.m. The trading day takes place in five stages: The

pre-opening phase, the market opening and the continuous market

From 7.45 a.m. to 9.00 a.m., the market is in its pre-opening phase and orders are

accumulated in the centralized order book without any transactions taking place. Each

time an order enters the system, a theoretical equilibrium price is computed.

At 9.00 a.m., the market opens with a batch auction. Depending on the limit orders

received, the central computer automatically calculates the opening price at which the

largest number of bids and asks can be matched.

From 9.00 a.m. to 5.25 p.m., trading takes place on a continuous basis, and the arrival of

a new order immediately triggers one (or several) transaction(s) if a matching order (or

orders) exists on the centralized book. The execution price is the price limit placed on


7

the matching order in the book. Assuming identical price limits, orders are executed as

they arrive: first entered, first matched.

From 5.25 p.m. to 5.30 p.m., the market is in its pre-closing phase and orders are

accumulated in the order book without any transactions taking place.

At 5.30 p.m., the market closes with a batch auction. Depending on the limit orders

received, the central computer automatically calculates the closing price at which the

largest number of bids and asks can be matched.

The database, BDM, we use contains millions data points on transactions: time stamped

stock prices volume, bid/ask spread…We have extracted from the database BDM bid-

ask spread of 41 shares – on the period from October 1st, 1997 to January 3rd, 2000 (that

it represents a little more than 500 consecutive trading days). We opt for a daily data to

estimate Value at Risk in a one day time horizon. This means that we estimate the

maximum loss for a one-day period.

2.2. Modelling Liquidity Adjusted Value at Risk

Following Bangia, Diebold, Schuermann and Stroughair (1999), we estimate the LA-

VaR model by proceeding to a decomposition in two types of risk: the price risk which

correspond to the potential of loss connected to the depreciation of the asset, and the

liquidity risk which corresponds to the liquidity cost supported by the investor who

want to sell his position. This model is described below.

)1(_ 33,2 tePVaRP tθσ−−= (1)

( )[ ]taSPECL σα ~2

1+= (2)

( )[ ]tt aSPePLoss t σαθσ ~2

1)1( 33,2* ++−= − (3)

Where: *Loss is the Liquidity Adjusted Value at Risk

ECL is the Exogenous Cost of Liquidation,

tP is the mid-price at date t ,


8

θ designs a correction factor for current VaR to take account of leptokurtic

return distribution,

tσ is the volatility of the asset at date t ,

αP is the price Value at Risk at date t ,

S is the average bid-ask spread,

a corresponds to a scaling factor that corrects the bid-ask spread distribution.

tσ~ represents the volatility of bid-ask spread.

Estimation of the current VaR

The first stage consists in modelling the conventional Value at Risk from the mid-price.

Generally, the assumption of normality is violated, that’s why Bangia, Diebold,

Schuermann and Stroughair (1999) propose to correct the fat-tails of returns

distributions by incorporating a correction factor θ . This factor is such that 1=θ if the

security return distribution is normal, and 1>θ is an increasing function of the tail

causing the deviation from normality. To estimate this correction factor, the author

consider a relationship between the kurtosis K and the factor θ :

⋅+=

31

KLnφθ (4)

Where φ is a constant value depends on the tail probability. Following the authors, we

estimated the value of this constant by regressing the right hand side of equation (1)

with historical Value at Risk for the stocks, which composed our sample. So, we have

got a value of 0.039. Then, we are able to estimate the correction factor for our sample.

Figure 4 displays the return distribution and the cumulative frequency of one stock, i.e.

Saint-Gobain chosen for its liquidity and capitalization. We can notice that return

distribution isn’t very far from normality. However, in our sample, as shown in table 1,

some securities such as Clarins and Montupet have a return distribution that doesn’t

look like a Gaussian distribution. Their Kurtosis are over 10. But, generally, return

distributions of the stocks are near the normality distribution.

[INSERT FIGURE 4]

[INSERT TABLE 1]


9

Estimation of the Exogenous Cost of Liquidity

The second unknown value that we have to estimate is the scaling factor a that we find

in the equation of Exogenous Cost of Liquidity (Eq. 2). Following Bangia, Diebold,

Schuermann and Stroughair (1999), we have considered two sub-samples: liquid stocks

compose the first one whereas illiquid stocks compose the second sub-sample. Then, we

estimate the scaling factor by regressing the right hand side of the Exogenous Cost of

Liquidity equation with the historical Value at Risk of the bid-ask spread for each sub-

sample. Figure 5 displays the bid-ask spread distribution and the cumulative frequency

of Saint-Gobain. Skewness and kurtosis are relatively high.

[INSERT FIGURE 5]

Hence, we get scaling factors equal to 6.724 for high liquid stock and 7.809 for little

liquidity stock. Effectively, the greater is the deviation from normality, the larger is the

scaling factor.

Estimation of the Liquidity Adjusted Value at Risk

Tables 2 reports the decomposition of market risks (uncertainty in asset returns and due

to liquidity risk) for Saint-Gobain stock.

[INSERT TABLE 2]

Our results can be interpreted as follows: the worst return, given a 99% confidence

level, is estimated like this:

%84,533,2*022,0*129,1%99GobainSaint −=−=−r

So, the Price Value at Risk, at 1% is the following:

06,182193 %84,5%99GobainSaint == −

− eP euros, so 94,10_ =VaRP euros.

The integration of liquidity risk reduces the price expectation:

( )[ ] 43.0%041.0724.6%208.006.1822

1=⋅+=ECL

Hence, 63,18143.006,182*int =−=−GobainSaP euros.

Hence, the overall value at risk, given a 99 percent confidence level for a one day time

horizon is:


10

37,1163,181193*GobainSaint =−=−Loss euros (5,89%).

The liquidity risk component represent only 3.8% of market risk for Saint-Gobain,

nevertheless table 3 indicates that the percentage can be higher for other stocks. Hence,

concerning the illiquid stock Fromagerie Bel, the liquidity risk represents more than a

half of the market risk.

[INSERT TABLE 3]

To complete this analysis, we have studied the relation between capitalisation and the

Exogenous Cost of Liquidation. Table 4 reports results of the following regression:

CapibaECL ⋅+= (5)

Our results indicate that Exogenous Cost of Liquidation is negatively correlated with

the capitalisation. Lower is the capitalisation of the society, more investors are exposed

to liquidity risk. This result isn’t a surprise but can be considered like an another proof

that small caps funds are aware of liquidity risk.

[INSERT TABLE 4]

2.3. Discussion

The major interest of the model proposed by Bangia, Diebold, Schuermann and

Stroughair (1999) isn’t the estimation of Value at Risk because it is based on historical

simulation, but the decomposition of the market risk in two types: return risk and

liquidity risk.

Nevertheless, the application of this model reveals some limits. The first concerns the

assumption that in adverse market environments extreme event in returns and extreme

events in spreads happen concurrently. The examination of the data showed us that the

widest spreads don’t appear during period of extreme price movements. So, the

Liquidity Adjusted Value at Risk overestimates the overall risk market. The second

limit concern trading volume and position size. The spread indicates the tightness but

not the resiliency. The model deals only exogenous liquidity that implies that overall

risk is underestimated.


11

That’s why, to conclude, we have built the same model with the Weight Average

Spread4 for Saint-Gobain stock instead of the bid-ask spread.

Table 4 reports our results. The component liquidity risk has strongly increased: 20.94%

against 3.81%. In the case of Saint-Gobain, the Weight Average Spread is calculated

from 5000 stocks. This means that the endogenous liquidity risk supported by an

investor who hold 5000 stocks is 17.13%.

[INSERT TABLE 5]

Everybody knows the principle of diversification: volatilities of asset risks don’t add

directly. Volatility of portfolio of risks is less than the sum of the individual of the

individual risks’volatilities. One of the consequences of our analyse is that

diversification reduce also endogenous liquidity risk. Financial institutions, which want

to reduce its value at risk, have to diversify its portfolio and so reduce the size of its

positions.

Conclusion

Liquidity risk is an aspect of market risk that has been largely neglected by standard

value at risk model. This negligence is certainly due to the fact that no single measure

captures the various aspect of liquidity in financial markets. In this paper, we apply the

Liquidity Adjusted Value at Risk model provides by Bangia, Diebold, Shuermann and

Stroughair (1999) on the French stock market and extend it incorporating the modelling

of the Weight Average Spread. We demonstrated that liquidity risk, endogenous and

exogenous, can be a very important component of risk market. This means that

nowadays, the risk is underestimated. These results are not without consequences on the

safety of financial institutions.

4 See Appendix for a definition of Weight Average Spread at Paris Bourse.


12

Figures and Tables

FIGURE 1

Value at Risk and holding period

VaR ( Illiquid Position )

VaR ( Liquid Position )

Holding Period

VaR

Source : Dowd (1998)

FIGURE 2

Effect of position size on liquidation value

Position size

Price Point of endogenousilliquidity

Bid

Ask

Quote depth

Source : Bangia, Diebold, Schuermann and Stroughair (1999).


13

FIGURE 3

Taxonomy of market risk

Uncertainty inMarket Value

Uncertainty inAsset Returns

Uncertainty due to Liquidity Risk

ExogenousIlliquidity

EndogenousIlliquidity

Source : Bangia, Diebold, Schuermann and Stroughair (1999).


14

FIGURE 4

Return Distribution and Cumulative Frequency

0%

2%

4%

6%

8%

10%

12%

-7% -6% -4% -3% -1% 1% 2% 4% 5% 7%

normal Saint-Gobain

0%

1%

2%

3%

4%

5%

6%

-7,0% -6,5% -6,0% -5,5% -5,0% -4,5% -4,0% -3,5%

normal Saint-Gobain

FIGURE 5

Bid-Ask spread Distribution and Cumulative Frequency

0%

5%

10%

15%

20%

25%

30%

35%

0 , 1 0 % 0 , 1 5 % 0 , 2 0 % 0 , 2 5 % 0 , 3 0 % 0 , 3 5 %

normal Saint-Gobain

0%

10%

20%

30%

40%

50%

60%

0 , 3 5 % 0 , 3 3 % 0 , 3 0 % 0 , 2 8 % 0 , 2 5 % 0 , 2 3 % 0 , 2 0 %

normal Saint-Gobain


15

TABLE 1

Estimation of Price Value at Risk

Name Price(euros)

Kurtosis Volatility Correctionfactor

VaR 99%(euros)

ACCOR 48 6,088 0,024 1,241 44,77

AIR LIQUIDE 169 3,427 0,021 1,045 160,51

ALCATEL 227,7 4,728 0,033 1,155 208,43

ATOS 172,8 7,804 0,029 1,325 157,83

BIC 44,01 4,036 0,025 1,101 41,30

BNP 92,5 4,928 0,028 1,169 85,60

BONGRAIN 331,4 5,864 0,020 1,228 313,33

BOUYGUES 636 7,667 0,026 1,319 587,15

CANAL + 135 7,571 0,026 1,315 124,80

CAP GEMINI 255,9 6,764 0,032 1,276 232,82

CARREFOUR 183,5 4,848 0,022 1,163 173,09

CASINO 115,1 6,428 0,019 1,259 108,85

CLARINS 118 11,628 0,023 1,461 109,10

CLUB MED 114,1 10,769 0,022 1,435 105,98

DYNACTION 28 5,334 0,021 1,196 26,44

ELF 149,1 7,176 0,026 1,297 137,89

FROM. BEL 700 5,305 0,016 1,194 669,05

INFOGRAMES. 35 4,685 0,025 1,152 32,76

LABINAL 110 4,106 0,026 1,107 102,80

LAFARGE 115,5 3,282 0,024 1,031 109,11

L'OREAL 789 4,448 0,024 1,134 740,04

LVMH 444 3,896 0,024 1,089 418,01

MICHELIN 39,79 4,688 0,025 1,152 37,16

MONTUPET 33 13,168 0,029 1,503 29,77

MOULINEX 10,1 5,090 0,026 1,180 9,40

PARIBAS 110,4 8,890 0,024 1,369 102,32

PENAUILLE 400 5,730 0,022 1,220 376,04

REXEL 88,45 4,399 0,024 1,130 83,11

SAINT-GOBAIN 193 4,388 0,022 1,129 182,06

SEB 74,8 6,177 0,026 1,246 69,27

SEITA 42,2 4,965 0,023 1,171 39,66

SKIS ROSS. 16 6,682 0,020 1,272 15,07

SODEXHO 168 3,777 0,023 1,078 158,58

SPIR COM. 77,5 10,968 0,024 1,441 71,46

SUEZ 159,9 4,446 0,018 1,134 152,56

TECHNIP 104,6 4,377 0,026 1,128 97,78

TOTAL 132 4,624 0,023 1,147 124,05

USINOR 18,92 6,094 0,026 1,241 17,55

VALEO 76,2 3,453 0,025 1,048 71,69

VIVENDI 87,2 3,793 0,018 1,080 83,32

ZODIAC 208 5,726 0,023 1,220 194,94


16

TABLE 2

Liquidity Risk Summarised of Saint-Gobain stock

Saint-Gobain

Price on January, 3rd (euros) 193

Return volatility 0,022

Correction factor 1,129

Price component 10.94

Average bid-ask spread 0,208%

Bid-ask spread volatility 0,041%

Liquidity component 0.43

Liquidity Adjusted Value at Risk (euros) 11.37

% Liquidity Component 3.81%


17

TABLE 3

Estimation of Liquidity Adjusted Value at RiskSummary

Name Price(euros)

VaR 99%

Average spread

LAVaR99%

%Liquidity

ACCOR 48 44,77 0,259% 44,59 5,05%

AIR LIQUIDE 169 160,51 0,215% 160,14 4,16%

ALCATEL 227,7 208,43 0,172% 208,02 2,11%

ATOS 172,8 157,83 0,502% 156,49 8,19%

BIC 44,01 41,30 0,417% 40,97 10,82%

BNP 92,5 85,60 0,189% 85,32 3,93%

BONGRAIN 331,4 313,33 0,811% 306,17 28,39%

BOUYGUES 636 587,15 0,369% 582,88 8,04%

CANAL + 135 124,80 0,315% 124,22 5,38%

CAP GEMINI 255,9 232,82 0,307% 231,36 5,94%

CARREFOUR 183,5 173,09 0,151% 172,80 2,71%

CASINO 115,1 108,85 0,264% 108,42 6,47%

CLARINS 118 109,10 0,514% 108,06 10,51%

CLUB MED 114,1 105,98 0,633% 104,51 15,28%

DYNACTION 28 26,44 0,886% 25,97 23,08%

ELF 149,1 137,89 0,231% 137,34 4,65%

FROM. BEL 700 669,05 1,376% 635,26 52,20%

INFOGRAMES 35 32,76 0,640% 32,32 16,54%

LABINAL 110 102,80 0,739% 101,17 18,51%

LAFARGE 115,5 109,11 0,241% 108,74 5,60%

L'OREAL 789 740,04 0,197% 738,34 3,35%

LVMH 444 418,01 0,197% 416,98 3,80%

MICHELIN 39,79 37,16 0,230% 37,03 4,75%

MONTUPET 33 29,77 0,971% 28,77 23,60%

MOULINEX 10,1 9,40 0,661% 9,26 17,21%

PARIBAS 110,4 102,32 0,243% 101,82 5,76%

PENAUILLE 400 376,04 1,434% 363,16 34,96%

REXEL 88,45 83,11 0,777% 81,76 20,26%

SEB 74,8 69,27 0,693% 68,37 13,91%

SEITA 42,2 39,66 0,646% 39,06 19,20%

SKIS ROSS. 16 15,07 0,904% 14,76 25,44%

SODEXHO 168 158,58 0,436% 157,08 13,71%

SPIR COM. 77,5 71,46 0,862% 69,69 22,70%

SUEZ 159,9 152,56 0,159% 152,18 4,81%

TECHNIP 104,6 97,78 0,653% 96,57 15,12%

TOTAL 132 124,05 0,187% 123,76 3,61%

USINOR 18,92 17,55 0,320% 17,47 5,52%

VALEO 76,2 71,69 0,387% 71,03 12,84%

VIVENDI 87,2 83,32 0,162% 83,10 5,48%

ZODIAC 208 194,94 0,573% 192,51 15,65%


18

TABLE 4

Regression between the Exogenous Cost of Liquidation and the capitalisation

CapibaECL ⋅+=

Coefficients Standard Error t-studentConstant 0,014 0,002 8,826Capitalisation -4,93E-10 1,15E-10 -4,279

R²=0,319 F=18,312

TABLE 5

Liquidity Risk Summarised of Saint-Gobain stockWeight Average Spread

Saint-Gobain

Price on January, 3rd (euros) 193

Return volatility 0.022

Correction factor 1.129

Price component 10.94

Average WAS 1,15%

Bid-ask spread volatility 0,31%

Liquidity component 2.90

Liquidity Adjusted Value at Risk (euros) 13.84

% Liquidity Component 20.94%


19

Appendix: The Weighted Average Spread

In 1994, a new block market was created to best meet domestic and international

investors' demand. Member firms are now allowed to buy and sell large blocks in a

single transaction and with a set price. This new rule is consistent with the recent

changes in French tax law: the FF 4,000 cap on stamp duty for transactions effective

after July 1993, and the complete exemption of non-residents from stamp duty since

January 1994.

The Stock Exchange Council selects eligible stocks. They include all component stocks

of the CAC 40 index and other stocks with market capitalization on a similar scale.

The number of shares in each transaction must exceed what is referred to as "Normal

Market Size", a figure based on average trade volumes in that stock. Total amount per

trade may not be less than FF 500,000.

Finally block trades must take place at a price which falls within the Weighted Average

Spread (WAS) for a standard-size block, as this results from visible buy and sell orders

placed through the CAC central trading system. This spread is calculated by adding up

orders within the system to reach standard block size and computing the average per

share.

TABLE A1

Weighted Average Spread Estimation (example)

CAC Central MarketXYZ 10.49 a.m.TNB 15000 WAS 627 - 631

Buy-orders Sell ordersQuantity Price Price Quantity

32002330227025304760

629628627626625

630631632633634

25601780502063705870

Bid :(3200*629) + (2330*628) + (2270*627) + (2530*626) + (4670*625) = 627

15000Ask :

(2560*630) + (1780*631) + (5020*632) + (5640*633) = 63115000


20

In the example above (Table A1), the weighted average spread for 15,000 shares

representing the standard-size block of XYZ is 627-631.

Thus, member firms can execute orders representing quantities equal to or more than

15,000 shares at a price within the current WAS of 627 to 631. They do this either by a

cross-order or by acting as principal with their clients.

The Weighted Average Spread for each stock eligible for block trades is calculated and

disseminated on-line throughout the trading day.

Block trading reporting and disclosure:

- Block reporting is immediate: all block trades must be immediately reported to the

Paris Bourse by brokerage firm. If two member firms are involved, both must file a

declaration.

- Block disclosure: the disclosure to the market is immediate when a member firm acts

as a broker between two clients for a block trade. Otherwise, timing of disclosure

depends on the transaction's size: trades of blocks less than five times the Normal

Market Size are disclosed within two hours from the time they are reported. Trades of

blocks more than five times the normal market size are disclosed when the market opens

on the following business day.

Using this methodology, we get the figure 9 which shows us evolution of the visible and

the real Weighted Average Spreads (WAS) during the day.


21

References

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Bangia, A., F.X. Diebold, T. Shuermann and J.D. Stroughair, "Modeling Liquidity Risk", Risk 12,january 1999, pp. 68-73.

Bank for International Settlements, “Market Liquidity: Research Findings ans Selected PolicyImplications”, Report, may 1999.

Bertsimas, D. and A.W. Lo, "Optimal control of execution costs", Journal of Financial Markets 1, 1998,pp. 1-50.

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Hisata Y. and Y. Yamai, “Research toward the practical application of liquidity risk evaluation methods”,Discussion Paper, IMES Bank of Japan.

Huberman G. and D. Halka, “Systematic liquidity”, Journal of Financial Research, 2001, forthcoming.

Jacoby G., D.J. Fowler and A.A. Gottesman, “The capital asset pricing model and the liquidity effect: Atheoretical approach”, Journal of Financial Markets, 3, 2000, pp. 69-81.

Jarrow, R. and A. Subramanian, "Mopping up liquidity", Risk 10, december 1997, pp. 170-173.

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Shamroukh, N., “Modelling liquidity risk in VaR models”, Working Paper, Algorithmics UK, 2000.

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Incorporating Liquidity Risk in VaR Models