market liquidity and its risk - an overview

Sebastian Stange and Prof. Christoph KasererChair of Financial Management and Capital MarketsTechnische Universität MünchenArcisstr. 21D-80290 MünchenTel.: +49 89 / 289 - 25485Mail: [email protected] URL: www.ifm.wi.tum.de

Market Liquidity and Its Risk

An Overview

2Sebastian Stange and Christoph Kaserer, Chair of Financial Management and Capital Markets

Market liquidity v090127b.ppt

Presentation aims to convey state of research on market liquidityGoals of this presentation

• Quick introduction to important aspects and developments

• Summary of current state of research

• Starting point for further research

• Practitioners

• Students

• Researchers

• Those interested

for

General financial background required



This presentation presents an overview on market liquidityAgenda

• Introduction

• Market liquidity

– Definition

– Characteristics

– Measurement

– Empirical facts

• Market liquidity risk

– Introduction

– Models

• Summary and open research questions



Liquidity has continuous attention in practicePress clippings

"Credit crisis puts heat on liquidityFinancial market liquidity can take months to build but just seconds to evaporate [...] Credit traders have received a painful reminder of [...] strangled trading liquidity"Financial Times, 30.07.2007

'Panicked Traders Take VW Shares on a Wild Ride - stock soared to as high as 1,005 euros a share ... after last week at 210 euros.... short sellers were forced to act"

NY Times, 28.08.2008

'Some less liquid strategies which also provided genuine portfolio diversification [...] have romped past the S&P 500'Michael Goldman, Global Investor, 04/2007

"Unless you include liquidity in your models, which some small funds don't, then the model may not always work."Euromoney, June 2007

'[Quantitative strategies] rely on their ability to trade with high frequency […] What if the model is built to sell a company at 20, but there is no buyer?'Euromoney, June 2007

Liquidity always a hot topic – especially in crises

• Liquidity always scarce when needed most

Institutional investors engage in illiquid strategies

• Sometimes large, concentrated position to exploit market inefficiencies

• Returns due to liquidity risk compensation?

Trading strategies rely on tradability of assets• Hedging often requires frequent trading

Risk management still needs to account for illiquidity

• Often neglected• Strong recent pressure from regulators

Introduction



Liquidity

Liquidity is approached from various research directions

Market micro-structure

Transaction costliterature

Factor in asset pricing Risk

management

Volume / volatilities literature

Anomalyexplanation

Asset management

= Causes

= Effect

Limits toarbitrage

Supply-demandcurve

Introduction



This presentation focuses on market liquidity only Delimitation of topic area

Monetary liquidityMonetary liquidity

• Liquidity of an economy

Funding liquidityFunding liquidity

• Liquidity of liabilities

• Perspective of a firm (solvency)

• Corporate finance view

Market liquidityMarket liquidity

• Also "asset liquidity"

• Liquidity of assets only

– "Marketability"

– "Ease of trading an asset"

• Perspective of an investor

• Capital market view

Introduction




• Introduction


– Definition

– Characteristics

– Measurement

– Empirical facts


– Introduction

– Models




Liquidity can be defined as the cost of trading an assetLiquidity cost has three components

Market liquidity – Definition

Liquidity

Lt(q)

Direct trading costs

D(q)

Price impact costs

PIt(q)

Delay costs

Dt(q)

=

+

+

• Cost L of trading a quantity q of an asset• Relative to fair value• Fair value often set at mid-price, i.e. mid-point of bid-ask-spread

• Includes exchange fees, commissions, taxes• Deterministic• Small for institutional investors

• Difference between transaction price and mid-price• Depends on order size q and point of time

• Includes search cost, cost due to add. risk during delay

Note: Definition similar to Amihud (2006), XXX noch ergänzen



• Tightness = "cost of turning a position around in a short time"

• Depth = "size of an order flow innovation required to change prices a given amount"

• Resiliency = "speed with which prices recover from a random, uninformative shock"

The cost perspective integrates older, more elusive definitions

Market liquidity – Definition

DefinitionDefinition

• "Ease of trading an asset"• "Marketability"

SourceSource

Longstaff (1995)

CommentComment

• Very general• Cost perspective more

specific

Kyle (1985) • Several dimensions• No unifying perspective

• Immediacy = time between order submission and settlement

Black (1971) • A new dimension• No unifying perspective

• Price• Time

Kempf (1999) • Very general

Backup



Asset type, order size and horizon are major liquidity determinants

Market liquidity – Characteristics

• Liquidity costs decrease with – Trading volume– Value certainty

Type of asset

exog

enou

s

Order size

• Liquidity costs increase with order size• Reasons

• Heterogeneous opinion• Delay probability• Capital restrictions

end

ogen

ous

Liquidation horizon

• Liquidity costs decrease with liquidation horizon• Costs relative to return are small when held over long period• Costs are zero for assets held to maturity

• Hence, liquidity is a characteristic of the trading processend

ogen

ous



Liquidity is a continuous characteristicLiquidity degrees and categories


Costly, continuous trading

Rel

ativ

e liq

uidi

ty c

osts

illiquid

Degree of illiquidity

liquid

Costless trading

Notrading

Costly, interruptedtrading

• All order sizes of the asset can be traded at zero costs

• Cash

• None, no liquidity adjustment necessary

• Order sizes can be traded at a cost

• Price impact cost important

• Limit order book markets of stocks

• Precise liquidity cost adjustment

• Asset are traded from time to time

• Zero trading days occur• Delay cost important

• OTC markets of more exotic bonds

• Liquidity cost and delay adjustment

• No order size of the asset is traded

• Prohibitive Liquidity costs

• Rare art, CDOs?

• Intrinsic value determination because price non-observable

Ca

teg

ory

Ex

.M

ain

is

su

e



Cost can be measured as price impact curveLiquidity costs increase with quantity transacted


mid price

bid price

Quote depth /Size of best limit orders

Price

Market depthQuantity

transacted

ask price

Size of next-bestbid order

buy price function

sell price function

Bid-ask-spread area = absolute liquidity costs



Optimal trading strategies

• Optimal trading strategies can be applied

– Delaying parts of the transaction reduces order size and hence liquidity costs

– But, uncertain future price and liquidity costs, i.e. delay costs, for delayed parts of the position

– Optimal strategy balances liquidity cost saving against increased delay costs

• Several optimization objectives possible

– Maximize expected liquidation proceeds

– Maximize expected liquidation proceeds with penalty for potential shortfall (proceed variance)

• Corresponds to maximizing proceeds VaR

• Immediate liquidation as benchmark strategy

– No optimization strategy is applied

– Proceeds are certain




Measurement of market liquidity is still difficultMultitude of direct measures and proxies available

Market liquidity – Measurement

Direct measures

• Fees• Quoted bid-ask-spread (Amihud, Mendelson, JFinEco 86)• Traded bid-ask-spread• Effective bid-ask-spread (Roll, JoF 84)• Relation between price change and order flow (Brennan, Subrahmanyam,

JFinEco, 96)• Price response to turnover (Amihud, JFinMar 02)• Volume related reversal (Pastor, Stambaugh, JPolEco 03)• Weighted spread by order size (Irvine et. al., working paper 00)

Indirect measures

• Depth• Volume• Number of transactions• Turnover rate (Datar et al, JFinMar 98)(1)• Proportion of zero-trading days (Bekaert et al., WP, 03)• Turnover-adjusted zero trading days (Liu, JFinEco 06)



Example: Weighted spread measures precise size-specific liquidity cost


Weigthed spread is precise measure...Weigthed spread is precise measure...

• Discount vs. achievable price in limit order book

• Equals area between limit order curves

• Generalization of bid-ask-spread to rest of the limit order book

• Precise price impact measure L(q)= WS(q) / 2

...under realistic assumptions...under realistic assumptions

• Direct trading costs are zero– Ok for institutional investors

• Asset position continuously tradable• Ok for developed markets and positions

smaller than market depth

• Immediate liquidation• Ok, if optimal trading strategies

neglectable

• Weighted spread data available• Ok in many electronic limit order book

markets

Source: Stange, Kaserer (2008a, b)



Liquidity cost quickly rise with order sizeExample: Weighted spread for German stocks (I/III)


146

110

5227

15

214

454

331

0

100

200

300

400

500

vol 10 vol 25 vol 50 vol 75 vol 100 vol 150 vol 250 vol 500 vol 750 vol 1000 vol 2000 vol 3000 vol 4000 vol 5000

DAX

MDAX

SDAX

TECDAX

Volume in k €(not to scale)

Average liquidity cost in bp

Note: Sample = daily data for 160 stocks in four major German stock indices over 5.5 years (II/02-1/08)Source: Stange, Kaserer (2008a)



Liquidity cost have strongly declined in 2002-2008Example: Average weighted spread for German stock indices (II/III)


Source: Stange, Kaserer (2008a)



Liquidity cost decline evident for all order sizesExample: Weighted spread for German stocks by selected order size, indexed (II/III)


Source: Stange, Kaserer (2008a)



Further empirical facts

• Liquidity costs can be substantial

– Price impact is concave (Hasbrouck 1991, Stange/Kaserer 2008)

– Over 50% of total trading cost from price impact and delay (Kritzman, Myrgren and Page 2006)

• There is strong variation over time

– Flight-to-liquidity asymmetry: Liquid assets become more liquid and less liquid less liquid in crises (Acharya and Pedersen (2005), Longstaff (2004))

• Liquidity measures determine asset prices

– Market liquidity esp. important for pricing – no full diversification possible(Acharya and Pedersen (2005) for stock market; Goyenko (2005) for integration between stock and bond market)

– Further sources: Amihud and Mendelson (1986); Datar, Y. Naik, and Radcliffe (1998); Amihud (2002); Pastor and Stambaugh (2003); Acharya and Pedersen (2005); Ang, Chen, and Xing (2006), Keene and Peterson (2007) and others

• There is strong liquidity commonality

Market liquidity – Empirical facts Backup




• Introduction


– Definition

– Characteristics

– Measurement

– Empirical facts


– Introduction

– Models




Traditional VaR neglects liquidity effects

Definition classical VaRDefinition classical VaR

• Value-at-Risk (VaR) measures worst loss in α% of the cases over a specific forecast horizon h

– (1-α) is confidence level– Loss is generally the forecasted loss in

market prices

CritiqueCritique

• Assumes that position can be liquidated without significant cost

– Bid-ask-spread neglected– Price impact of position size neglected– Market conditions and liquidation horizon

neglected

• Assumes that position can be liquidated within any given horizon

– No delay costs

• Sometimes ad-hoc adjustments from expert estimates used, but only rough proxy for true liquidity risk

– Flat lengthening of horizon– Artificial increase of volatilities– Flat liquidity cost deduction ("hair cut") by

asset class

Market liquidity risk – Introduction

Future market price distribution at horizon h



Traditional VaR assumes 'mark-to-market'-price by conventionSeveral price definitions can be used

Before transaction pricesBefore transaction prices

Mid-price = mark-to-market price• Middle of bid-ask-spread

Bid- / ask-price• Usually quoted by market maker

– But sometimes best limit order prices if no market maker coverage

• Ex-ante achievable transaction price for buy/sell-transaction

– But for small volume (=bid-ask-depth) only

Achievable price in limit order book• Ex-ante price when transacting larger

orders as market order against limit order book

After transaction pricesAfter transaction prices

Transaction price• Ex-post achieved transaction price• Can be inside bid-ask-spread if market

maker transacts within spread• Usually outside bid-ask-spreads for

larger order sizes

'Mark-to-market' simple, but not most realistic assumption




Market liquidity risk is worst loss due to liquidity cost

• Liquidity component usually neglected in standard risk models

– Usual assumption that liquidity cost can be neglected if horizon is long enough

– Partially accounted for via asset-class-specific "hair cuts"

• Expert estimates of liquidity cost deduction

• However, liquidity costs are substantial and strongly vary between securities

– 25-30 % underestimation of total risk in emerging market currencies (Bangia et al. 1999)

– Bid-ask-spread component over 50 % of total risk for illiquid stocks (Le Saout 2002)

– 30 % liquidity contribution to intraday risk in small price stocks (Lai 2007)

– Up to 25-30 % liquidity impact on price risk at 10-day horizons (Stange/Kaserer 2008a)

• More than doubles at daily horizons

• Large variance between stocks and position sizes




We will survey eight different liquidity risk modelsModel overview

Market liquidity risk – Models

Model categoriesModel categories

• Available data

• Type of liquidity measurement

• Assumptions on the structure of liquidity

ModelsModels

1. Bangia et al. (1999): Add-on model with bid-ask-spread

2. Ernst et al. (2008): Modified add-on model with bid-ask-spread

3. Berkowitz (2000): Transaction regression model

4. Cosandey (2001): Volume based price impact

5. Angelidis, Benos (2006): Structurally implied spread

6. Francois-Heude, Wynendaele (2001): Limit order model

7. Giot, Gramming (2008): T-distributed net return model with weighted spread

8. Stange, Kaserer (2008): Empirical net-return model with weighted spread

Note: Untraceable models excluded from overview.



A simple model deducts worst bid-ask-spreadBangia et al. (1999): Add-on model with bid-ask-spread


Liquidity Measure

Liquidity Risk Measurement

Advantages and Disadvantages

• Data available in many markets• Simple add-on, hence quickly implementable

– Assumes that position can be traded at bid-ask-spread

• However, liquidity costs can quickly rise beyond bid-ask-spread when trading positions larger than bid-ask-depth

• Tends to underestimate risk– Assumes perfect liquidity – price correlation

• Worst spread and worst price occur simultaneously

• Tends to overestimate risk– Logically inconsistent because worst spread

deducted from current, not worst prices• Easily correctable• Tends to overestimate risk

– Historical spread distribution might poorly proxy for future distribution

• Bid-ask-spread

• Worst spread added as cost to worst price

• Empirical distribution ( ) used for worst spread estimation

• Normal distribution used for price risk

1



Non-normality of liquidity can be explicitly taken into accountErnst et al. (2008): Modified add-on model with bid-ask-spread (I/II)


Liquidity Measure Advantages and Disadvantages

• Similar to Bangia et al. (1999), but specifically accounting for non-normality via Cornish-Fisher approximation

• Provides empirically more precise results than Bangia et al. (1999)

• See Ernst et al. (2008)• Can be applied to other liquidity cost

measures as well• See Ernst et al. (2009)

– Skewness and kurtosis need to be additionally estimated

• Bid-ask-spread• Other liquidity measures can be used

analogously

• Worst cost added to worst price

• Cornish-Fisher approximated percentiles, which take skewness ( ) and excess-kurtosis ( ) into account


2



Modified risk model performs better than Bangia et al. (1999)Ernst et al. (2008): Modified add-on model with bid-ask-spread (II/II)


Note: "Risk correctly estimated" is determined via standard Kupiec (1995)-statistic; Sample = 160 stocks in four major German stock indices over 5.5 yearsSource: Ernst, Stange, Kaserer (2008)

2



Price impact of order size distilled from transaction dataBerkowitz (2000): Transaction regression model



• Integrates price impact of order size

– High data requirements– Liquidity measure highly approximate

• Measurement very noisy– Assumption of zero price-liquidity correlation

• Independence between price risk and liquidity impact

• Abs. liquidity cost per share ( ) derived from linear regression of transaction prices when controlling for other risk factor changes (x)

• Not explicitly defined


3



Simple price impact approximation via relative traded shares Cosandey (2001): Price impact derived from volume



• Market volume data available• Accounts for price impact of order size via

simple theoretical assumption

– No time variation of liquidity (here measured with traded share volume)

– Price impact linear to relative traded shares• Concavity of price impact function

neglected

• Worst price risk adjusted for relative increase of traded shares


• Relative increase of traded shares by position

• Assumes that position increases number of shares but total traded value

4



Liquidity cost derived from theoretical driversAngelidis, Benos (2006): Structurally-implied spread



• Partially accounts for price impact of order size via increased volume percentile

– Unclear if structural model is correct– Complicated estimation of parameters in

intraday data required– Possible overestimation because liquidity-

return correlation assumed perfect

• Structurally-implied spread added to price risk• Calculated with top-percentile of volume• Assumes that individual position size

dissipates in market


• Spread model estimated from intraday data• Model derived from theoretical ideas on

liquidity drivers• Traded shares N, degree of info assym.

theta, price elasticity to volume kappa, liquidity fixed cost Phi

5



Using more limit order book data increases measure precisenessFrancois-Heude and Wynendaele (2001): Price impact from best limit orders



• Accounts for price impact of order size• Price impact more precise because directly

measured in limit order book

– Only applicable in electronic limit order book markets

– Time variation of liquidity neglected– Assumes perfect correlation between liquidity

and price– Five best limit orders need to be available– Intraday only– Liquidity cost only extrapolated for medium to

large order sizes– Somewhat arbitrary spread adjustment– Provides empirically imprecise results than

other models using limit order data• See Ernst et al. (2008)

• Normal price risk adjusted for average price impact

• Correction term for difference between average and stock-specific price impact


• Price impact curve estimated from best five limit orders

• Available from Paris Bourse• Extrapolated for larger sizes

6



Precise price impact measurement with limit order book dataGiot, Gramming (2005): T-distributed net-return model with weighted spread



• Accounts for price impact of order size in very precise way

• Correctly accounts for liquidity-return correlation


– Intraday data required if lower frequencies not provided by exchange

– Possible overestimation if instant liquidation assumption is suboptimal

– Possible distortion through assumption of t-distributed net-returns


• Size-specific liquidity cost extracted as weighted spread from limit order book

• at(n) and bt(n) are weighted ask and bid-prices for trading n = q/Pmid shares

• T-distribution percentile of historical net return distribution

• Net return is mid-price return net of weighted spread liquidity costs

7



Precise empirical price impact measurement with limit order book dataStange and Kaserer (2008): Price impact measured with weighted spread



• Accounts for price impact of order size in very precise way

• Correctly accounts for liquidity-return correlation


– Intraday data required if lower frequencies not provided by exchange

– Possible overestimation if instant liquidation assumption is suboptimal

• Empirical percentile of historical net return distribution

• Net return is mid-price return net of weighted spread liquidity costs


• Size-specific liquidity cost extracted as weighted spread from limit order book

• at(n) and bt(n) are weighted ask and bid-prices for trading n = q/Pmid shares

8

Source: Stange, Kaserer (2008b)



Model overview


Source: Stange, Kaserer (2009)



Limit order data models with superior performance in stocksModel performance


Note: "Acceptance rate" is fraction of stocks where Kupiec (1995)-statistic could not reject deviation between realized and predicted loss frequency; ; Sample = 160 stocks in four major German stock indices over 5.5 yearsSource: Ernst, Stange, Kaserer (2009)

However, models including delay costs not developed yet




• Introduction


– Definition

– Characteristics

– Measurement

– Empirical facts


– Introduction

– Models




Summary Market Liquidity

Market liquidity is cost of trading an asset• Components: Direct trading costs, price impact costs, delay costs• Determinants: type of asset, order size, liquidation horizon• Continuous liquidity degrees – different treatment required• Optimal trading strategies developed to minimize sum of cost components

– Balance increased delay cost against reduced price impact– Less relevant for risk management

• Several liquidity measures available– Direct liquidity measure promise increased precise liquidity measurement

Several models can be chosen to measure market liquidity risk• Market liquidity risk is substantial, but often neglected• Models based on limit order data perform better in backtests• Modified risk model (Ernst et al. 2008) consistently outperforms



Interesting open research topics1. Can the superiority of the model of Ernst et al. (2008) be improved via better moment estimation techniques?**2. Estimation and validity of optimal trading strategies (OTS)*

– How can parameters of theoretical models with optimal trading strategies be estimated?– In which situations are optimal trading strategies beneficial compared with instant liquidation - in normal times or also

in crises?3. In which situations are liquidity costs efficient?

• How should arbitrage strategies be constructed?• What drives the efficiency of markets?

4. Are total liquidation costs per stock an asset pricing factor?– Total liquidation costs can be estimated via weighted spread times traded size distribution

5. Can the price impact curve be described via theoretical processes?– Similar to interest rate curve– Arbitrage conditions also apply if liquidity price are efficient– Can be helpful when describing unobservable / hidden liquidity

6. Is it possible to construct liquidity options – in analogy to volatility options?7. How high are liquidity cost / risk levels between different asset classes?8. Can the stability of liquidity cost for relative order size be used in liquidity risk measurement?

– Liquidity costs are relatively constant for order size in relation to volume and market value in the cross section (Stange, Kaserer 2008)

– Is this helpful in implementing an asset class, not asset specific liquidity risk approach?9. How should liquidity risk be integrated into portfolios?

– What is the role of liquidity commonality in the covariance matrix?

Source: Stange, Kaserer (2009)

Backup



Further references

• Bervas (2006) "Market Liquidity and its Incorporation Into Risk Management", Banque de France technical report, http://www.gloriamundi.org

• Ernst, C., S. Stange. and C. Kaserer (2008a) "Accounting for Non-normality in Liquidity Risk", CEFS working paper 2008 No. 14, www.cefs.de

• Ernst, C., S. Stange. and C. Kaserer (2008b) "Empirical evaluation of market liquidity risk models", CEFS working paper 2009 No. 1, www.cefs.de

• Erzegovesi (2002) "VaR and Liquidity Risk. Impact on Market Behaviour and Measurement Issues", Alea Technical Reports Nr. 14, http://eprints.biblio.unitn.it

• Jorion (2007) "Value at risk: the new benchmark for managing Financial risk", 2. Ed., McGraw-Hill, New York

• Loebnitz (2006) "Market Liquidity Risk: Elusive no more - Defining and quantifying market liquidity risk", diploma thesis, University of Twente, http://purl.org/utwente/e582

• Mahadevan, A. (2001) "Incorporating Liquidity Risk in VAR estimation", ICICI Working paper, http://www.gloriamundi.org

• Stange, S. and C. Kaserer (2008a): "The Impact of Order Size on Stock Liquidity - A Representative Study", CEFS working paper, www.cefs.de

• Stange, S. and C. Kaserer (2008b) "Why and How to Measure Liquidity Risk", CEFS working paper, www.cefs.de

• Stange, S. and C. Kaserer (2009) "Market Liquidity Risk – An Overview", CEFS working paper, www.cefs.de

Backup



Thank you for your attention!

Comments are warmly welcome.

SebastianStange

Prof. ChristophKaserer

market liquidity and its risk - an overview

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