Liquidity ALM or Market Risk Jrme Lebuchoux Liquidity

Liquidity ALM or Market Risk ? Jérôme Lebuchoux

Liquidity Vague concept ? Standard approach § § Related to market liquidity on asset (volume, trades, prices, etc…) microstructure Major risk § § § Macro impact Credit crunch Crisis

Market liquidity Classical approach for liquidity § Execution price depends on the volume Execution § § Take into account the asymmetry (buy and sell) Optimal execution model for block trade Allocation § Rebalance the portfolio according to the liquidity Risk § § Gap risk Limits It is a vision of liquidity related to buy / sell action

Market liquidity The regulators are imposing new constraints New pools of liquidity have emerged § § § New exchanges Dark pool Long term investors This approach is not appropriate for many markets (Fixed income) Is there something else ?

Market liquidity Investors are not operating with the same objective nor under the same rules § § § Pension funds Hedge fund Insurance… The buy and sell are only the visible actions but behind every operations there is a financing part § § Cash Margin Borrow Collateral

Examples Buy a future at an exchange § Post the initial margin Sell short a financial stock § Borrow the stock Buy a swap § Post collateral

ALM liquidity If there is no financing there is no investment If one could not buy it may be able to borrow If one could not sell it may be able to repo or post for collateral Example : Corporate bonds § § § No price on secondary market Accepted as collateral Borrow money, post the bond as collateral and invest into new asset • Spread position Borrowing cost, repo market are good indicators for liquidity, it could be used to get a long or a short position on liquidity on FI market.

Hedge Fund utility ? Optimal Capital allocation § § § Diversification Arbitrage New risk profile Liquidity provider § § To the Market To the investors

Facts Old concept but a young industry Asset Management industry has been hit by the crisis : ● Asset under management has been reduced. ● Performance was poor. ● Risk management has shown its limits ● Authorities are putting pressure for new standards and regulation. ● The confidence of the investors is low Consequences : ● Revenues are declining ● Customers are more demanding ● The image of the industry is deteriorated

A step back Main drivers of the asset management industry : ● Economy ● ● Growth of economy Capital needs to sustain the economy growth and restructuring ● Demography ● ● Life expectancy Human capital growth ● Globalization ● ● Free trade Communication and mobility ● Politics ● ● Tax regime Labour / Capital Social security vs individual savings

Hope An evolution or a revolution ? : ● Only the first point (Economy) is directly impacted by the crisis ● There are second order effects on the other points ● ● ● Returns of protectionism Nationalisation of the economies Political instability… ● World AL balance has evolved (geographically, private/public…) but is growing A threat or an opportunity ? : ● Adequacy between the offer and the demand has been challenged ● Leaders are under pressure and Darwinism is ongoing Our opinion: The asset management starts restructuring The window for change and opportunity is now

AUM & Actors A steady increase of AUM and of number of HF until 2007…the crisis changes the picture

Performance The decorrelation of the HF performance with the indexes in question

Alternative investment and liquidity crisis The financial crisis impacts the HF industry A performance issue § Weak and correlated performance § Limited number of strategies § Small capacity wrt performance impact Poor liquidity § Limited financing facility § Illiquidity of the underlying Investors on hold § Fall in AUM § Investors raise their standards

Liquidity risk Hedge fund are § § Long correlation in stable market and short the systemic correlation Long the spread of liquidity between investors - market Standard Liquidity indicators § § Market impact Number of days to close the positions Features to manage the liquidity § § Lock up Gates… Unfortunately the set up of the fund have been made according to § § Market practice : Lock up Emergency : Gates But not wrt the “real” liquidity risk

An asymmetric risk / bubble A toy example Fund with a stock X in illiquid asset (price impact / NAV) § § Buy an extra x of asset -> move the price up by y% -> NAV of fund + y% on the full AUM Sell x of asset -> move the price down by -y% -> NAV of fund - y% on the full AUM A liquidity trap / gap risk buy NAV Tomatoes fund New investment It is always easier to buy than to sell Tomatoes producer

A simple framework Needs to move from a pure performance / risk model to an Asset and Liability model (which is the difference between the P&L and the NAV) § Liability : Investors, fees, etc… § Asset : investment Model of investors portfolio § Each investors and prospects are ranked wrt its category, size of investment and probability to invest or redeem. § Today AUM : 100 M$, new potential investors : 5 M$

A simple framework Model : simple copula with three parameters § § § One correlation intra category One correlation existing / new investors At a given date (1 M or according to fund liquidity) we get the pdf of the AUM Avg AUM : 94 M$

Allocation model Portfolio model § One risky and non risky asset, no rate and dividend, simple BS model One period model § At the end of the period the AUM is impacted by the redemption and the new investment § Rebalancing without impacting the portfolio risk profile § Where is the growth of the AUM

Allocation model Cost of rebalancing according to an average liquidity L Optimal portfolio Utility function Special case

Intuitive approach The optimal allocation leads to an option on AUM The optimal allocation accounts for the hedge of the option The optimal allocation could be seen as the classical allocation minus the risk on the spread AUM / Asset

Simple model result Target allocation in risky asset 55% § Beta : 10% § L : 20 % % Change in risky asset allocation If the proba of redemption increases, the investment in risky asset should decrease If the investors are “correlated”, the investment in risky asset should decrease

Combined model We have looked at a single asset manager, now we explore the case of multiple managers trading the same asset N agents, they “share” the liquidity option, the impact on the given asset Two extreme cases for 2 agents (Proba redemption : 20, corr : 50%) Same investors : - 14. 6% Independent investors : - 7, 9% Intuitive result : at the limit, if the investors are “random”, almost no impact but if the investors are “shared” the risk is huge

Conclusion The HF industry moved from “random” or “positive” flow of AUM to highly correlated outflows It is crucial to quantify and manage the investors risk Key points § Better knowledge of investors § Diversify the strategies § Don’t be short of liquidity option Extensions § Investors redemption / fund performance correlation § Multi period § Define optimal liquidity of the fund (lock up, gates) § Model the correlation to exogenous factor (demography, etc…)