Liquidity ALM or Market Risk ?

1. Liquidity ALM or Market Risk ? Jérôme Lebuchoux

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

3. 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

4. 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 ?

5. 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

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

7. 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.

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

9. 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

10. 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

11. 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

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

13. Performance • The decorrelation of the HF performance with the indexes in question

14. 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

15. 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

16. 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 • It is always easier to buy than to sell Tomatoes producer buy Tomatoes fund NAV New investment

17. 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$, new potential investors : 5 M$

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

19. 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

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

21. 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

22. 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

23. 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

24. 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…)