Why do hedge funds’ worst returns cluster? Common liquidity shocks vs. contagion Nicole M. Boyson, Northeastern University Christof W. Stahel, George Mason University and FDIC René M. Stulz, The Ohio State University Workshop on Hedge Fund Disclosure, Leverage, and Regulation Imperial College, London July 6, 2009 Disclaimer : The views expressed in this paper are those of the authors and are not necessarily reflective of the views of the Federal Deposit Insurance Corporation.

Questions this paper investigates Are clusters of extreme negative return events (statistically) common? –Extreme return event A month in our sample period in which a single style index has a return in the bottom 10% tail of all observations –Clustering of worst returns Observing a number of simultaneous extreme return events across single style hedge fund indices What can explain such episodes? 2

Clustering of extreme return events 3

Why clustering? Puzzle: Hedge fund styles have different strategies and invest in potentially different assets Explanation I: Common shocks Explanation II: Dynamic spillovers – Contagion Other explanation 4

Common shock explanation Broad Markets Liquidity Hedge funds require asset liquidity to implement trades Hedge funds require funding liquidity to fund trades Brunnermeier and Pedersen (RFS, 2009) Asset liquidity and funding liquidity interact Shocks to liquidity have adverse impact on hedge funds of different styles 5

Dynamic Spillover or Contagion explanation Generally, contagion means that adverse developments spread without justification from fundamentals or common shocks Healthy hedge funds are adversely affected by poor performance of other hedge funds December 30, 2008 “… in a cascade effect, funds of funds will need to redeem money from funds that are performing well to cover those [funds] that have lost money.” 6

Contagion explanation cont. Use and test a narrow definition of dynamic effects after controlling for contemporaneous fundamentals –Multi-strategy fund effect: Khandani and Lo (2007) –Funding effect: sick hedge funds constrain providers of funding liquidity and subsequently affect healthy funds 7

Main results Use monthly style index data from 1990 to 2007 Strong evidence of clustering: probability of an extreme return event in a style goes from 2% to 19% as the number of other styles with extreme return events increases from 0 to 7 Strong evidence of a common liquidity shock effect Mixed support for contagion 8

Data Hedge funds: Single style return indices from Hedge Fund Research (HFR) Convertible Arbitrage, Distressed Securities, Equity Hedge, Equity Market Neutral, Event Driven, Global Macro, Merger Arbitrage, and Relative Value Arbitrage January 1990 – August 2007: 212 observations No size requirement; no track record requirement; over 1600 funds Constructed to reduce survivorship and backfilling biases Main markets: from DataStream and Federal Reserve Board Russell 3000, Lehman Brothers bond index, USD exchange rate index Lipper/TASS (individual hedge fund data) used to construct flow variables Standardize returns by using residuals from univariate AR-GARCH models 9

Estimate the conditional probability that a single style hedge fund index has an extreme return event on a given date Conditional probability models: Logit regressions Dependent variable: {0,1} indicator variable set to 1 if the hedge fund index i has an extreme return event at time t Positive and significant coefficients on COUNT7 imply clustering Clustering test regressions 10

Table II: Clustering Results COUNT7 7 11

Factor exposure and clustering Hedge funds employ dynamic strategies, use derivatives, and have leverage Could clustering result from exposure to similar nonlinear risk factors? We add the Fung and Hsieh (2004) factor variables Could clustering result from exposure to liquidity risk? We add liquidity proxies as continuous variables to our model Yield spread of Baa over 10 year CMT Treasury Repo volume Bank index return Prime broker index return CSS stock market liquidity measure Contemporaneous hedge fund flows Quasi-complete separation and stepwise iterative regressions  Result: We still find clustering 12

Economic significance of results For each style index, calculate the probability of an extreme return event for different realizations of COUNT7 Set all explanatory variables, except COUNT7, to their mean values and evaluate the regression at all levels of the COUNT7 variable {0,…,7} Average (median) conditional probability that a style index has an extreme return event increases from 2% for COUNT7 = 0 to 21% for COUNT7 = 7 COUNT7 13

Determinants of clustering: Funding liquidity and asset liquidity Funding liquidity: Significant losses in one hedge fund style can reduce lending across all styles Asset liquidity: Levered funds that need to reduce leverage and sell large holdings put pressure on prices and can significantly reduce asset liquidity affecting all styles Reductions in funding and asset liquidity lead to adverse trading and funding liquidity spirals which lead to poor returns across all hedge fund styles Brunnermeier and Pedersen (2009) 14

Determinants tests Multinomial Logit Regression approach Model jointly the conditional probabilities associated with m categories for each channel Multivariate models controlling for (standardized) risk factors Clustering categories Base case or NO clustering: if 0 or 1 style experience extreme event LOW clustering: if 2 or 3 styles experience extreme event HIGH clustering: if 4 or more styles experience extreme event Different parameters for low and high clustering levels measure impact relative to base case Stepwise iterative regression approach as in clustering tests for control variables to generate parsimonious regression models 15

Determinants tests, continued Create “large liquidity shock” indicator variables For each liquidity proxy variable set indicator to 1 if the liquidity proxy variable experiences a “large shock” – if the realization of the variable is in the bottom (or top) quartile of all realizations – and 0 otherwise Funding Liquidity: INDPBI; INDBANK; INDCRSPRD; INDREPO Asset Liquidity: INDSTKLIQ; INDFLOW Add “large liquidity shock” indicator variables to parsimonious multivariate regression models A positive and significant coefficient on any of these indicator variables indicates that large liquidity shocks are associated with clustering in hedge fund index extreme return events Models separately include contemporaneous (Table V) and lagged (Table VI) liquidity shock variables 16

Table V: Determinants tests (selected results) 17

Can contagion explain clustering? Contagion has a temporal dimension Two channels: Test 1: Multi-strategy fund channel Khandani and Lo (2007) Previous multinomial regression approach with same 3 categories Control for fundamentals and liquidity variables – stepwise approach Test significance of lagged extreme return multi-strategy fund index indicator Test 2: Other style channel Test whether extreme event in any single style can increase the likelihood of extreme events in many other styles “Reverse clustering tests” and categorize COUNT7 variable Control for fundamentals and liquidity variables – stepwise approach Test significance of lagged extreme event indicator for each style Results are mixed 18

Conclusions No systematic evidence of clustering between broad markets and individual hedge fund styles Strong evidence of clustering between different hedge fund styles Support for common liquidity shock explanation Mixed support at best for contagion 19

New Version Data Updated sample period through October 2008 Filter style returns with AR-GARCH and Fung and Hsieh (2004) factors Conditional Probabilities Increase in the left tail if other styles experience left tail events Adrian and Brunnermeier (2008) Our 10% left tail extreme event classification is not special New results consistent with evidence from current version 20