The Premium for Hedge Fund Lockups

1. The Premium for Hedge Fund Lockups Emanuel Derman George Constantinides University of Chicago

2. Overview of Derman • Claim: annual hedge fund returns are predictable by past returns • Absent a lockup provision, investors should annually re-allocate assets across hedge funds to chase predictable abnormal returns • Lockup provisions hinder asset re-allocation George Constantinides University of Chicago

3. Equilibrium Implications • Derman calibrates a model of correlated hedge fund returns • He compares two funds with 1-year and 2-year lockups • Claim: in equilibrium, the fund with 2-year lockup should command an annual premium of ~ 90 bps George Constantinides University of Chicago

4. Nun Lectures Hedge-Fund Managers on Sex Education (and Alphas) • Are annual returns predictable? • What annual premium, if any, should the fund with 2-year lockup command? George Constantinides University of Chicago

5. Methodological issues • Survivorship bias—dead funds are dropped from a data base • Practically all studies account for it • See: Brown S., W. Goetzmann, R. Ibbotson and S. Ross, 1992, “Survivorship Bias in Performance Studies”, Review of Financial Studies 5, 553-580 George Constantinides University of Chicago

6. Methodological issues continued... • Backfill bias—successful funds bring their history when they join a database • Self reporting—ailing funds stop reporting • Self reporting—funds closed to new investors stop reporting • Serial correlation due to stale NAV reporting • Dynamic strategies result in skewed returns • Betas are underestimated George Constantinides University of Chicago

7. Empirical Evidence—1Brown, Goetzmann, Ibbotson (1999) • Off-shore funds • No persistence in annual raw returns: in 3 yrs, positive slopes, in 3 yrs negative slopes • Same results with style benchmarking • Same results with risk-adjusted returns • See: “Offshore Hedge Funds: Survival and Performance: 1989-1995”, Journal of Business 72, 91-118 George Constantinides University of Chicago

8. Empirical Evidence—2Agarwal and Naik (2000) • On-shore and off-shore funds • Pre-fee and net-of-fee returns • Persistence of quarterly returns • Insignificant persistence in annual returns • Persistence is unrelated to fund strategy • See: “Multi-Period Performance Persistence Analysis of Hedge Funds” Journal of Financial and Quantitative Analysis 35, 327-342 George Constantinides University of Chicago

9. Empirical Evidence—3Baquero, ter Horst, Verbeek (2005) • Account for self selection bias • Highest persistence in quarterly returns but statistically weak in annual returns • The winners-minus-losers deciles annual premium is 8%, but t-statistic is ~ 1 • See: “Survival, Look-Ahead Bias, and Persistence in Hedge Fund Performance”, Journal of Financial and Quantitative Analysis 40, 493-517 George Constantinides University of Chicago

10. Why Do We Observe High-Frequency Persistence? • Annual only reporting—stale NAV • Illiquid fund assets—stale NAV • Fund performance smoothing Therefore: • High-frequency persistence not due to unexploitable investment opportunities • It is impractical for fund investors to switch funds on a monthly or quarterly basis • High-frequency persistence may be unexploitable by investors George Constantinides University of Chicago

11. See: Getmansky, M., A. Lo and I. Makarov (2004) “An Econometric Model of Serial Correlation and Illiquidity in Hedge Fund Returns”, Journal of Financial Economics 74, 529-609 • See: Chan, N., M. Getmansky, S. M. Haas and A. W. Lo 2006, “Systemic Risk and Hedge Funds”, Journal of Financial Economics, forthcoming George Constantinides University of Chicago

12. Empirical Evidence—4Jagannathan, Malakhov, Novikov (2006) • Account for all three biases: -backfill -self selection -serial correlation • Find persistence in annual returns • See, “Do Hot Hands Persist Among Hedge Fund Managers? An Empirical Evaluation” NBER Working Paper George Constantinides University of Chicago

13. Jagannathan et. al. Results George Constantinides University of Chicago

14. Implied Probability of Fund Transition from Superior to Neutral • Transition probability from superior to neutral: p • Transition probability from superior to superior : 1-p (I follow Derman’s assumption that a superior fund cannot become inferior in 1 year) • 0.051 x p + 1.277 x (1-p) = 0.797 • p ~ 39 % George Constantinides University of Chicago

15. Annual Premium on Fund with 2-year Lockup • Without lockup, 2nd-period alpha: 0.797 % • With lockup, superior fund becomes neutral with probability 39% and has 2nd-period alpha 0.133 • With lockup, superior fund remains superior with probability 61% and has 2nd-period alpha 0.797 • With lockup, expected 2nd-period alpha: 0.133 x 39% + 0.797 x 61% = 0.538 % • Annual premium: [0.797 - 0.538] / 2 = 0.13 % George Constantinides University of Chicago

16. Summary vs. • Emanuel says... in equilibrium, the fund with 2-year lockup should command an annual premium of ~ 90 bps • Nun says... at most ~ 13 bps • Lockup provisions may or may not impose other handicaps on fund investors George Constantinides University of Chicago