A SIMPLE MODEL FOR THE EXPECTED PREMIUM FOR HEDGE FUND LOCKUPS

Emanuel Derman

What excess return should a fund of funds expect to earn for investing in a hedge fund with an extended lockup?

In this paper, we present a simple model for estimating the premium for long-term lockups. Because there is a demonstrated statistical persistence to the quality of hedge fund returns within a particular hedge fund strategy—above average funds tend to continue to do well, and below average funds continue to falter—a lockup deprives an investor of the opportunity to redeem an investment in poorly performing funds and reinvest the proceeds in successful ones. The value of that lost future opportunity is the expected premium for committing to the lockup.

We estimate the value of the premium for multi-year lockups in a variety of strategies using a discrete-time Markov chain model for the evolution of hedge funds, in which a hedge fund at any time can be in one of three states: Good, Sick or Dead. For convertible bond funds, for example, the return premium for a two-year lockup over a one-year lockup is approximately 48 basis points (b.p.) per year. The premium rises to 76 b.p. per year for a three-year lockup, and approaches a limit of 156 b.p. as the duration of the lockup becomes infinite. The premium is proportional to the standard deviation of the returns themselves, so that strategies with greater standard deviations of returns require greater compensating lockup premiums.