Markov Chain Models to Estimate the Premium for Extended Hedge Fund Lockup

A lockup period for investment in a hedge fund is a time period after making the investment during which the investor cannot freely redeem his investment. It is routine to have a one-year lockup period, but recently the requested lockup periods have grown longer. Assuming that the investor will rebalance his portfolio of hedge funds on a yearly basis, if permitted, we define the annual lockup premium as the difference between the expected return per year from an investment in a hedge fund with a nominal one-year lockup period and the expected return per year from an investment in a hedge fund with an extended lockup period, as a function of the length of that extended lockup period. We develop Markov chain models to estimate this lockup premium function. By solving systems of equations, we fit the Markov chain transition probabilities to three directly observable hedge fund performance measures: the persistence of return, the variance of return and the hedge-fund death rate. The model quantifies the way the lockup premium increases as a function of both the persistence of return and the variance of return, but decreases as a function of the hedge-fund death rate. Increasing death rate lowers the lockup premium because investors can redeem their investment when the hedge fund fails, even when a lockup condition is in force.