Markov chain models to estimate the premium for extended hedge fund lockups

Abstract

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. We estimate the premium for such extended lockup, taking the point of view of a manager of a fund of funds, who has to choose between two investments in similar funds in the same strategy category, the first having a one-year lockup and the second having an n-year lockup. Assuming that the manager will rebalance his portfolio of hedge funds on a yearly basis, if permitted, we define the annual lockup premium as the difference between the rates of return from these investments. We develop a Markov chain model to estimate this lockup premium. 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 depends on these parameters. Data from the TASS database are used to estimate the persistence, which is found to be statistically significant. Keywordshedge funds, liquidity, extended hedge fund lockups, persistence of hedge fund returns, Markov chains, stochastic processes Published online in Wiley InterScience | wilmott Journal | 265where δ is the death rate, γ is the persistence and σ is the standard deviation of the yearly relative returns (under parametric assumptions to be explained later).Organization of the paper. We start in Section 2 by reviewing the related literature on liquidity, including premiums for hedge fund lockup. In Section 3 we carefully specify what we mean by the lockup premium. In Section 4 we discuss persistence of hedge fund returns, reviewing the literature and analyzingPublished online in Wiley InterScience |

Locked Up by a Lockup: Valuing Liquidity as a Real Option

“…Our model of the hedge fund failure process extends the Markov chain model employed by Derman et al (2009) to shift the baseline default intensity up and down by a performance covariate. Denote the baseline density of durations as  …”

Locked Up by a Lockup: Valuing Liquidity as a Real Option

“…Our model of the hedge fund failure process extends the Markov chain model employed by Derman, Park, and Whitt (2009) to shift the baseline default intensity up and down by a performance covariate. Denote the baseline density of durations as f b ( t ) with cumulative density function .…”

“…Our paper is most closely related to Derman (2007), who models hedge fund returns using a three‐state model in which hedge funds are good, sick, or dead. Derman, Park, and Whitt (2009) extend this approach to allow for more complex Markov chain models. In both approaches, lockups prevent an investor from withdrawing capital from a sick fund and investing the proceeds in a good fund.…”

A Stochastic Model for Hedge Fund Relative Returns

“…To build a model, we draw on our previous work in Derman et al (2007), hereafter referred to as DPW, which developed (different, e.g., three-state Markov-chain) models to estimate the premium from extended hedge-fund lockup. In DPW we discussed the TASS data; see especially the Appendix of DPW.…”