The Value of Liquidity and Option Timing from a Simple Game

In a previous paper, Bhaduri and Whelan (2008), we presented a simple model of hedge fund liquidity. That paper explored the fact that not being able to pull one’s money out of an investment instantaneously at a fair price can have a powerful impact on the portfolio. Real world examples include the 1993 Metallgesellschaft debacle (Smithson, 1998) and the recent difficulties experienced by the Bank of Montreal (Perkins and Stewart, 2007), as they attempt to exit from some thinly traded OTC energy derivatives. As we pointed out in our earlier paper, liquidity is a growing issue in the hedge funds arena; increased regulatory pressure has led various hedge funds to extend their lock-up period to avoid more scrutiny. Locking up investments represents a loss of liquidity to the investors and, despite its growing importance, very little quantitative work has been done to understand it in the context of hedge funds. In this paper, we explore the impact of liquidity in a simple model.