Numerical Solution

The Value of Liquidity investments and derivatives space, and this paper provides some quantitative insights on the value of liquidity. Abstract We present a game-theoretic example that helps to illustrate the value of liquidity. These insights are applicable to hedge fund investors since hedge funds have different lock-up and redemption terms. This game also shows the danger of relying on intuition to determine the value of liquidity. We also demonstrate that the value of liquidity is different for different types of investors; the value is less for investors with less ability. Liquidity has become an increasingly important issue in the alternative Liquidity risk arises from not being able to pull one's money out of an investment instantaneously at fair price. It can have a powerful impact on the portfolio as witnessed by the 1993 Metallgesellschaft debacle (Smithson [1998]). Liquidity is becoming a growing issue in the hedge funds arena where increased regulatory pressure by the SEC has resulted in several hedge funds lengthening their lockup period to two years in order to avoid more scrutiny. Even though liquidity risk is important, very little work has been done to quantitatively understand it in the context of lockup periods. This paper, via an illustrative example, demonstrates the impact of liquidity. The Game – Balls in a Hat " Business is a game. " IBM founder Thomas J. Watson In physics and other physical sciences, it is common to create deliberately simplified " toy " models in the expectation that understanding of the model will lead to intuition about the fuller problem. In this paper we present such a model for the value associated with the lockup period in a hedge fund, in the form of a one person game. We are also inspired by game theory, first invented by the mathematician John von Neumann, which has had many useful applications in economics and finance (Thomas [1986]). Consider a hat with b black balls and w white balls. At each turn the player chooses whether to draw out a single ball at random, without replacement. The game ends when the player chooses not to remove any further balls or when the hat is empty. The player gains $1 for each white ball drawn, and loses $1 for each black ball drawn. An important feature is that without replacement, the player's draws affect the relative probabilities of subsequent draws. We consider this game an …