Limits of Arbitrage: Understanding How Hedge Funds Fail

Even if arbitrage opportunities are found in a statistical sense, they might not be exploitable due to unexpected widening of spreads. This paper models such a case in the framework of a hedge fund. Specifically, Long Term Capital Management is presented as a case study. In particular, we calculate the likelihood of hedge fund failure and survival given different statistical arbitrage opportunities and hedge fund risk management decisions. Dynamic relationships between a hedge fund, dealer, and market (investor) are modeled. The model explores phenomenon when a fund manager who engages in arbitrage and uses high leverage might lose all his money before realizing positions at a profit. As assets go down in value, the firm has to post more collateral or decrease position exposure. We observe if positions converge before all collateral has been exhausted, the most profitable strategy is to post more collateral and increase position exposure. However, if positions diverge beyond the point of remaining cash, a hedge fund will avoid collapse if it decreases position exposure