Adam Tashman (Ivy Asset Management, New York, NY)

Modeling Risk in Arbitrage Strategies Using Finite Mixtures

Arbitrage strategies produce stable, modest returns punctuated by intervals of dramatically poor performance. The weakness stems from an oversight in modeling: seemingly independent bets infrequently become highly correlated to market variables. Thus, the risk in arbitrage strategies is systematically underestimated, and hedging is not properly implemented. This paper illustrates the fitting and application of a mixture model to a series of hedge fund index returns, for the purpose of more effectively hedging downside risk. The model captures the regime-switching nature of the process in a general setting, free from the assumption of a linear relationship between explanatory and response variables. A logistic regression function is used to predict the acting regime, and linear regression functions relate explanatory variables to the expected hedge fund return in each regime. The covariates considered are stock market returns, volatility of the stock market, the slope of the US swap curve, and credit spreads. The dependent variable under investigation is the HFRI Merger Arbitrage Index. The model is applied in a novel hedging strategy, termed mixture hedging. The strategy is back tested over the period 1990-2005, and its performance is compared against the prevalent beta-neutral hedging strategy. The merger arbitrage index exhibited strong evidence of a regime-switching process, and the proposed model offered an improved fit relative to standard regression techniques. Mixture hedging was more effective at reducing downside risk than beta-neutral hedging. Maximum drawdown was 5.50% for the mixture strategy, versus 5.98% for beta-neutral hedging and 6.46% for an unhedged portfolio. The improvement will be more pronounced if the portfolio is levered.