Hedge Fund Investing or Mutual Fund Investing: An Application of Multi-Attribute Utility Theory

Abstract

This paper contrasts high-risk, hedge fund trading, with low-risk, mutual fund trading, in terms of their differing utility functions. We envision hedge funds, led by informed traders who use information to seek out investment opportunities, timing market conditions, with the expectation that prices will move in their favor. Directional hedge funds act to influence prices, while non-directional hedge funds do not act to influence prices. We present utility functions based on steeply-sloping Laplace distributions and hyperbolic cosine distributions, to describe the actions of directional hedge fund traders. Less steeply-sloping lognormal distributions, Coulomb wave functions, quadratic utility functions, and Bessel utility functions are used to describe the investing style of non-directional hedge fund traders. Flatter Legendre utility functions and inverse sine utility functions describe the modest profit-making aspirations of mutual fund traders. The paper’s chief contribution is to develop optimal prices quantitatively, by intersecting utility functions with price distributions. Price distributions for directional hedge fund returns are portrayed as sharp increases and decreases, in the form of jumps, in a discrete arrival Poisson-distributed process. Separate equations are developed for direc tional hedge fund strategies, including event-driven arbitrage, and global ma cro strategies. Non-directional strategies include commodity trading, risk-neutral arbitrage, and convertible arbitrage, with primarily lognormal pricing distributions, and some Poisson jumps. Mutual funds are perceived to be Markowitz portfolios, lying on the Capital Market Line, or the International Capital Market Line, tangent to the Efficient Frontier of minimum variance-maximum return portfolios.