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 directional hedge fund strategies, including event-driven arbitrage, and global macro 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.
Highlights
Hedge funds, which attract large cash inflows per investor, operate with minimum regulations, and strict entry barriers
We present utility functions based on steeply-sloping Laplace distributions and hyperbolic cosine distributions, to describe the actions of directional hedge fund traders
Traders expect modest gains in short selling the acquirer stock. They benefit from exponential increases in utility, as target prices soar in Poisson jumps, exiting target purchases as prices peak, and herd to purchase put options, maximizing gain by driving prices to a minimum
Summary
Hedge funds, which attract large cash inflows per investor, operate with minimum regulations, and strict entry barriers. Arbitrage, short selling, and derivative strategies are permitted. We consider hedge funds to engage in some combination of three activities, i.e. actively seeking out investment opportunities, predicting market conditions through timing strategies, or herding to influence prices. Directional hedge funds predict that certain mergers are not going to be completed. They purchase the target stock, using timing to predict the date of announcement of deal failure. A non-directional hedge fund strategy could be the carry trade of borrowing funds at low-interest rates in US dollars, say at 3%, to invest in high-interest Australian dollars, at about 8%. Mutual funds attract investable funds from small investors, pool the funds, investing them in stocks, bonds, or money market debt, in a passive buy-and-hold strategy. A sector fund would invest in a particular industry, such as biotechnology. [4] reports a 6.7% return on S & P 500 index funds in 2010-2011, though estimates of about 12% on similar funds have been observed, as well
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