Hedge Funds' Long-Short Strategy

This paper analytically studies the long short strategy, one of the most popular trading strategies undertaken by hedge funds. Using Markowitz's portfolio theory as a starting point, I expand the modern portfolio theory to a more general theory to include assets that have negative expected returns, in which a higher return can be associated with a lower risk and a lower return can be with a higher risk. Given that there is a perfect positive or negative correlation between the two assets, it may appear that there are two distinct risk-free returns on the return-volatility graph but it turns out that the both are identical in terms of the ratio of the weights to the individual assets and that the other one is a leveraged version of the one risk-free return. There are two distinct styles of long-short strategy: long-short equity and fixed-income arbitrage. Long-short equity is applicable in a situation where the expected returns of the pair of the assets have different signs while the correlation of the returns is expected to be close to 1. In contrast, fixed income arbitrage is attempted in case where the expected returns of the pair of the assets are similar and positive, while the correlation of the returns is expected to be close to 1. Due to the fact that the expected risk-free return of the fixed income arbitrage is tiny compared to that of long-short equity, it typically entails a significant level of leverage, which explains why it could blow up so devastatingly when the anticipated correlation is not realized. Last, the robustness of the strategies is analyzed through sensitivity analysis of the return with respect to individual assets' expected return, standard deviation, and the correlation between them.