Hedge Fund Performance During and After the Financial Crisis

Fund performance has been earlier evaluated by the measures developed by Sharpe (1966), Treynor (1965) and Jensen (1968). The Sharpe ratio of a portfolio (Sp) measures the excess return of portfolio, relative to the risk-free rate divided by its standard deviation, and is defined as

$\mathrm{Sp}=\frac{\mathrm{E}(\mathrm{Rpi}-\mathrm{rfi})}{\sigma \mathrm{p}}$

The Sharpe measure takes into account the total risk of returns, whilst the Treynor and Jensen measures rate a fund, just on its market risk. More recently, to account for asymmetricities in returns and not only the market risk, alternative reward-risk evaluation measures, such as the Sortino ratio (Sortino and Price (1994)), and Upside Potential ratio (Sortino et al. (1999)) were proposed.

The Sortino ratio of a portfolio is defined as

$\operatorname{SOR} p=\frac{\mathrm{E}(\mathrm{Rpi}-\mathrm{MAR})}{\sqrt{\left.\mathrm{E}(\operatorname{Min}(\mathrm{Rpi}-\mathrm{MAR}), 0)^{2}\right)}}$

where Rpi is the return of the portfolio at time i, MAR is the minimum acceptable return, and $\sqrt{ \left.\mathrm{E}(\mathrm{Min}(\mathrm{Rpi}-\mathrm{MAR}), 0)^{2}\right)}$ is the Downside risk (DR).

The Upside Potential ratio of a portfolio is defined as

$\mathrm{UPR} p=\frac{\mathrm{E}(\operatorname{Max}(\mathrm{Rpi}-\mathrm{MAR}), 0)}{\sqrt{\left.\mathrm{E}(\operatorname{Min}(\mathrm{Rpi}-\mathrm{MAR}), 0)^{2}\right)}}$

The upside potential ratio divides the average of the excess positive returns, compared to the minimum acceptable return (MAR), by the downside risk (DR).