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).