Upside potential ratio


The upside-potential ratio is a measure of a return of an investment asset relative to the minimal acceptable return. The measurement allows a firm or individual to choose investments which have had relatively good upside performance, per unit of downside risk.
where the returns have been put into increasing order. Here is the probability of the return and which occurs at is the minimal acceptable return. In the secondary formula and.
The upside-potential ratio may also be expressed as a ratio of partial moments since is the first upper moment and is the second lower partial moment.
The measure was developed by Frank A. Sortino.

Discussion

The upside-potential ratio is a measure of risk-adjusted returns. All such measures are dependent on some measure of risk. In practice, standard deviation is often used, perhaps because it is mathematically easy to manipulate. However, standard deviation treats deviations above the mean exactly the same as it treats deviations below the mean. In practice, rational investors have a preference for good returns and an aversion to bad returns.
Sortino further found that investors are averse not to deviations below the mean, but to deviations below some "minimal acceptable return", which is meaningful to them specifically. Thus, this measure uses deviations above the MAR in the numerator, rewarding performance above the MAR. In the denominator, it has deviations below the MAR, thus penalizing performance below the MAR.
Thus, by rewarding desirable results in the numerator and penalizing undesirable results in the denominator, this measure attempts to serve as a pragmatic measure of the goodness of an investment portfolio's returns in a sense that is not just mathematically simple, but one that considers the realities of investor psychology and behavior.