calculate Upside Potential Ratio of upside performance over downside risk

Sortino proposed an improvement on the Sharpe Ratio to better account for skill and excess performance by using only downside semivariance as the measure of risk. That measure is the SortinoRatio. This function, Upside Potential Ratio, was a further improvement, extending the measurement of only upside on the numerator, and only downside of the denominator of the ratio equation.

UpsidePotentialRatio(R, MAR = 0, method = c("subset", "full"))

Arguments

R	an xts, vector, matrix, data frame, timeSeries or zoo object of asset returns
MAR	Minimum Acceptable Return, in the same periodicity as your returns
method	one of "full" or "subset", indicating whether to use the length of the full series or the length of the subset of the series above(below) the MAR as the denominator, defaults to "subset"

Details

calculate Upside Potential Ratio of upside performance over downside risk

Sortino proposed an improvement on the Sharpe Ratio to better account for skill and excess performance by using only downside semivariance as the measure of risk. That measure is the SortinoRatio. This function, Upside Potential Ratio, was a further improvement, extending the measurement of only upside on the numerator, and only downside of the denominator of the ratio equation.

Sortino contends that risk should be measured in terms of not meeting the investment goal. This gives rise to the notion of “Minimum Acceptable Return” or MAR. All of Sortino's proposed measures include the MAR, and are more sensitive to downside or extreme risks than measures that use volatility(standard deviation of returns) as the measure of risk.

Choosing the MAR carefully is very important, especially when comparing disparate investment choices. If the MAR is too low, it will not adequately capture the risks that concern the investor, and if the MAR is too high, it will unfavorably portray what may otherwise be a sound investment. When comparing multiple investments, some papers recommend using the risk free rate as the MAR. Practitioners may wish to choose one MAR for consistency, several standardized MAR values for reporting a range of scenarios, or a MAR customized to the objective of the investor. $$ UPR=\frac{ \sum^{n}_{t=1} (R_{t} - MAR) }{ \delta_{MAR} } $$ where \(\delta_{MAR}\) is the DownsideDeviation.

The numerator in UpsidePotentialRatio only uses returns that exceed the MAR, and the denominator (in DownsideDeviation) only uses returns that fall short of the MAR by default. Sortino contends that this is a more accurate and balanced protrayal of return potential, wherase SortinoRatio can reward managers most at the peak of a cycle, without adequately penalizing them for past mediocre performance. Others have used the full series, and this is provided as an option by the method argument.

References

Sortino, F. and Price, L. Performance Measurement in a Downside Risk Framework. Journal of Investing. Fall 1994, 59-65.

Plantinga, A., van der Meer, R. and Sortino, F. The Impact of Downside Risk on Risk-Adjusted Performance of Mutual Funds in the Euronext Markets. July 19, 2001. Available at SSRN: http://ssrn.com/abstract=277352

See also

SharpeRatio SortinoRatio DownsideDeviation SemiVariance SemiDeviation InformationRatio

Examples

data(edhec)
UpsidePotentialRatio(edhec[, 6], MAR=.05/12) #5 percent/yr MAR
#>                               Event Driven
#> Upside Potential (MAR = 0.4%)    0.5376613
UpsidePotentialRatio(edhec[, 1:6], MAR=0)
#>                             Convertible Arbitrage CTA Global
#> Upside Potential (MAR = 0%)             0.4450702   1.174942
#>                             Distressed Securities Emerging Markets
#> Upside Potential (MAR = 0%)              0.646571        0.5684649
#>                             Equity Market Neutral Event Driven
#> Upside Potential (MAR = 0%)             0.5200563    0.6294689