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.
SortinoRatio(R, MAR = 0, ..., weights = NULL)
| 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 |
| … | any other passthru parameters |
| weights | portfolio weighting vector, default NULL |
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.
$$ SortinoRatio=\frac{(\overline{R_{a} - MAR})}{\delta_{MAR}} $$ where
\(\delta_{MAR}\) is the DownsideDeviation.
Sortino, F. and Price, L. Performance Measurement in a Downside Risk Framework. Journal of Investing. Fall 1994, 59-65.
SharpeRatio DownsideDeviation
SemiVariance SemiDeviation
InformationRatio
data(managers) round(SortinoRatio(managers[, 1]),4)#> HAM1 #> Sortino Ratio (MAR = 0%) 0.7649round(SortinoRatio(managers[, 1:8]),4)#> HAM1 HAM2 HAM3 HAM4 HAM5 HAM6 EDHEC LS EQ #> Sortino Ratio (MAR = 0%) 0.7649 1.222 0.7172 0.3234 0.1343 0.9102 0.9691 #> SP500 TR #> Sortino Ratio (MAR = 0%) 0.3064