upside risk, variance and potential of the return distribution

Upside Risk is the similar of semideviation taking the return above the Minimum Acceptable Return instead of using the mean return or zero. To calculate it, we take the subset of returns that are more than the target (or Minimum Acceptable Returns (MAR)) returns and take the differences of those to the target. We sum the squares and divide by the total number of returns and return the square root.

UpsideRisk(R, MAR = 0, method = c("full", "subset"), stat = c("risk",
  "variance", "potential"), ...)

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 below the MAR as the denominator, defaults to "full"
stat	one of "risk", "variance" or "potential" indicating whether to return the Upside risk, variance or potential
…	any other passthru parameters

Details

$$ UpsideRisk(R , MAR) = \sqrt{\sum^{n}_{t=1}\frac{ max[(R_{t} - MAR), 0]^2}{n}}$$ $$ UpsideVariance(R, MAR) = \sum^{n}_{t=1}\frac{max[(R_{t} - MAR), 0]^2} {n}$$ $$UpsidePotential(R, MAR) = \sum^{n}_{t=1}\frac{max[(R_{t} - MAR), 0]} {n}$$

where \(n\) is either the number of observations of the entire series or the number of observations in the subset of the series falling below the MAR.

References

Carl Bacon, Practical portfolio performance measurement and attribution, second edition 2008

Examples

data(portfolio_bacon)
MAR = 0.005
print(UpsideRisk(portfolio_bacon[,1], MAR, stat="risk")) #expected 0.02937
#> [1] 0.02937332
print(UpsideRisk(portfolio_bacon[,1], MAR, stat="variance")) #expected 0.08628
#> [1] 0.0008627917
print(UpsideRisk(portfolio_bacon[,1], MAR, stat="potential")) #expected 0.01771
#> [1] 0.01770833

MAR = 0
data(managers)
print(UpsideRisk(managers['1996'], MAR, stat="risk"))
#>                              HAM1       HAM2       HAM3      HAM4 HAM5 HAM6
#> Upside Risk (MAR = 0%) 0.01799111 0.05916453 0.04002169 0.0321782    0    0
#>                        EDHEC LS EQ   SP500 TR  US 10Y TR    US 3m TR
#> Upside Risk (MAR = 0%)           0 0.03204533 0.01397565 0.004324785
print(UpsideRisk(managers['1996',1], MAR, stat="risk")) #expected 1.820
#> [1] 0.01799111