Volatility and variability of the return distribution
Volatility skewness is a similar measure to omega but using the second partial moment. It's the ratio of the upside variance compared to the downside variance. Variability skewness is the ratio of the upside risk compared to the downside risk.
VolatilitySkewness(R, MAR = 0, stat = c("volatility", "variability"), ...)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 |
stat |
one of "volatility", "variability" indicating whether to return the volatility skewness or the variability skweness |
... |
any other passthru parameters |
VolatilitySkewness(R, MAR) = UpsideVariance / DownsideVariance
VariabilitySkewness(R, MAR) = UpsideRisk / DownsideRisk
where σ_U is the Upside risk and σ_D is the Downside Risk
Matthieu Lestel
Carl Bacon, Practical portfolio performance measurement and attribution, second edition 2008 p.97-98
data(portfolio_bacon) MAR = 0.005 print(VolatilitySkewness(portfolio_bacon[,1], MAR, stat="volatility")) #expected 1.32 print(VolatilitySkewness(portfolio_bacon[,1], MAR, stat="variability")) #expected 1.15 MAR = 0 data(managers) # print(VolatilitySkewness(managers['1996'], MAR, stat="volatility")) print(VolatilitySkewness(managers['1996',1], MAR, stat="volatility"))
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