PerformanceAnalytics (version 2.0.4)

# VolatilitySkewness: Volatility and variability of the return distribution

## Description

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.

## Usage

VolatilitySkewness(R, MAR = 0, stat = c("volatility", "variability"), ...)

## 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

stat

one of "volatility", "variability" indicating whether to return the volatility skewness or the variability skweness

any other passthru parameters

## Details

$$VolatilitySkewness(R , MAR) = \frac{\sigma_U^2}{\sigma_D^2}$$

$$VariabilitySkewness(R , MAR) = \frac{\sigma_U}{\sigma_D}$$

where $$\sigma_U$$ is the Upside risk and $$\sigma_D$$ is the Downside Risk

## References

Carl Bacon, Practical portfolio performance measurement and attribution, second edition 2008 p.97-98

## Examples

# NOT RUN {
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"))

# }