# 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"))
# }