PerformanceAnalytics (version 1.1.0)

MSquared: M squared of the return distribution

Description

M squared is a risk adjusted return useful to judge the size of relative performance between differents portfolios. With it you can compare portfolios with different levels of risk.

Usage

MSquared(Ra, Rb, Rf = 0, ...)

Arguments

Ra

an xts, vector, matrix, data frame, timeSeries or zoo object of asset return

Rb

return vector of the benchmark asset

Rf

risk free rate, in same period as your returns

...

any other passthru parameters

Details

$$M^2 = r_P + SR * (\sigma_M - \sigma_P) = (r_P - r_F) * \frac{\sigma_M}{\sigma_P} + r_F$$

where $r_P$ is the portfolio return annualized, $\sigma_M$ is the market risk and $\sigma_P$ is the portfolio risk

References

Carl Bacon, Practical portfolio performance measurement and attribution, second edition 2008 p.67-68

Examples

data(portfolio_bacon)
print(MSquared(portfolio_bacon[,1], portfolio_bacon[,2])) #expected 0.1068

data(managers)
print(MSquared(managers['1996',1], managers['1996',8]))
print(MSquared(managers['1996',1:5], managers['1996',8]))