MSquared {PerformanceAnalytics}

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

Author(s)

Matthieu Lestel

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 0.10062

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