M squared excess of the return distribution
M squared excess is the quantity above the standard M. There is a geometric excess return which is better for Bacon and an arithmetic excess return
MSquaredExcess(Ra, Rb, Rf = 0, Method = c("geometric", "arithmetic"), ...)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 |
Method |
one of "geometric" or "arithmetic" indicating the method to use to calculate MSquareExcess |
... |
any other passthru parameters |
MSquared excess (geometric) = (1+M^2)/(1+b) - 1
MSquared excess (arithmetic) = M^2 - b
where M^2 is MSquared and b is the benchmark annualised return.
Matthieu Lestel
Carl Bacon, Practical portfolio performance measurement and attribution, second edition 2008 p.68
data(portfolio_bacon) MSquaredExcess(portfolio_bacon[,1], portfolio_bacon[,2]) #expected -0.00998 MSquaredExcess(portfolio_bacon[,1], portfolio_bacon[,2], Method="arithmetic") #expected -0.011 data(managers) MSquaredExcess(managers['1996',1], managers['1996',8]) MSquaredExcess(managers['1996',1:5], managers['1996',8])
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