% Generated by roxygen2: do not edit by hand

% Please edit documentation in R/MSquaredExcess.R

\name{MSquaredExcess}

\alias{MSquaredExcess}

\title{M squared excess of the return distribution}

\usage{

MSquaredExcess(Ra, Rb, Rf = 0, Method = c("geometric", "arithmetic"), ...)

}

\arguments{

\item{Ra}{an xts, vector, matrix, data frame, timeSeries or zoo object of

asset return}

\item{Rb}{return vector of the benchmark asset}

\item{Rf}{risk free rate, in same period as your returns}

\item{Method}{one of "geometric" or "arithmetic" indicating the method to use

to calculate MSquareExcess}

\item{\dots}{any other passthru parameters}

}

\description{

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

}

\details{

\deqn{M^2 excess (geometric) = \frac{1 + M^2}{1 + b} - 1}{MSquared excess (geometric) = (1+M^2)/(1+b) - 1}

\deqn{M^2 excess (arithmetic) = M^2 - b}{MSquared excess (arithmetic) = M^2 - b}

where \eqn{M^2} is MSquared and \eqn{b} is the benchmark annualised return.

}

\examples{

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])

}

\references{

Carl Bacon, \emph{Practical portfolio performance measurement

and attribution}, second edition 2008 p.68

}

\author{

Matthieu Lestel

}