R/SharpeRatio.annualized.R

In PerformanceAnalytics: Econometric Tools for Performance and Risk Analysis

#' calculate annualized Sharpe Ratio
#' 
#' The Sharpe Ratio is a risk-adjusted measure of return that uses standard
#' deviation to represent risk.
#' 
#' The Sharpe ratio is simply the return per unit of risk (represented by
#' variance).  The higher the Sharpe ratio, the better the combined performance
#' of "risk" and return.
#' 
#' This function annualizes the number based on the scale parameter.
#' 
#' \deqn{\frac{\sqrt[n]{prod(1+R_{a})^{scale}}-1}{\sqrt{scale}\cdot\sqrt{\sigma}}}
#' 
#' Using an annualized Sharpe Ratio is useful for comparison of multiple return
#' streams.  The annualized Sharpe ratio is computed by dividing the annualized
#' mean monthly excess return by the annualized monthly standard deviation of
#' excess return.
#' 
#' William Sharpe now recommends Information Ratio preferentially to the
#' original Sharpe Ratio.
#' 
#' @param R an xts, vector, matrix, data frame, timeSeries or zoo object of
#' asset returns
#' @param Rf risk free rate, in same period as your returns
#' @param scale number of periods in a year (daily scale = 252, monthly scale =
#' 12, quarterly scale = 4)
#' @param geometric utilize geometric chaining (TRUE) or simple/arithmetic chaining (FALSE) to aggregate returns,
#' default TRUE
#' @author Peter Carl
#' @seealso \code{\link{SharpeRatio}} \cr \code{\link{InformationRatio}} \cr
#' \code{\link{TrackingError}} \cr \code{\link{ActivePremium}} \cr
#' \code{\link{SortinoRatio}}
#' @references Sharpe, W.F. The Sharpe Ratio,\emph{Journal of Portfolio
#' Management},Fall 1994, 49-58.
###keywords ts multivariate distribution models
#' @examples
#' 
#' data(managers)
#' SharpeRatio.annualized(managers[,1,drop=FALSE], Rf=.035/12) 
#' SharpeRatio.annualized(managers[,1,drop=FALSE], Rf = managers[,10,drop=FALSE])
#' SharpeRatio.annualized(managers[,1:6], Rf=.035/12) 
#' SharpeRatio.annualized(managers[,1:6], Rf = managers[,10,drop=FALSE])
#' SharpeRatio.annualized(managers[,1:6], Rf = managers[,10,drop=FALSE],geometric=FALSE)
#' 
#' @export
SharpeRatio.annualized <-
function (R, Rf = 0, scale = NA, geometric=TRUE)
{ # @author Peter Carl

    # DESCRIPTION:

    # Using an annualized Sharpe Ratio is useful for comparison.  The annualized
    # Sharpe ratio is computed by dividing the annualized mean monthly excess
    # return by the annualized monthly standard deviation of excess return.

    # @todo: monthly standard deviation of ***excess*** return

    # Inputs:
    # R: in this case, the function anticipates having a return stream as input,
    #     rather than prices.
    # Rf: the risk free rate MUST be in the same periodicity as the data going in.

    # FUNCTION:
    R = checkData(R)
    if(!is.null(dim(Rf)))
        Rf = checkData(Rf)

    if(is.na(scale)) {
        freq = periodicity(R)
        switch(freq$scale,
            minute = {stop("Data periodicity too high")},
            hourly = {stop("Data periodicity too high")},
            daily = {scale = 252},
            weekly = {scale = 52},
            monthly = {scale = 12},
            quarterly = {scale = 4},
            yearly = {scale = 1}
        )
    }

    sr <-function (R, Rf, scale)
    {
        xR = Return.excess(R, Rf)
        SR = Return.annualized(xR, scale=scale, geometric=geometric)/StdDev.annualized(R, scale=scale)
        SR
    }

    result = sapply(R, sr, Rf=Rf, scale=scale)
    dim(result) = c(1,NCOL(R))
    colnames(result) = colnames(R)
    rownames(result) = paste("Annualized Sharpe Ratio (Rf=", round(mean(Rf)*scale*100,1), "%)", sep="")
    return (result)

}

###############################################################################
# R (http://r-project.org/) Econometrics for Performance and Risk Analysis
#
# Copyright (c) 2004-2020 Peter Carl and Brian G. Peterson
#
# This R package is distributed under the terms of the GNU Public License (GPL)
# for full details see the file COPYING
#
# $Id$
#
###############################################################################