sandbox/Shubhankit/noniid.sm/R/SterlingRatio.Norm.R

In naturalsmen/PerformanceAnalytics: Econometric Tools for Performance and Risk Analysis

#' @title Normalized Sterling Ratio
#'  
#' @description Normalized Sterling Ratio is  another method of creating a
#' risk-adjusted measure for ranking investments similar to the Sharpe Ratio.
#' 
#' @details 
#' Both the Normalized Sterling and the Calmar ratio are the ratio of annualized return
#' over the absolute value of the maximum drawdown of an investment. The
#' Sterling ratio adds an \bold{excess risk} measure to the maximum drawdown,
#' traditionally and defaulting to 10\%.
#' 
#' \deqn{Sterling Ratio  =   [Return over (0,T)]/[max Drawdown(0,T) - 10\%]}
#' It is also \emph{traditional} to use a three year return series for these
#' calculations, although the functions included here make no effort to
#' determine the length of your series.  If you want to use a subset of your
#' series, you'll need to truncate or subset the input data to the desired
#' length.
#' Malik Magdon-Ismail  impmemented a sclaing law for different \eqn{\mu ,\sigma and T}
#' @param R an xts, vector, matrix, data frame, timeSeries or zoo object of
#' asset returns
#' @param scale number of periods in a year (daily scale = 252, monthly scale =
#' 12, quarterly scale = 4)
#' @param excess for Sterling Ratio, excess amount to add to the max drawdown,
#' traditionally and default .1 (10\%)
#' @param tau parameter used for time translation
#' @author Brian G. Peterson , Peter Carl , Shubhankit Mohan
#' @references Bacon, Carl, Magdon-Ismail, M. and Amir Atiya,\emph{ Maximum drawdown. Risk Magazine,} 01 Oct 2004.
#' \url{http://www.cs.rpi.edu/~magdon/talks/mdd_NYU04.pdf}
#' @keywords ts multivariate distribution models
#' @examples
#' 
#'     data(managers)
#'     SterlingRatio.Norm(managers[,1,drop=FALSE])
#'     SterlingRatio.Norm(managers[,1:6]) 
#' @export 
#' @rdname SterlingRatio.Norm

SterlingRatio.Norm <-
  function (R, tau=1,scale=NA, excess=.1)
  { # @author Brian G. Peterson
    
    # DESCRIPTION:
    # Inputs:
    # Ra: in this case, the function anticipates having a return stream as input,
    #    rather than prices.
    # scale: number of periods per year
    # Outputs:
    # This function returns a Sterling Ratio
    
    # FUNCTION:
    Time = nyears(R)
    R = checkData(R)
    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}
      )
    }
    annualized_return = Return.annualized(R, scale=scale)
    drawdown = abs(maxDrawdown(R)+excess)
    result = annualized_return/drawdown*(QP.Norm(R,Time)/QP.Norm(R,tau))*(tau/Time)
    rownames(result) = paste("Normalized Sterling Ratio (Excess = ", round(excess*100,0), "%)", sep="")
    return(result)
  }