[Returnanalytics-commits] r2165 - pkg/PortfolioAnalytics/sandbox/attribution/R

[noreply at r-forge.r-project.org]

Author: ababii
Date: 2012-07-16 13:30:54 +0200 (Mon, 16 Jul 2012)
New Revision: 2165

Added:
   pkg/PortfolioAnalytics/sandbox/attribution/R/AppraisalRatio.R
Log:
- Appraisal Ratio

Added: pkg/PortfolioAnalytics/sandbox/attribution/R/AppraisalRatio.R
===================================================================
--- pkg/PortfolioAnalytics/sandbox/attribution/R/AppraisalRatio.R	                        (rev 0)
+++ pkg/PortfolioAnalytics/sandbox/attribution/R/AppraisalRatio.R	2012-07-16 11:30:54 UTC (rev 2165)
@@ -0,0 +1,72 @@
+#' Apraisal ratio = alpha / residual return
+#' 
+#' The alpha from CAPM divided by the standard deviation of residuals
+#' 
+#' \deqn{A_{p}=\frac{\alpha_{p}}{\sigma(\varepsilon_{p})}}{Ap = alphap / 
+#' sigmap(epsilonp)}
+#' 
+#' Is appropriate for evaluating security selection ability. It captures the 
+#' idea that an active portfolio manager has t odepart from the benchmark, that
+#' is, take on residual risk, in order to produce alpha. The more alpha the 
+#' investor produces for a given amout of residual risk, the higher the ratio.
+#' 
+#' @param Ra an xts, vector, matrix, data frame, timeSeries or zoo object of
+#' the asset returns
+#' @param Rb an xts, vector, matrix, data frame, timeSeries or zoo object of 
+#' the benchmark asset return
+#' @param Rf risk free rate, in same period as your returns
+#' @param \dots any other passthrough parameters
+#' @author Andrii Babii
+#' @seealso \code{\link{InformationRatio}}
+#' @references J. Christopherson, D. Carino, W. Ferson. \emph{Portfolio 
+#' Performance Measurement and Benchmarking}. 2009. McGraw-Hill, p. 101. \cr
+#' Jack Treynor and Fischer Black, "How t oUse Security Analysis to Improve 
+#' Portfolio Selection," \emph{Journal of Business}, vol.46, no.1, 
+#' January 1973, pp. 66-86. \cr
+#' 
+#' @examples
+#' 
+#' data(managers)
+#' AppraisalRatio(managers[,1,drop=FALSE], managers[,8,drop=FALSE], Rf=.035/12)
+#' AppraisalRatio(managers[80:120,1:6], managers[80:120,7,drop=FALSE], managers[80:120,10,drop=FALSE])
+#' AppraisalRatio(managers[80:120,1:6], managers[80:120,8:7], managers[80:120,10,drop=FALSE])
+#' 
+#' @export
+AppraisalRatio <- function (Ra, Rb, Rf = 0, ...)
+{ # @author Andrii Babii
+    
+    # DESCRIPTION
+    # AppraisalRatio = alpha / residual return
+  
+    # FUNCTION
+  
+    Ra = checkData(Ra)
+    Rb = checkData(Rb)
+    if (!is.null(dim(Rf))) 
+      Rf = checkData(Rf)
+    Ra.ncols = NCOL(Ra)
+    Rb.ncols = NCOL(Rb)
+    pairs = expand.grid(1:Ra.ncols, 1:Rb.ncols)
+    
+    ar <- function (Ra, Rb, Rf)
+    {
+      alpha = CAPM.alpha(Ra, Rb, Rf)
+      beta = CAPM.beta(Ra, Rb, Rf)
+      epsilon = Ra - Rf - rep(alpha, nrow(Ra)) - beta %x% Rb
+      sigma = diag(t(epsilon) %*% epsilon) / (length(managers) - 2)
+      AR = alpha / sigma
+      return(AR)
+    }
+      
+    result = apply(pairs, 1, FUN = function(n, Ra, Rb, Rf) 
+      ar(Ra[, n[1]], Rb[, n[2]], Rf), Ra = Ra, Rb = Rb, Rf = Rf)
+    
+    if(length(result) == 1)
+      return(result)
+    else {
+      result = matrix(result, ncol = Ra.ncols, nrow = Rb.ncols, byrow = TRUE)
+      rownames(result) = paste("Appraisal Ratio:", colnames(Rb))
+      colnames(result) = colnames(Ra)
+      return(result)
+    }
+}