calculate Ekholm ActiveAlpha , ActiveBeta , SelectionShare , TimingShare in R

Readme.md

Anders Ekholm's Decomposition of Mutual Fund Returns

Calculate Ekholm SelctionShare & TimingShare in R based on TimelyPortfolio post SelectionShare & TimingShare | Masterfully Written by Delightfully Responsive Author.

Example with Fidelity Contrafund (FCNTX)

library(Quandl)
library(xts)
library(pipeR)

# get function from this gist
source(paste0(
  "https://gist.githubusercontent.com/timelyportfolio/e5728c8c7fb45dbdb6e0",
  "/raw/e124379f19225fcdee18f30cb848da6fc6cae764/ekholm.R"
))

f <- Quandl("KFRENCH/FACTORS_D",type = "xts") / 100

"FCNTX" %>>%
  getSymbols( from = "1896-01-01", auto.assign = F ) %>>%
  ( 
    structure(
      ROC( .[,6], n = 1, type  = "discrete" )
      ,dimnames = list(
        NULL
        ,gsub(x = colnames(.)[6], pattern  = "[\\.]Adjusted", replacement = "")
      )
    )
  ) %>>%
  merge(f) %>>% # Quandl("KFRENCH/FACTORS_D",type = "xts") / 100
  na.omit %>>%
  jensen_ekholm

ekholm.R

# see post http://timelyportfolio.blogspot.com/2014/10/selectionshare-timingshare-masterfully.html

###### bibliography / reference ##############################################
# perform Ekholm (2012,2014) analysis on mutual fund return data

# Ekholm, A.G., 2012
# Portfolio returns and manager activity:
#    How to decompose tracking error into security selection and market timing
# Journal of Empirical Finance, Volume 19, pp 349-358

# Ekholm, Anders G., July 21, 2014
# Components of Portfolio Variance:
#    R2, SelectionShare and TimingShare
# Available at SSRN: http://ssrn.com/abstract=2463649
##############################################################################

# return a list with
# 1. a data.frame of ActiveAlpha, ActiveBeta, SelectionShare, and TimingShare
# 2. the first linear regression
jensen_ekholm <- function( data, ticker = NULL ){
  
  library(pipeR)
  
  if(is.null(ticker)) ticker <- colnames(data)[1]

  # subtract risk free from manager return
  # not sure if better to assume already done or not
  data[,ticker] <- data[,ticker] - data[,"RF"]
  
  # convert a guessed Mkt.Rf to Mkt.Rf to standardize
  colnames(data)[grep(x=colnames(data),pattern="[Mkt,mkt,MKT][-,~,\\.][Rf,RF,rf]")] = "Mkt.RF"
  
  as.formula ( paste0(ticker, " ~  Mkt.RF" ) ) %>>%
    ( lm( data = data, . ) -> jensenLM )
  
  jensenLM %>>%
    residuals %>>%
    (. ^ 2 ) %>>%
    (
      data.frame(
        data
        , "fitted_sq" = .
        , lapply(data[,2],function(x){
          structure(
            data.frame( as.numeric(x) ^ 2 )
            , names = paste0(names(x),"_sq")
          ) %>>%
            return
        }) %>>% ( do.call( cbind, . ) )
      ) -> return_data_jensen
    )
  
  return_data_jensen %>>%
    ( lm( fitted_sq ~ Mkt.RF_sq, data = . ) )%>>%
    coefficients %>>%
    ( . ^ (1/2) ) %>>%
    t %>>%
    (
      structure(
        data.frame(.),
        names = c("ActiveAlpha", paste0("ActiveBeta_",colnames(.)[-1]))
      )
    ) %>>% 
    (
      data.frame(
        .
        , "SelectionShare" = .$ActiveAlpha ^ 2 / (var(return_data_jensen[,ticker]) * (nrow(return_data_jensen) - 1) / nrow(return_data_jensen))
        , "TimingShare" = .$ActiveBeta_Mkt.RF_sq ^ 2* mean( return_data_jensen$Mkt.RF_sq ) / (var(return_data_jensen[,ticker]) * (nrow(return_data_jensen) - 1) / nrow(return_data_jensen))
      )
    ) %>>%
    (
      list( "ekholm" = ., "linmod" = jensenLM )
    ) %>>%
    return
}