[Uwgarp-commits] r93 - pkg/GARPFRM/sandbox
noreply at r-forge.r-project.org
noreply at r-forge.r-project.org
Mon Feb 24 17:51:52 CET 2014
Author: mllabovitz
Date: 2014-02-24 17:51:52 +0100 (Mon, 24 Feb 2014)
New Revision: 93
Modified:
pkg/GARPFRM/sandbox/test_performance_measure.r
Log:
Revision 2_24_2014 Making some of changes suggested by Ross as well as computing some of results using Lipper methodology
Modified: pkg/GARPFRM/sandbox/test_performance_measure.r
===================================================================
--- pkg/GARPFRM/sandbox/test_performance_measure.r 2014-02-21 21:01:08 UTC (rev 92)
+++ pkg/GARPFRM/sandbox/test_performance_measure.r 2014-02-24 16:51:52 UTC (rev 93)
@@ -1,302 +1,368 @@
-# 'Load the GARPFRM package and the CAPM dataset.
-suppressMessages(library(GARPFRM))
-options(digits=3)
-data(crsp.short)
-stock_rets.df <- largecap.ts
-Measures = rep(NULL,4)
-
-## keep it simple and use this thoughout
-## no need to transform to zoo, matrix, or df objects
-# Equal weight portfolio
-R.portfolio <- Return.portfolio(largecap.ts[, 1:5])
-
-# Market returns
-R.market <- largecap.ts[, "market"]
-
-# risk free rate
-rf <- largecap.ts[, "t90"]
-##
-
-# Definitioned/Constant variables
-relation = c("Less Than","Equal To","Greater Than")
-
-# Some of run time parameters
-# Should be amongst the input for shiny
-# Minimum Acceptable Return for Sortino Ratio or Downside Deviation
-# defaults to 0
-MAR_set = 0
-
-# Denominator for Sortino Ratio or Downside Deviation
-# one of "full" or "subset", indicating whether to use the length of the full series
-# or the length of the subset of the series below the MAR as the denominator,
-# defaults to "full"
-denom = "full"
-
-# Portfolio name used in output
-PortName = "Portfolio"
-
-# Market name used in output
-MrktName ="Market"
-
-#Market Name in data set
-mrktDataName = "market"
-
-# Risk free rate name used in output
-RFName="Risk_Free_Rate"
-
-# Risk Free Name in data set
-rfDataName = "t90"
-
-Measures = rbind(Measures, c("Series Name",PortName,MrktName,RFName))
-colnames(Measures) = c("Measure","Portfolio","Market","RiskFree")
-
-# List column headers predominantly tickers/name of securities
-
-# Summarize the first and last data values corresponding to the first 5 dates for the first 5 returns.
-
-colnames(stock_rets.df)
-head(stock_rets.df)
-tail(stock_rets.df)
-
-
-# Number time periods for year for data set
-freQ = 12
-
-# Estimate a zooreg object: regularly spaced zoo object.
-#
-stock.z = zooreg(stock_rets.df[,-1], start=c(1993, 1), end=c(2013,11),
- frequency=freQ)
-
-index(stock.z) = as.yearmon(index(stock.z))
-
-# Summarize Start, End, and Number of Rows
-start(stock.z)
-end(stock.z)
-nRow = nrow(stock.z)
-nRow
-
-# pointer to column with the market returns
-ptrMkt = which(colnames(stock.z)==mrktDataName,arr.ind=TRUE)
-ptrMkt
-# pointer to column of Risk Free Ratw
-ptrRF = which(colnames(stock.z)==rfDataName,arr.ind=TRUE)
-ptrRF
-
-# as.data.frame to check if an object is a data frame, or coerce it if possible.
-returns.mat = as.matrix(coredata(stock.z))
-
-# Number of time series in data set
-nSec = ncol(returns.mat)
-
-# Random create a portfolio from the non-market non RF series
-# Get a normalized set of weights
-# Could set up the application to create a random portfolio from a subset or
-# Input specific securities and weights
-coefs = runif(nSec-2)
-alphas = coefs/sum(coefs)
-sum(alphas)
-
-
-portfolio = returns.mat[,1:(nSec-2)]%*%as.vector(alphas)
-colnames(portfolio) ="PortRets"
-
-salient = matrix(data=c("Mean",mean(portfolio),mean(returns.mat[,ptrMkt]),mean(returns.mat[,ptrRF]),
- "Stdev",sd(portfolio),sd(returns.mat[,ptrMkt]),sd(returns.mat[,ptrRF]),
- "AnnuallyFrequency",rep(freQ,3),
- "Number of Samples",rep(nRow,3)),nrow=4,ncol=4,byrow=TRUE)
-
-Measures = rbind(Measures, salient)
-
-
-# Start to compute performance measures using performance analytic and as a check
-# compute from underlying formula
-
-# Some of comparison match, but some are inexplicable different.
-# Really should investigate the latter, I am sure the users will do so
-
-# Compute beta
-beta = cov(portfolio[,1],returns.mat[,ptrMkt])/var(returns.mat[,ptrMkt])
-cat('\n Beta =',beta,', between the portfolio represented by ',PortName,' and the market represented by ',MrktName,' \n')
-
-Measures = rbind(Measures,c("Beta",beta,"",""))
-
-# Compute Treynor
-
- # Performance Analytics (PA) computation of Treynor for portfolio and market
-tr = TreynorRatio(portfolio[,1,drop=FALSE], returns.mat[,ptrMkt,drop=FALSE],returns.mat[,ptrRF,drop=FALSE],freQ )
-trMarket = TreynorRatio(returns.mat[,ptrMkt,drop=FALSE], returns.mat[,ptrMkt,drop=FALSE],returns.mat[,ptrRF,drop=FALSE],freQ )
-
- # From formula (Hand) computation of Treynor for portfolio and market
-trHand = freQ*(mean(portfolio[,1])-mean(returns.mat[,ptrRF]))/beta
-# beta of Treynor for market is 1
-trHandM = freQ*(mean(returns.mat[,ptrMkt])-mean(returns.mat[,ptrRF]))
-
- # Output results from Treynor Ratio computation
-cat('\n PA computed for ',PortName,' Treynor Ratio = ',tr,'\n')
-cat('\n Hand computed for ',PortName,' Treynor Ratio = ',trHand,'\n')
-cat('\n PA computed for ',MrktName,' Treynor Ratio = ',trMarket,'\n')
-cat('\n Hand computed for ',MrktName,' Treynor Ratio = ',trHandM,'\n')
-
-Measures = rbind(Measures,c("Treynor Ratio",tr,trMarket,""))
-
- # Compare Treynor Ratio for market returns against Treynor Ratio for portfolio returns
-cat('\n Treynor Ratio of ',MrktName,' is ',relation[sign(trMarket - tr) + 2],' Treynor Ratio of ',PortName,'\n' )
-TR_Mrkt2Port = relation[sign(trMarket - tr) + 2]
-
-##
-# calculate excess returns of R.portfolio
-R.portfolio.x <- R.portfolio - rf
-
-# calculate excess returns of R.market
-R.market.x <- R.market - rf
-
-# run regression to get beta
-fit <- lm(R.portfolio.x ~ R.market.x)
-beta.lm <- coef(fit)[2]
-
-# calculate beta another way
-beta <- as.numeric(cov(R.portfolio.x, R.market.x) / var(R.market.x))
-
-# Annualized portfolio excess returns / beta
-# This should match the TreynorRatio from PerformanceAnalytics
-TR.rb <- as.numeric(Return.annualized(R.portfolio.x) / beta.lm)
-
-as.numeric(Return.annualized(R.portfolio.x) / beta)
-
-# Calcualte Treynor Ratio with PerformanceAnalytics
-TR.PA <- TreynorRatio(R.portfolio, R.market, rf)
-
-all.equal(TR.rb, TR.PA)
-cat("Treynor Ratio by hand: ", TR.rb, "\n")
-cat("Treynor Ratio with PerformanceAnalytics: ", TR.PA, "\n")
-##
-
-# Compute Sharpe
-
- # PA computation of Sharpe
-shr = SharpeRatio(portfolio[,1,drop=FALSE], returns.mat[,ptrRF,drop=FALSE], p = 0.95,
-FUN = "StdDev")
-
- # Compute excess portfolio returns (portfolio returns net of RF returns)
-xCess = portfolio[,1] - returns.mat[,ptrRF]
- # Hand computation of Sharpe
-shrHand = mean(xCess)/sd(xCess)
-
- # Output results from Sharpe Ratio computation
-cat('\n PA computed ',PortName,' Sharpe Ratio = ',shr,'\n')
-cat('\n Hand computed ',PortName,' Sharpe Ratio = ',shrHand,'\n')
-
-Measures = rbind(Measures,c("Sharpe Ratio",shr,"",""))
-
-# Compute Jensen's Alpha
-
- # Mean of risk free rate over sampling time series
-meanRF = mean(returns.mat[,ptrRF])
-
- # PA computation of Jensen's Alpha
-ja = CAPM.jensenAlpha(portfolio[,1,drop=FALSE], returns.mat[,ptrMkt,drop=FALSE],meanRF)
-
-# Hand computation of Jensen's Alpha using regression apprach
-
-
- # Precompute excess returns
-## The risk-free rate varies through time so just computing the mean
-## is oversimplifying and could be part of the reason for the differences
-## you are seeing between your hand calculation and PerformanceAnalytics
-xCessP1 = portfolio[,1]-meanRF
-xCessM1 = returns.mat[,ptrMkt]-meanRF
-
- # Regression computation and salient results
-lm_ja1.fit = lm(xCessP1 ~ xCessM1)
-values1 = summary(lm_ja1.fit)
-values1
-analT1 = values1[[4]]
-
- # Annualize Jensen's Alpha
-jaHand = (1+(mean(portfolio[,1]) - meanRF - beta*(mean(returns.mat[,ptrMkt])-meanRF)))^12 -1
-
- # Use Delta Method to approximate standard error of analyzed Jensen's Alpha
-deltaCoef = (freQ*(1+analT1[1,1])^(freQ-1))^2
-
- # Output salient results for Jensen's Alpha
-cat('\n PA computed ',PortName,' Jensen\'s Alpha = ',ja,'\n')
-cat('\n Regression computed ',PortName,' Jensen\'s Alpha, Not Annualized= ',analT1[1,1],'\n')
-cat('\n Hand computed Annualized ',PortName,' Jensen Alpha = ',jaHand,'\n')
-cat('\n Delta Method Coefficient Value = ', deltaCoef,'\n')
-
- # t stat and pvalue under H0: alpha = 0 against HA: alpha != 0
-tStat = jaHand/(analT1[1,2]*deltaCoef^0.5)
-pValue = 2*(1-pt(tStat,nRow-2))
-cat('\n H0: alpha = 0, HA: alpha != 0 p-value: ',pValue,'\n')
-
-Measures = rbind(Measures,c("Jensen's Alpha",ja,"",""))
-Measures = rbind(Measures,c("Jensen's Alpha P Value",pValue,"",""))
-
-# Compute Tracking Error
-
- # PA computation of Tracking Error
-te = TrackingError(portfolio[,1,drop=FALSE], returns.mat[,ptrMkt,drop=FALSE], scale = freQ)
-
- # Precompute required values to computr Tracking Error by Hand
-RR = portfolio[,1]-returns.mat[,ptrMkt]
-ARR = mean(RR)
-
- # Hand computation of Tracking Error
-teHand = sqrt(sum((RR-ARR)^2)/(nRow-1))*sqrt(freQ)
-
- # Output results from Tracking Error computation
-cat('\n PA computed ',PortName,' Tracking Error = ',te,'\n')
-cat('\n Hand computed ', PortName,' Tracking Error = ',teHand,'\n')
-
-Measures = rbind(Measures,c("Tracking Error",te,"",""))
-
-# Compute Information Ratio
-
- # PA computation of Information Ratio
-ir = InformationRatio(portfolio[,1,drop=FALSE], returns.mat[,ptrMkt,drop=FALSE], scale = freQ)
-
- # Hand computation of Information Ratio
-irHand = (ARR/(sqrt(sum((RR-ARR)^2)/(nRow-1))))*sqrt(freQ)
-
- # Output results from Information Ratio computation
-cat('\n PA computed ',PortName,' Information Ratio = ',ir,'\n')
-cat('\n Hand computed ',PortName,' Information Ratio = ',irHand,'\n')
-
-Measures = rbind(Measures,c("Information Ratio",ir,"",""))
-
-# Compute Sortino Ratio (including Downside Deviation)
-
- # PA computation of Sortino Ratio
-sr = SortinoRatio(portfolio[,1,drop=FALSE], MAR = MAR_set, weights = NULL)
-
- # Set value of denominator for Downside Deviation from the parameter denom set earlier
-denomVal = nRow
-if (denom != "full")
- {
- denomVal = sum(ifelse((portfolio[,1] - MAR_set)<0,1,0))
- }
-cat('\n Denominator parameter is set to: ',denom,' which results in a denominator value of ',denomVal,'\n')
-
- # PA computation of Downside Deviation
-dwn = DownsideDeviation(portfolio[,1], MAR = MAR_set, method = "full")
-
- # Hand computation of Downside Deviation
-dwnHand = sqrt(sum((min((portfolio[,1,drop=FALSE] - MAR_set),0))^2)/(denomVal))
-
- # Output computation of Downside Deviation
-cat('\n PA computed ',PortName,' Downside Deviation = ',dwn,'\n')
-cat('\n Hand computed ',PortName,' Downside Deviation = ',dwnHand,'\n')
-
- # Hand computation of Sortino Ratio
-srHand = sqrt(freQ)*ARR/dwn
-
- # Output computation of Sortino Ratio
-cat('\n PA computed ',PortName,' Sortino Ratio = ',sr,'\n')
-cat('\n Hand computed ',PortName,' Sortino Ratio = ',srHand,'\n')
-
-Measures = rbind(Measures,c("Downside Deviation",dwn,"",""))
-Measures = rbind(Measures,c("Denominator DD",denomVal,"",""))
-Measures = rbind(Measures,c("Sortino Ratio",sr,"",""))
-Measures.df= as.data.frame(Measures,stringsAsFactors=FALSE)
-
-print(Measures.df)
+# 'Load the GARPFRM package and the CAPM dataset.
+suppressMessages(library(GARPFRM))
+options(digits=5)
+data(crsp.short)
+
+# Make the assumption that the last two time series are the Market and RF series
+
+#stock_rets.df <- largecap.ts
+
+# Store results
+Measures = rep(NULL,4)
+
+
+
+# If equalWts is true portfolio weights will be 1/numberOfSecurities
+equalWts = TRUE
+
+randWts = TRUE
+if(equalWts) randWts = FALSE
+
+# Number of securities to use is
+numberOfSecurities = 3
+
+# type of chaining in forming the aggregate return
+# If geometric is TRUE use geometric chaining if False use arithemetic chaining
+geometricB = TRUE
+
+# Definitioned/Constant variables
+relation = c("Less Than","Equal To","Greater Than")
+
+# Some of run time parameters
+# Should be amongst the input for shiny
+# Minimum Acceptable Return for Sortino Ratio or Downside Deviation
+# defaults to 0
+MAR_set = 0
+
+# Denominator for Sortino Ratio or Downside Deviation
+# one of "full" or "subset", indicating whether to use the length of the full series
+# or the length of the subset of the series below the MAR as the denominator,
+# defaults to "full"
+denom = "full"
+
+# Portfolio name used in output
+PortName = "Portfolio"
+
+# Market name used in output
+MrktName ="Market"
+
+#Market Name in data set
+mrktDataName = "market"
+
+# Risk free rate name used in output
+RFName="Risk_Free_Rate"
+
+# Risk Free Name in data set
+rfDataName = "t90"
+
+Measures = rbind(Measures, c("Series Name",PortName,MrktName,RFName))
+colnames(Measures) = c("Measure","Portfolio","Market","RiskFree")
+
+# List column headers predominantly tickers/name of securities
+
+# Summarize the first and last data values corresponding to the first 5 dates for the first 5 returns.
+
+colnames(largecap.ts)
+head(largecap.ts)
+tail(largecap.ts)
+
+# Number time periods for year for data set
+freQ = 12
+
+
+
+nRow = nrow(largecap.ts)
+nRow
+
+# pointer to column with the market returns
+# ptrMkt = which(colnames(stock.z)==mrktDataName,arr.ind=TRUE)
+ptrMkt = which(colnames(largecap.ts)==mrktDataName,arr.ind=TRUE)
+ptrMkt
+# pointer to column of Risk Free Ratw
+ptrRF = which(colnames(largecap.ts)==rfDataName,arr.ind=TRUE)
+ptrRF
+
+# Market returns
+R.market <- largecap.ts[, ptrMkt]
+
+# risk free rate
+rf <- largecap.ts[, ptrRF]
+##
+
+
+# Number of time series in data set
+nSec = ncol(largecap.ts)
+
+if (numberOfSecurities>(nSec-2)) numberOfSecurities = nSec - 2
+cat('\n Number of Securities being used in portfolio = ',numberOfSecurities, '\n')
+
+# Random create a portfolio from the non-market non RF series
+# Get a normalized set of weights
+# Could set up the application to create a random portfolio from a subset or
+# Input specific securities and weights
+#
+if (randWts){
+ coefs = runif(nSec-2)
+ alphas = coefs/sum(coefs)
+ sum(alphas)
+}
+
+if (equalWts) {
+ R.portfolio <- Return.portfolio(largecap.ts[, 1:numberOfSecurities],geometric=geometricB)
+} else {
+ R.portfolio = Return.portfolio(largecap.ts[, 1:numberOfSecurities],weights=alphas,geometric=geometricB)
+}
+
+colnames(portfolio) ="PortRets"
+
+salient = matrix(data=c("Mean",mean(R.portfolio),mean(R.market),mean(rf),
+ "Stdev",sd(R.portfolio),sd(R.market),sd(rf),
+ "NbrSecuritiesInPort",numberOfSecurities,"","",
+ "AnnuallyFrequency",rep(freQ,3),
+ "Number of Samples",rep(nRow,3)),ncol=4,byrow=TRUE)
+
+Measures = rbind(Measures, salient)
+
+
+# Start to compute performance measures using performance analytic and as a check
+# compute from underlying formula
+
+# Some of comparison match, but some are inexplicable different.
+# Really should investigate the latter, I am sure the users will do so
+
+# Compute beta
+beta = cov(R.portfolio,R.market)/var(R.market)
+betaRF = cov((R.portfolio[,1]-rf),(R.market-rf))/var((R.market-rf))
+
+cat('\n Beta =',beta,', between the portfolio represented by ',PortName,' and the market represented by ',MrktName,' \n')
+cat('\n Beta =',betaRF,', between the excess portfolio represented by ',PortName,' and the excess market represented by ',MrktName,' \n')
+
+Measures = rbind(Measures,c("Beta",betaRF,"",""))
+
+# Compute Treynor
+
+ # Performance Analytics (PA) computation of Treynor for portfolio and market
+tr = TreynorRatio(R.portfolio, R.market,rf,freQ )
+trMarket = TreynorRatio(R.market,R.market,rf,freQ )
+
+ # From formula (Hand) computation of Treynor for portfolio and market
+trHandGeom = (prod(1+(R.portfolio-rf))^(freQ/nRow) - 1)/betaRF
+trHand = freQ*mean(R.portfolio-rf)/betaRF
+
+# beta of Treynor for market is 1
+trHandMGeom = (prod(1+(R.market-rf))^(freQ/nRow) - 1)
+trHandM = freQ*(mean(R.market-rf))
+
+ # Output results from Treynor Ratio computation
+cat('\n PA computed for ',PortName,' Treynor Ratio = ',tr,'\n')
+cat('\n Hand computed for ',PortName,' Treynor Ratio = ',trHand,'\n')
+cat('\n PA computed for ',MrktName,' Treynor Ratio = ',trMarket,'\n')
+cat('\n Hand computed for ',MrktName,' Treynor Ratio = ',trHandM,'\n')
+
+Measures = rbind(Measures,c("Treynor Ratio",tr,trMarket,""))
+
+ # Compare Treynor Ratio for market returns against Treynor Ratio for portfolio returns
+cat('\n Treynor Ratio of ',MrktName,' is ',relation[sign(trMarket - tr) + 2],' Treynor Ratio of ',PortName,'\n' )
+TR_Mrkt2Port = relation[sign(trMarket - tr) + 2]
+
+##
+# calculate excess returns of R.portfolio
+R.portfolio.x <- R.portfolio - rf
+
+# calculate excess returns of R.market
+R.market.x <- R.market - rf
+
+# run regression to get beta
+fit <- lm(R.portfolio.x ~ R.market.x)
+beta.lm <- coef(fit)[2]
+
+# calculate beta another way
+beta2 <- as.numeric(cov(R.portfolio.x, R.market.x) / var(R.market.x))
+
+# Annualized portfolio excess returns / beta
+# This should match the TreynorRatio from PerformanceAnalytics
+TR.rb <- as.numeric(Return.annualized(R.portfolio.x,scale=12) / beta.lm)
+TR.rb2 <- as.numeric(Return.annualized(R.portfolio.x,scale=12,geometric=FALSE) / beta.lm)
+
+as.numeric(Return.annualized(R.portfolio.x) / beta2)
+
+# Calcualte Treynor Ratio with PerformanceAnalytics
+TR.PA <- TreynorRatio(R.portfolio, R.market, rf)
+
+all.equal(TR.rb, TR.PA)
+cat("Treynor Ratio by hand: ", TR.rb, "\n")
+cat("Treynor Ratio with PerformanceAnalytics: ", TR.PA, "\n")
+##
+
+# Compute Sharpe
+
+ # PA computation of Sharpe
+shr = SharpeRatio(R.portfolio, rf, FUN = "StdDev")
+shrAnn = SharpeRatio.annualized(R.portfolio, rf, scale=freQ, geometric=TRUE)
+
+ # Compute excess portfolio returns (portfolio returns net of RF returns)
+xCess = R.portfolio - rf
+ # Hand computation of Sharpe
+
+shrHand = mean(xCess)/sd(xCess)
+
+shrHandAnn =((prod(1+xCess))^(freQ/nRow) - 1)/(sqrt(freQ)*sd(xCess))
+
+ # Output results from Sharpe Ratio computation
+cat('\n PA computed ',PortName,' Sharpe Ratio = ',shr,'\n')
+cat('\n Hand computed ',PortName,' Sharpe Ratio = ',shrHand,'\n')
+
+cat('\n PA computed ',PortName,' Annualized Sharpe Ratio = ',shrAnn,'\n')
+cat('\n Hand computed ',PortName,' Annualized Sharpe Ratio = ',shrHandAnn,'\n')
+
+cat('\n Difference PA and hand computed Sharpe Ratio = ',as.numeric(shr) - as.numeric(shrHand),'\n')
+
+
+Measures = rbind(Measures,c("Sharpe Ratio",shr,"","","Sharpe Ratio Annualized",shrAnn,"",""))
+
+# Compute Jensen's Alpha
+
+ # Mean of risk free rate over sampling time series
+meanRF = mean(rf)
+
+ # PA computation of Jensen's Alpha
+
+## The risk-free rate varies through time so just computing the mean
+## is oversimplifying and could be part of the reason for the differences
+## you are seeing between your hand calculation and PerformanceAnalytics
+
+ # True but If put rf rather than meanRF will get a series of ja's
+ # rather than a single value
+
+ # It appears to be an annualized value
+
+ # Produces one value
+jaStatic = CAPM.jensenAlpha(R.portfolio,R.market,meanRF)
+
+ # Produces multiple values
+jaTV = CAPM.jensenAlpha(R.portfolio, R.market,rf)
+
+
+# Hand computation of Jensen's Alpha using regression apprach
+
+
+ # Precompute excess returns
+
+xCessP1 = R.portfolio - rf
+xCessM1 = R.market - rf
+
+ # Regression computation and salient results
+lm_ja1.fit = lm(xCessP1 ~ xCessM1)
+values1 = summary(lm_ja1.fit)
+values1
+analT1 = values1[[4]]
+
+ # Annualize Jensen's Alpha
+ # (mean(R.portfolio) - meanRF - betaRF*(mean(R.market)-meanRF)) same as regression coefficent
+jaHandA = (1+(mean(R.portfolio) - meanRF - betaRF*(mean(R.market)-meanRF)))^freQ -1
+
+ # Alternative annualization using individual values
+jaHandA2 = prod((1+((R.portfolio - rf) - as.numeric(betaRF)*(R.market-rf))))^(freQ/nRow) - 1
+
+
+ # Use Delta Method to approximate standard error of analyzed Jensen's Alpha
+deltaCoef = (freQ*(1+analT1[1,1])^(freQ-1))^2
+
+ # Output salient results for Jensen's Alpha
+cat('\n PA computed ',PortName,' Static Jensen\'s Alpha = ',jaStatic,'\n')
+cat('\n Regression computed ',PortName,' Jensen\'s Alpha, Not Annualized= ',analT1[1,1],'\n')
+cat('\n Hand computed Annualized ',PortName,' Jensen Alpha = ',jaHandA,'\n')
+cat('\n Delta Method Coefficient Value = ', deltaCoef,'\n')
+
+ # t stat and pvalue under H0: alpha = 0 against HA: alpha != 0
+tStat = jaHandA/(analT1[1,2]*deltaCoef^0.5)
+pValue = 2*(1-pt(tStat,nRow-2))
+cat('\n H0: alpha = 0, HA: alpha != 0 p-value: ',pValue,'\n')
+
+Measures = rbind(Measures,c("Jensen's Alpha",ja,"",""))
+Measures = rbind(Measures,c("Jensen's Alpha P Value",pValue,"",""))
+
+
+
+# Compute Tracking Error
+
+ # PA computation of Tracking Error
+te = TrackingError(R.portfolio, R.market, scale = freQ)
+
+ # Precompute required values to computr Tracking Error by Hand
+ # Lipper Definition ARR =SUM(sp RR)/n sp, where sp == sub-period
+
+RR = R.portfolio-R.market
+ARR = mean(RR)
+
+ # Hand computation of Tracking Error
+teHand = sqrt(sum((RR-ARR)^2)/(nRow-1))*sqrt(freQ)
+
+ # Output results from Tracking Error computation
+cat('\n PA computed ',PortName,' Tracking Error = ',te,'\n')
+cat('\n Hand computed ', PortName,' Tracking Error = ',teHand,'\n')
+cat('\n Difference PA_TE - Hand_TE = ',te - teHand,'\n')
+
+Measures = rbind(Measures,c("Tracking Error",te,"",""))
+
+# Compute Information Ratio
+
+ # PA computation of Information Ratio
+ir = InformationRatio(R.portfolio, R.market, scale = freQ)
+
+ # Hand computation of Information Ratio
+ # Lipper definition = ARR/TE
+irHand = (ARR/te)*sqrt(freQ)
+
+# Definition PA, InformationRatio = ActivePremium/TrackingError
+#Active Premium = Investment's annualized return - Benchmark's annualized return
+irHand2 = ((prod(1+(R.portfolio))^(freQ/nRow) - prod(1+(R.market))^(freQ/nRow))/te)
+
+# Output results from Information Ratio computation
+cat('\n PA computed ',PortName,' Information Ratio = ',ir,'\n')
+cat('\n Hand computed ',PortName,' Lipper Method Information Ratio = ',irHand,'\n')
+cat('\n Hand computed ',PortName,' PA formula Information Ratio = ',irHand,'\n')
+
+Measures = rbind(Measures,c("Information Ratio",ir,"",""))
+
+# Compute Sortino Ratio (including Downside Deviation)
+
+ # PA computation of Sortino Ratio
+sr = SortinoRatio(R.portfolio, MAR = MAR_set, weights = NULL)
+
+ # Set value of denominator for Downside Deviation from the parameter denom set earlier
+denomVal = nRow
+if (denom != "full")
+ {
+ denomVal = sum(ifelse((R.portfolio - MAR_set)<0,1,0))
+ }
+cat('\n Denominator parameter is set to: ',denom,' which results in a denominator value of ',denomVal,'\n')
+
+ # PA computation of Downside Deviation
+dwn = DownsideDeviation(R.portfolio, MAR = MAR_set, method = "full")
+
+ # Hand computation of Downside Deviation
+ # Lipper Difference is denom d.f.
+dwnHand = sqrt(sum(apply(cbind((R.portfolio - MAR_set),rep(0,nRow)),1,min)^2)/(denomVal-1))
+
+ # Output computation of Downside Deviation
+cat('\n PA computed ',PortName,' Downside Deviation = ',dwn,'\n')
+cat('\n Hand computed ',PortName,' Downside Deviation = ',dwnHand,'\n')
+
+ # Hand computation of Sortino Ratio Lipper
+srHand = sqrt(freQ)*ARR/dwn
+
+ # Hand computation PA Formula
+srHand2 = mean(R.portfolio-MAR_set)/dwn
+
+ # Output computation of Sortino Ratio
+cat('\n PA computed ',PortName,' Sortino Ratio = ',sr,'\n')
+cat('\n Hand computed ',PortName,' Annualized Lipper Sortino Ratio = ',srHand,'\n')
+cat('\n Hand computed ',PortName,' PA formula Sortino Ratio = ',srHand2,'\n')
+
+Measures = rbind(Measures,c("Downside Deviation",dwn,"",""))
+Measures = rbind(Measures,c("Denominator DD",denomVal,"",""))
+Measures = rbind(Measures,c("Sortino Ratio",sr,"",""))
+Measures.df= as.data.frame(Measures,stringsAsFactors=FALSE)
+
+print(Measures.df)
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