Chapter 3: Portfolio Returns

Key Issues

portfolio returns = returns of basket of securities benchmark portfolio = hypothetical portfolio that we can compare the performance of our portf

3.1 Constructing Portfolio Returns (Long Way)

Portfolio return is the weighted average of the returns of the individual securities in the portfolio. Suppose we invested $50K in AMZN, $10 in TSLA, $30 in AAPL, and $10 in IBM How much would this portfolio return b/t December 31, 2010 and December 31, 2013?

Step 0: Import Price Data

# To clean up the memory of your current R session run the following line
rm(list=ls(all=TRUE))

library(quantmod)
library(xts)

#Importing Price Data
data.AMZN <- getSymbols("AMZN", from = "2013-12-31", to = "2017-10-01", auto.assign = FALSE)
data.AAPL <- getSymbols("AAPL", from = "2013-12-31", to = "2017-10-01", auto.assign = FALSE)
data.IBM <- getSymbols("IBM", from = "2013-12-31", to = "2017-10-01", auto.assign = FALSE)
data.TSLA <- getSymbols("TSLA", from = "2013-12-31", to = "2017-10-01", auto.assign = FALSE)
data.FB <- getSymbols("FB", from = "2013-12-31", to = "2017-10-01", auto.assign = FALSE)
data.MSFT <- getSymbols("MSFT", from = "2013-12-31", to = "2017-10-01", auto.assign = FALSE)
#to = "2013-12-31" in the book was replaced by to = "2014-01-01"
#B/c that code doesn't produce the output that includes stock price of 2013-12-31the date. 

multi <- data.AMZN[, 6] # Need to create a new data object before cbinding
multi <- cbind(multi, data.TSLA[, 6], data.AAPL[, 6], data.IBM[, 6], data.FB[, 6], data.MSFT[, 6])

Step 1: Find First and Last Adjusted Closing Price for Each Security Over the Investmet Period

period.ret <- multi[c(1, nrow(multi)), ]
period.ret
##            AMZN.Adjusted TSLA.Adjusted AAPL.Adjusted IBM.Adjusted
## 2013-12-31        398.79        150.43      74.57128      166.089
## 2017-09-29        961.35        341.10     154.11999      145.080
##            FB.Adjusted MSFT.Adjusted
## 2013-12-31       54.65      33.91713
## 2017-09-29      170.87      74.49000

Step 2: Calculate Returns for Each Security Over the Investment Period

rets <- lapply(period.ret, Delt) # lapply returns output in a list
rets
## $AMZN.Adjusted
##            Delt.1.arithmetic
## 2013-12-31                NA
## 2017-09-29          1.410667
## 
## $TSLA.Adjusted
##            Delt.1.arithmetic
## 2013-12-31                NA
## 2017-09-29            1.2675
## 
## $AAPL.Adjusted
##            Delt.1.arithmetic
## 2013-12-31                NA
## 2017-09-29          1.066747
## 
## $IBM.Adjusted
##            Delt.1.arithmetic
## 2013-12-31                NA
## 2017-09-29        -0.1264924
## 
## $FB.Adjusted
##            Delt.1.arithmetic
## 2013-12-31                NA
## 2017-09-29          2.126624
## 
## $MSFT.Adjusted
##            Delt.1.arithmetic
## 2013-12-31                NA
## 2017-09-29          1.196236
#rets <- mapply(Delt, data.frame(period.ret)) #mapply does the same but returns output in DF

Step 3: Convert to a data.frame and Clean up Data

rets <- data.frame(rets)
rets
##            Delt.1.arithmetic Delt.1.arithmetic.1 Delt.1.arithmetic.2
## 2013-12-31                NA                  NA                  NA
## 2017-09-29          1.410667              1.2675            1.066747
##            Delt.1.arithmetic.3 Delt.1.arithmetic.4 Delt.1.arithmetic.5
## 2013-12-31                  NA                  NA                  NA
## 2017-09-29          -0.1264924            2.126624            1.196236
rets <- rets[2, ] * 100
names(rets) <- paste(c("AMZN", "TSLA", "AAPL", "IBM", "FB", "MSFT"))
rets
##                AMZN   TSLA     AAPL       IBM       FB     MSFT
## 2017-09-29 141.0667 126.75 106.6747 -12.64924 212.6624 119.6236

Step 4: Calculate Weight of Each Security in the Portfolio

i.AMZN <- 40000
i.TSLA <- 20000
i.AAPL <- 10000
i.IBM <- 10000
i.FB <- 10000
i.MSFT <- 10000

w.AMZN <- i.AMZN / (i.AMZN + i.TSLA + i.AAPL + i.IBM + i.FB + i.MSFT)
w.TSLA <- i.TSLA / (i.AMZN + i.TSLA + i.AAPL + i.IBM + i.FB + i.MSFT)
w.AAPL <- i.AAPL / (i.AMZN + i.TSLA + i.AAPL + i.IBM + i.FB + i.MSFT)
w.IBM <- i.IBM / (i.AMZN + i.TSLA + i.AAPL + i.IBM + i.FB + i.MSFT)
w.FB <- i.FB / (i.AMZN + i.TSLA + i.AAPL + i.IBM + i.FB + i.MSFT)
w.MSFT <- i.MSFT / (i.AMZN + i.TSLA + i.AAPL + i.IBM + i.FB + i.MSFT)
w.AMZN
## [1] 0.4
w.TSLA
## [1] 0.2
w.AAPL
## [1] 0.1
w.IBM
## [1] 0.1
w.FB
## [1] 0.1
w.MSFT
## [1] 0.1

Step 5: Calculate Portfolio Return

port.ret.4asset <- w.AMZN * rets$AMZN + w.TSLA * rets$TSLA + w.AAPL * rets$AAPL + w.IBM * rets$IBM + w.FB * rets$FB + w.MSFT + rets$MSFT
port.ret.4asset 
## [1] 232.169

Interpretation

This portfolio would return 232.169 *Facebook performed the best during the time period
The alternate portfolio returned 199.99
The first portfolio outpeforms the second portfolio

Alternate Portfolio