Chapter 3: Portfolio Returns
Construct an equal-weighted (EW) and value-weighted (VW) portfolio, consisting of AMZN, MSFT, AAPL, and TSLA.
In this section, prepare an object, port, which will be used later to build EW and VW portfolio.
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)## Loading required package: xts## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric## Loading required package: TTR## Version 0.4-0 included new data defaults. See ?getSymbols.library(xts)
#Importing Price Data
data.AMZN <- getSymbols("AMZN", from = "2016-12-30", to = "2017-07-03", auto.assign = FALSE)## 'getSymbols' currently uses auto.assign=TRUE by default, but will
## use auto.assign=FALSE in 0.5-0. You will still be able to use
## 'loadSymbols' to automatically load data. getOption("getSymbols.env")
## and getOption("getSymbols.auto.assign") will still be checked for
## alternate defaults.
##
## This message is shown once per session and may be disabled by setting
## options("getSymbols.warning4.0"=FALSE). See ?getSymbols for details.##
## WARNING: There have been significant changes to Yahoo Finance data.
## Please see the Warning section of '?getSymbols.yahoo' for details.
##
## This message is shown once per session and may be disabled by setting
## options("getSymbols.yahoo.warning"=FALSE).data.MSFT <- getSymbols("MSFT", from = "2016-12-30", to = "2017-07-03", auto.assign = FALSE)
data.AAPL <- getSymbols("AAPL", from = "2016-12-30", to = "2017-07-03", auto.assign = FALSE)
data.TSLA <- getSymbols("TSLA", from = "2016-12-30", to = "2017-07-03", auto.assign = FALSE)Step 1: Importing the Price Data
data.AMZN[c(1:3, nrow(data.AMZN)), ]## AMZN.Open AMZN.High AMZN.Low AMZN.Close AMZN.Volume
## 2016-12-30 766.47 767.40 748.28 749.87 4139400
## 2017-01-03 757.92 758.76 747.70 753.67 3521100
## 2017-01-04 758.39 759.68 754.20 757.18 2510500
## 2017-06-30 980.12 983.47 967.61 968.00 3390300
## AMZN.Adjusted
## 2016-12-30 749.87
## 2017-01-03 753.67
## 2017-01-04 757.18
## 2017-06-30 968.00data.MSFT[c(1:3, nrow(data.MSFT)), ]## MSFT.Open MSFT.High MSFT.Low MSFT.Close MSFT.Volume
## 2016-12-30 64.366 64.396 63.415 62.14 25579900
## 2017-01-03 64.192 64.243 63.517 62.58 20694100
## 2017-01-04 63.875 64.151 63.507 62.30 21340000
## 2017-06-30 69.494 70.100 69.453 68.93 24161100
## MSFT.Adjusted
## 2016-12-30 60.78280
## 2017-01-03 61.21319
## 2017-01-04 60.93930
## 2017-06-30 68.22208data.AAPL[c(1:3, nrow(data.AAPL)), ]## AAPL.Open AAPL.High AAPL.Low AAPL.Close AAPL.Volume
## 2016-12-30 118.526 119.085 117.286 115.82 30586300
## 2017-01-03 117.662 118.201 116.605 116.15 28781900
## 2017-01-04 117.713 118.384 117.611 116.02 21118100
## 2017-06-30 145.539 146.052 144.864 144.02 23024100
## AAPL.Adjusted
## 2016-12-30 113.9870
## 2017-01-03 114.3118
## 2017-01-04 114.1838
## 2017-06-30 142.9428data.TSLA[c(1:3, nrow(data.TSLA)), ]## TSLA.Open TSLA.High TSLA.Low TSLA.Close TSLA.Volume
## 2016-12-30 216.30 217.50 211.68 213.69 4642600
## 2017-01-03 214.86 220.33 210.96 216.99 5923300
## 2017-01-04 214.75 228.00 214.31 226.99 11213500
## 2017-06-30 363.71 366.77 359.62 361.61 5848500
## TSLA.Adjusted
## 2016-12-30 213.69
## 2017-01-03 216.99
## 2017-01-04 226.99
## 2017-06-30 361.61Step 2: Create Object with Only the Relevant Data
port <- data.AMZN[, c(4, 6)]
port <- merge(port, data.MSFT[, c(4, 6)])
port <- merge(port, data.AAPL[, c(4, 6)])
port <- merge(port, data.TSLA[, c(4, 6)])
#port <- cbind(port, data.MSFT[, c(4, 6)], data.AAPL[, c(4, 6)])
port[c(1:3, nrow(port)), ]## AMZN.Close AMZN.Adjusted MSFT.Close MSFT.Adjusted AAPL.Close
## 2016-12-30 749.87 749.87 62.14 60.78280 115.82
## 2017-01-03 753.67 753.67 62.58 61.21319 116.15
## 2017-01-04 757.18 757.18 62.30 60.93930 116.02
## 2017-06-30 968.00 968.00 68.93 68.22208 144.02
## AAPL.Adjusted TSLA.Close TSLA.Adjusted
## 2016-12-30 113.9870 213.69 213.69
## 2017-01-03 114.3118 216.99 216.99
## 2017-01-04 114.1838 226.99 226.99
## 2017-06-30 142.9428 361.61 361.61Step 3: Calculate Returns of Each Security
port$AMZN.ret <- Delt(port$AMZN.Adjusted)
port$MSFT.ret <- Delt(port$MSFT.Adjusted)
port$AAPL.ret <- Delt(port$AAPL.Adjusted)
port$TSLA.ret <- Delt(port$TSLA.Adjusted)
port[c(1:3, nrow(port)), ]## AMZN.Close AMZN.Adjusted MSFT.Close MSFT.Adjusted AAPL.Close
## 2016-12-30 749.87 749.87 62.14 60.78280 115.82
## 2017-01-03 753.67 753.67 62.58 61.21319 116.15
## 2017-01-04 757.18 757.18 62.30 60.93930 116.02
## 2017-06-30 968.00 968.00 68.93 68.22208 144.02
## AAPL.Adjusted TSLA.Close TSLA.Adjusted AMZN.ret
## 2016-12-30 113.9870 213.69 213.69 NA
## 2017-01-03 114.3118 216.99 216.99 0.005067529
## 2017-01-04 114.1838 226.99 226.99 0.004657224
## 2017-06-30 142.9428 361.61 361.61 -0.008125576
## MSFT.ret AAPL.ret TSLA.ret
## 2016-12-30 NA NA NA
## 2017-01-03 0.007080902 0.002849238 0.015442945
## 2017-01-04 -0.004474330 -0.001119264 0.046085072
## 2017-06-30 0.006424249 0.002366525 0.002383881Step 4: Convert to data.frame Object and Subset Data
port <- cbind(index(port), data.frame(port))
names(port)[1] <- "date"
port[c(1:3, nrow(port)), ]## date AMZN.Close AMZN.Adjusted MSFT.Close MSFT.Adjusted
## 2016-12-30 2016-12-30 749.87 749.87 62.14 60.78280
## 2017-01-03 2017-01-03 753.67 753.67 62.58 61.21319
## 2017-01-04 2017-01-04 757.18 757.18 62.30 60.93930
## 2017-06-30 2017-06-30 968.00 968.00 68.93 68.22208
## AAPL.Close AAPL.Adjusted TSLA.Close TSLA.Adjusted AMZN.ret
## 2016-12-30 115.82 113.9870 213.69 213.69 NA
## 2017-01-03 116.15 114.3118 216.99 216.99 0.005067529
## 2017-01-04 116.02 114.1838 226.99 226.99 0.004657224
## 2017-06-30 144.02 142.9428 361.61 361.61 -0.008125576
## MSFT.ret AAPL.ret TSLA.ret
## 2016-12-30 NA NA NA
## 2017-01-03 0.007080902 0.002849238 0.015442945
## 2017-01-04 -0.004474330 -0.001119264 0.046085072
## 2017-06-30 0.006424249 0.002366525 0.002383881port <- subset(port,
port$date >= "2016-12-30" &
port$date <= "2017-12-29")
port[c(1:3, nrow(port)), ]## date AMZN.Close AMZN.Adjusted MSFT.Close MSFT.Adjusted
## 2016-12-30 2016-12-30 749.87 749.87 62.14 60.78280
## 2017-01-03 2017-01-03 753.67 753.67 62.58 61.21319
## 2017-01-04 2017-01-04 757.18 757.18 62.30 60.93930
## 2017-06-30 2017-06-30 968.00 968.00 68.93 68.22208
## AAPL.Close AAPL.Adjusted TSLA.Close TSLA.Adjusted AMZN.ret
## 2016-12-30 115.82 113.9870 213.69 213.69 NA
## 2017-01-03 116.15 114.3118 216.99 216.99 0.005067529
## 2017-01-04 116.02 114.1838 226.99 226.99 0.004657224
## 2017-06-30 144.02 142.9428 361.61 361.61 -0.008125576
## MSFT.ret AAPL.ret TSLA.ret
## 2016-12-30 NA NA NA
## 2017-01-03 0.007080902 0.002849238 0.015442945
## 2017-01-04 -0.004474330 -0.001119264 0.046085072
## 2017-06-30 0.006424249 0.002366525 0.0023838813.3.1 Equal-Weighted Portfolio
considerd as an approach to capture the small capitalization stock premeum (the belief that small cap stock yield higher returns over larger cap stocks) An example is the S&P 500 Equal Weight Index
Step 1: Keep Only Variables We Need to Construct EW Portfolio
ewport <- port[, c(1, 10:13)]
ewport[c(1:3, nrow(ewport)), ]## date AMZN.ret MSFT.ret AAPL.ret TSLA.ret
## 2016-12-30 2016-12-30 NA NA NA NA
## 2017-01-03 2017-01-03 0.005067529 0.007080902 0.002849238 0.015442945
## 2017-01-04 2017-01-04 0.004657224 -0.004474330 -0.001119264 0.046085072
## 2017-06-30 2017-06-30 -0.008125576 0.006424249 0.002366525 0.002383881names(ewport)[2:5] <- c("AMZN", "MSFT", "AAPL", "TSLA")
rownames(ewport) <- seq(1, nrow(ewport), 1)
ewport[c(1:3, nrow(ewport)), ]## date AMZN MSFT AAPL TSLA
## 1 2016-12-30 NA NA NA NA
## 2 2017-01-03 0.005067529 0.007080902 0.002849238 0.015442945
## 3 2017-01-04 0.004657224 -0.004474330 -0.001119264 0.046085072
## 126 2017-06-30 -0.008125576 0.006424249 0.002366525 0.002383881Step 2: Convert Net Returns to Gross Returns
ewport[2:5] <- ewport[2:5] + 1
ewport[c(1:3, nrow(ewport)), ]## date AMZN MSFT AAPL TSLA
## 1 2016-12-30 NA NA NA NA
## 2 2017-01-03 1.0050675 1.0070809 1.0028492 1.015443
## 3 2017-01-04 1.0046572 0.9955257 0.9988807 1.046085
## 126 2017-06-30 0.9918744 1.0064242 1.0023665 1.002384Step 3: Calculate EW Portfolio Values for 1Q 2013
# Subset ewport by data from December 31, 2012 to March 31, 2013
ewq1 <- subset(ewport,
ewport$date >= "2016-12-30" &
ewport$date <= "2017-04-01" )
ewq1[c(1:3, nrow(ewq1)), ]## date AMZN MSFT AAPL TSLA
## 1 2016-12-30 NA NA NA NA
## 2 2017-01-03 1.005068 1.0070809 1.0028492 1.015443
## 3 2017-01-04 1.004657 0.9955257 0.9988807 1.046085
## 63 2017-03-31 1.011639 1.0022828 0.9981242 1.001367# Calculate the cumulative gross returns fro each security for Q1
ewq1[1, 2:5] <- 1
ewq1[2:5] <- cumprod(ewq1[2:5])
ewq1[c(1:3, nrow(ewq1)), ]## date AMZN MSFT AAPL TSLA
## 1 2016-12-30 1.000000 1.000000 1.000000 1.000000
## 2 2017-01-03 1.005068 1.007081 1.002849 1.015443
## 3 2017-01-04 1.009748 1.002575 1.001727 1.062240
## 63 2017-03-31 1.182258 1.066290 1.245751 1.302354# Calculate the index value for each security for Q1
num.sec <- 4
ewq1$AMZN.ind <- ewq1$AMZN / num.sec
ewq1$MSFT.ind <- ewq1$MSFT / num.sec
ewq1$AAPL.ind <- ewq1$AAPL / num.sec
ewq1$TSLA.ind <- ewq1$TSLA / num.sec
ewq1[c(1:3, nrow(ewq1)), ]## date AMZN MSFT AAPL TSLA AMZN.ind MSFT.ind
## 1 2016-12-30 1.000000 1.000000 1.000000 1.000000 0.2500000 0.2500000
## 2 2017-01-03 1.005068 1.007081 1.002849 1.015443 0.2512669 0.2517702
## 3 2017-01-04 1.009748 1.002575 1.001727 1.062240 0.2524371 0.2506437
## 63 2017-03-31 1.182258 1.066290 1.245751 1.302354 0.2955646 0.2665726
## AAPL.ind TSLA.ind
## 1 0.2500000 0.2500000
## 2 0.2507123 0.2538607
## 3 0.2504317 0.2655599
## 63 0.3114377 0.3255885# Calculate the agrregate portfolio value on each day
q1.val <- data.frame(rowSums(ewq1[, 5:8]))
q1.val[c(1:3, nrow(q1.val)), ]## [1] 1.750000 1.769192 1.815752 2.175929names(q1.val) <- paste("port.val")
q1.val$date <- ewq1$date
q1.val[c(1:3, nrow(q1.val)), ]## port.val date
## 1 1.750000 2016-12-30
## 2 1.769192 2017-01-03
## 3 1.815752 2017-01-04
## 63 2.175929 2017-03-31# Pass the aggregate portfolio value at the end of Q1 to Q2
q2.inv <- q1.val[nrow(q1.val), 1]
q2.inv## [1] 2.175929Step 4: Calculate EW Portfolio Values for 2Q 2013
# Subset ewport by data from April 1, 2013 to June 30, 2013
ewq2 <- subset(ewport,
ewport$date >= "2016-04-01" &
ewport$date <= "2017-07-03")
ewq2[c(1:3, nrow(ewq2)), ]## date AMZN MSFT AAPL TSLA
## 1 2016-12-30 NA NA NA NA
## 2 2017-01-03 1.0050675 1.0070809 1.0028492 1.015443
## 3 2017-01-04 1.0046572 0.9955257 0.9988807 1.046085
## 126 2017-06-30 0.9918744 1.0064242 1.0023665 1.002384# Calculate the cumulative gross returns fro each security for Q2
#ewq2[1, 2:5] <- 1 This is the difference from Q1
ewq2[1, 2:5] <- cumprod(ewq2[2:5])## Warning in `[<-.data.frame`(`*tmp*`, 1, 2:5, value = structure(list(AMZN =
## c(NA_real_, : replacement element 1 has 126 rows to replace 1 rows## Warning in `[<-.data.frame`(`*tmp*`, 1, 2:5, value = structure(list(AMZN =
## c(NA_real_, : replacement element 2 has 126 rows to replace 1 rows## Warning in `[<-.data.frame`(`*tmp*`, 1, 2:5, value = structure(list(AMZN =
## c(NA_real_, : replacement element 3 has 126 rows to replace 1 rows## Warning in `[<-.data.frame`(`*tmp*`, 1, 2:5, value = structure(list(AMZN =
## c(NA_real_, : replacement element 4 has 126 rows to replace 1 rowsewq2[c(1:3, nrow(ewq2)), ]## date AMZN MSFT AAPL TSLA
## 1 2016-12-30 NA NA NA NA
## 2 2017-01-03 1.0050675 1.0070809 1.0028492 1.015443
## 3 2017-01-04 1.0046572 0.9955257 0.9988807 1.046085
## 126 2017-06-30 0.9918744 1.0064242 1.0023665 1.002384# Calculate the index value for each security for Q2
ewq2$AMZN.ind <- (q2.inv / num.sec) * ewq2$AMZN #a difference from Q1
ewq2$MSFT.ind <- (q2.inv / num.sec) * ewq2$MSFT
ewq2$AAPL.ind <- (q2.inv / num.sec) * ewq2$AAPL
ewq2$TSLA.ind <- (q2.inv / num.sec) * ewq2$TSLA
ewq2[c(1:3, nrow(ewq2)), ]## date AMZN MSFT AAPL TSLA AMZN.ind MSFT.ind
## 1 2016-12-30 NA NA NA NA NA NA
## 2 2017-01-03 1.0050675 1.0070809 1.0028492 1.015443 0.5467388 0.5478341
## 3 2017-01-04 1.0046572 0.9955257 0.9988807 1.046085 0.5465156 0.5415482
## 126 2017-06-30 0.9918744 1.0064242 1.0023665 1.002384 0.5395620 0.5474768
## AAPL.ind TSLA.ind
## 1 NA NA
## 2 0.5455321 0.5523829
## 3 0.5433733 0.5690516
## 126 0.5452695 0.5452790# Calculate the agrregate portfolio value on each day
q2.val <- data.frame(rowSums(ewq2[, 5:8]))
q2.val[c(1:3, nrow(q2.val)), ]## [1] NA 2.655548 2.677522 2.634692names(q2.val) <- paste("port.val")
q2.val$date <- ewq2$date
q2.val[c(1:3, nrow(q2.val)), ]## port.val date
## 1 NA 2016-12-30
## 2 2.655548 2017-01-03
## 3 2.677522 2017-01-04
## 126 2.634692 2017-06-30#$1.121 at the end of Q1 and 1.125
#Means the portfolio grown from $1.121 at the end of Q1 to $1.125 at the end of Q2
#Note that it doesn't mean that the portfolio grew 12.5% during Q2 but 12.5% during Q1-Q2
#b/c this is a cumulative measure Step 7: Combine Quarterly EW Portfolio Values into One Data Object
ew.portval <- rbind(q1.val, q2.val)
ew.portval[c(1:3, nrow(ew.portval)), ]## port.val date
## 1 1.750000 2016-12-30
## 2 1.769192 2017-01-03
## 3 1.815752 2017-01-04
## 126 2.634692 2017-06-303.3.2 Value-Weighted Portfolio
It’s considerd as an approach to track the changes in the size of the sector. Larger firms are given more weight in VW, whereas equal weights are given in EW portfolio. An example is the S&P 500 Index. It rebalances only at the beginning of each quarter.
Step 1: Keep Only Variables We Need to Construct EW Portfolio
vwport <- port[, c(1, 2, 4, 6, 8, 10:13)] #port is from 3.3 Constructing Benchmark Portfolio Returns
vwport[c(1:3, nrow(vwport)), ]## date AMZN.Close MSFT.Close AAPL.Close TSLA.Close
## 2016-12-30 2016-12-30 749.87 62.14 115.82 213.69
## 2017-01-03 2017-01-03 753.67 62.58 116.15 216.99
## 2017-01-04 2017-01-04 757.18 62.30 116.02 226.99
## 2017-06-30 2017-06-30 968.00 68.93 144.02 361.61
## AMZN.ret MSFT.ret AAPL.ret TSLA.ret
## 2016-12-30 NA NA NA NA
## 2017-01-03 0.005067529 0.007080902 0.002849238 0.015442945
## 2017-01-04 0.004657224 -0.004474330 -0.001119264 0.046085072
## 2017-06-30 -0.008125576 0.006424249 0.002366525 0.002383881rownames(vwport) <- seq(1:nrow(vwport))
vwport[c(1:3, nrow(vwport)), ]## date AMZN.Close MSFT.Close AAPL.Close TSLA.Close AMZN.ret
## 1 2016-12-30 749.87 62.14 115.82 213.69 NA
## 2 2017-01-03 753.67 62.58 116.15 216.99 0.005067529
## 3 2017-01-04 757.18 62.30 116.02 226.99 0.004657224
## 126 2017-06-30 968.00 68.93 144.02 361.61 -0.008125576
## MSFT.ret AAPL.ret TSLA.ret
## 1 NA NA NA
## 2 0.007080902 0.002849238 0.015442945
## 3 -0.004474330 -0.001119264 0.046085072
## 126 0.006424249 0.002366525 0.002383881Step 2: Convert Net Returns to Gross Returns
vwport$AMZN.ret <- vwport$AMZN.ret + 1
vwport$MSFT.ret <- vwport$MSFT.ret + 1
vwport$AAPL.ret <- vwport$AAPL.ret + 1
vwport$TSLA.ret <- vwport$TSLA.ret + 1
vwport[c(1:3, nrow(vwport)), ]## date AMZN.Close MSFT.Close AAPL.Close TSLA.Close AMZN.ret
## 1 2016-12-30 749.87 62.14 115.82 213.69 NA
## 2 2017-01-03 753.67 62.58 116.15 216.99 1.0050675
## 3 2017-01-04 757.18 62.30 116.02 226.99 1.0046572
## 126 2017-06-30 968.00 68.93 144.02 361.61 0.9918744
## MSFT.ret AAPL.ret TSLA.ret
## 1 NA NA NA
## 2 1.0070809 1.0028492 1.015443
## 3 0.9955257 0.9988807 1.046085
## 126 1.0064242 1.0023665 1.002384Step 3: Calculate the Market Capitalization of Each Security in the Portfolio
# Construct Series of Calendar Days
date <- seq(as.Date("2016-12-30"), as.Date("2017-12-29"), by = 1)
date <- data.frame(date)
date[c(1:3, nrow(date)), ]## [1] "2016-12-30" "2016-12-31" "2017-01-01" "2017-12-29"# Create Data Object with Daily Prices
PRICE.qtr <- vwport[, 1:5]
PRICE.qtr[c(1:3, nrow(PRICE.qtr)), ]## date AMZN.Close MSFT.Close AAPL.Close TSLA.Close
## 1 2016-12-30 749.87 62.14 115.82 213.69
## 2 2017-01-03 753.67 62.58 116.15 216.99
## 3 2017-01-04 757.18 62.30 116.02 226.99
## 126 2017-06-30 968.00 68.93 144.02 361.61# Filling in Last Available Price on Non-trading Days
PRICE.qtr <- na.locf(merge(x = date, y = PRICE.qtr, by = "date", all.x = TRUE))
#all.x=T tells R to keep all the data in the "by" varialble that is available in x=date
#na.locf tells R to copy over the last available data in y
#when there is a date in x that is not available in y
PRICE.qtr[c(1:3, nrow(PRICE.qtr)), ]## date AMZN.Close MSFT.Close AAPL.Close TSLA.Close
## 1 2016-12-30 749.87 62.14 115.82 213.69
## 2 2016-12-31 749.87 62.14 115.82 213.69
## 3 2017-01-01 749.87 62.14 115.82 213.69
## 365 2017-12-29 968.00 68.93 144.02 361.61# Keep Only Prices at the End of Each Calendar Quarter
PRICE.qtr <- subset(PRICE.qtr,
PRICE.qtr$date == as.Date("2016-12-30") |
PRICE.qtr$date == as.Date("2017-03-31") |
PRICE.qtr$date == as.Date("2017-06-30") |
PRICE.qtr$date == as.Date("2017-09-30"))
PRICE.qtr## date AMZN.Close MSFT.Close AAPL.Close TSLA.Close
## 1 2016-12-30 749.87 62.14 115.82 213.69
## 92 2017-03-31 886.54 65.86 143.66 278.30
## 183 2017-06-30 968.00 68.93 144.02 361.61
## 275 2017-09-30 968.00 68.93 144.02 361.61# Obtain Share Outstanding Data from SEC Filings
#http://www.sec.gov/edgar/searchedgar/companysearch.html
#Interactive Data / Financial Statements / Condensed Consolidated Balance Sheets
PRICE.qtr$AMZN.shout <- c(477000000, 478000000, 480000000, 482000000)
PRICE.qtr$MSFT.shout <- c(7784000000, 7730000000, 7723000000, 7720000000)
PRICE.qtr$AAPL.shout <- c(538443000, 5246540000, 5213840000, 5165228000)
PRICE.qtr$TSLA.shout <- c(149891190, 164259736, 166887023, 168067395)
PRICE.qtr## date AMZN.Close MSFT.Close AAPL.Close TSLA.Close AMZN.shout
## 1 2016-12-30 749.87 62.14 115.82 213.69 4.77e+08
## 92 2017-03-31 886.54 65.86 143.66 278.30 4.78e+08
## 183 2017-06-30 968.00 68.93 144.02 361.61 4.80e+08
## 275 2017-09-30 968.00 68.93 144.02 361.61 4.82e+08
## MSFT.shout AAPL.shout TSLA.shout
## 1 7.784e+09 538443000 149891190
## 92 7.730e+09 5246540000 164259736
## 183 7.723e+09 5213840000 166887023
## 275 7.720e+09 5165228000 168067395# Calculate Market Capitalization of Each Security
str(PRICE.qtr)## 'data.frame': 4 obs. of 9 variables:
## $ date : chr "2016-12-30" "2017-03-31" "2017-06-30" "2017-09-30"
## $ AMZN.Close: chr " 749.87" " 886.54" " 968.00" " 968.00"
## $ MSFT.Close: chr "62.14" "65.86" "68.93" "68.93"
## $ AAPL.Close: chr "115.82" "143.66" "144.02" "144.02"
## $ TSLA.Close: chr "213.69" "278.30" "361.61" "361.61"
## $ AMZN.shout: num 4.77e+08 4.78e+08 4.80e+08 4.82e+08
## $ MSFT.shout: num 7.78e+09 7.73e+09 7.72e+09 7.72e+09
## $ AAPL.shout: num 5.38e+08 5.25e+09 5.21e+09 5.17e+09
## $ TSLA.shout: num 1.50e+08 1.64e+08 1.67e+08 1.68e+08PRICE.qtr$date <- as.Date(PRICE.qtr$date)
PRICE.qtr$AMZN.Close <- as.numeric(PRICE.qtr$AMZN.Close)
PRICE.qtr$MSFT.Close <- as.numeric(PRICE.qtr$MSFT.Close)
PRICE.qtr$AAPL.Close <- as.numeric(PRICE.qtr$AAPL.Close)
PRICE.qtr$TSLA.Close <- as.numeric(PRICE.qtr$TSLA.Close)
str(PRICE.qtr)## 'data.frame': 4 obs. of 9 variables:
## $ date : Date, format: "2016-12-30" "2017-03-31" ...
## $ AMZN.Close: num 750 887 968 968
## $ MSFT.Close: num 62.1 65.9 68.9 68.9
## $ AAPL.Close: num 116 144 144 144
## $ TSLA.Close: num 214 278 362 362
## $ AMZN.shout: num 4.77e+08 4.78e+08 4.80e+08 4.82e+08
## $ MSFT.shout: num 7.78e+09 7.73e+09 7.72e+09 7.72e+09
## $ AAPL.shout: num 5.38e+08 5.25e+09 5.21e+09 5.17e+09
## $ TSLA.shout: num 1.50e+08 1.64e+08 1.67e+08 1.68e+08weights <- PRICE.qtr
weights$AMZN.mcap <- weights$AMZN.Close * weights$AMZN.shout
weights$MSFT.mcap <- weights$MSFT.Close * weights$MSFT.shout
weights$AAPL.mcap <- weights$AAPL.Close * weights$AAPL.shout
weights$TSLA.mcap <- weights$TSLA.Close * weights$TSLA.shout
weights## date AMZN.Close MSFT.Close AAPL.Close TSLA.Close AMZN.shout
## 1 2016-12-30 749.87 62.14 115.82 213.69 4.77e+08
## 92 2017-03-31 886.54 65.86 143.66 278.30 4.78e+08
## 183 2017-06-30 968.00 68.93 144.02 361.61 4.80e+08
## 275 2017-09-30 968.00 68.93 144.02 361.61 4.82e+08
## MSFT.shout AAPL.shout TSLA.shout AMZN.mcap MSFT.mcap
## 1 7.784e+09 538443000 149891190 357687990000 483697760000
## 92 7.730e+09 5246540000 164259736 423766120000 509097800000
## 183 7.723e+09 5213840000 166887023 464640000000 532346390000
## 275 7.720e+09 5165228000 168067395 466576000000 532139600000
## AAPL.mcap TSLA.mcap
## 1 62362468260 32030248391
## 92 753717936400 45713484529
## 183 750897236800 60348016387
## 275 743896136560 60774850706# Calculate Quarter-end Aggregate Market Capitalization
weights$tot.mcap <- rowSums(weights[, 10:13])
weights## date AMZN.Close MSFT.Close AAPL.Close TSLA.Close AMZN.shout
## 1 2016-12-30 749.87 62.14 115.82 213.69 4.77e+08
## 92 2017-03-31 886.54 65.86 143.66 278.30 4.78e+08
## 183 2017-06-30 968.00 68.93 144.02 361.61 4.80e+08
## 275 2017-09-30 968.00 68.93 144.02 361.61 4.82e+08
## MSFT.shout AAPL.shout TSLA.shout AMZN.mcap MSFT.mcap
## 1 7.784e+09 538443000 149891190 357687990000 483697760000
## 92 7.730e+09 5246540000 164259736 423766120000 509097800000
## 183 7.723e+09 5213840000 166887023 464640000000 532346390000
## 275 7.720e+09 5165228000 168067395 466576000000 532139600000
## AAPL.mcap TSLA.mcap tot.mcap
## 1 62362468260 32030248391 9.357785e+11
## 92 753717936400 45713484529 1.732295e+12
## 183 750897236800 60348016387 1.808232e+12
## 275 743896136560 60774850706 1.803387e+12Step 4: Calculate Quarter-end Weights of Each Security in the Portfolio
weights$AMZN.wgt <- weights$AMZN.mcap / weights$tot.mcap
weights$MSFT.wgt <- weights$MSFT.mcap / weights$tot.mcap
weights$AAPL.wgt <- weights$AAPL.mcap / weights$tot.mcap
weights$TSLA.wgt <- weights$TSLA.mcap / weights$tot.mcap
weights## date AMZN.Close MSFT.Close AAPL.Close TSLA.Close AMZN.shout
## 1 2016-12-30 749.87 62.14 115.82 213.69 4.77e+08
## 92 2017-03-31 886.54 65.86 143.66 278.30 4.78e+08
## 183 2017-06-30 968.00 68.93 144.02 361.61 4.80e+08
## 275 2017-09-30 968.00 68.93 144.02 361.61 4.82e+08
## MSFT.shout AAPL.shout TSLA.shout AMZN.mcap MSFT.mcap
## 1 7.784e+09 538443000 149891190 357687990000 483697760000
## 92 7.730e+09 5246540000 164259736 423766120000 509097800000
## 183 7.723e+09 5213840000 166887023 464640000000 532346390000
## 275 7.720e+09 5165228000 168067395 466576000000 532139600000
## AAPL.mcap TSLA.mcap tot.mcap AMZN.wgt MSFT.wgt AAPL.wgt
## 1 62362468260 32030248391 9.357785e+11 0.3822358 0.5168934 0.06664234
## 92 753717936400 45713484529 1.732295e+12 0.2446269 0.2938863 0.43509783
## 183 750897236800 60348016387 1.808232e+12 0.2569582 0.2944017 0.41526606
## 275 743896136560 60774850706 1.803387e+12 0.2587221 0.2950779 0.41249954
## TSLA.wgt
## 1 0.03422845
## 92 0.02638897
## 183 0.03337405
## 275 0.03370040weights <- weights[, c(1, 15:18)]
weights## date AMZN.wgt MSFT.wgt AAPL.wgt TSLA.wgt
## 1 2016-12-30 0.3822358 0.5168934 0.06664234 0.03422845
## 92 2017-03-31 0.2446269 0.2938863 0.43509783 0.02638897
## 183 2017-06-30 0.2569582 0.2944017 0.41526606 0.03337405
## 275 2017-09-30 0.2587221 0.2950779 0.41249954 0.03370040weights[1, "date"] <- weights[1, "date"]+2
weights[2, "date"] <- weights[2, "date"]+1
weights## date AMZN.wgt MSFT.wgt AAPL.wgt TSLA.wgt
## 1 2017-01-01 0.3822358 0.5168934 0.06664234 0.03422845
## 92 2017-04-01 0.2446269 0.2938863 0.43509783 0.02638897
## 183 2017-06-30 0.2569582 0.2944017 0.41526606 0.03337405
## 275 2017-09-30 0.2587221 0.2950779 0.41249954 0.03370040Step 5: Calculate the Quarterly VW Portfolio Values
q1.vw.wgt <- subset(weights, date == "2017-01-01") #I'm not sure why author took the long way
q2.vw.wgt <- subset(weights, date == "2017-04-01")
q3.vw.wgt <- subset(weights, date == "2017-07-03")
q4.vw.wgt <- subset(weights, date == "2017-10-01")
q1.vw.wgt## date AMZN.wgt MSFT.wgt AAPL.wgt TSLA.wgt
## 1 2017-01-01 0.3822358 0.5168934 0.06664234 0.03422845q2.vw.wgt## date AMZN.wgt MSFT.wgt AAPL.wgt TSLA.wgt
## 92 2017-04-01 0.2446269 0.2938863 0.4350978 0.02638897q3.vw.wgt## [1] date AMZN.wgt MSFT.wgt AAPL.wgt TSLA.wgt
## <0 rows> (or 0-length row.names)q4.vw.wgt## [1] date AMZN.wgt MSFT.wgt AAPL.wgt TSLA.wgt
## <0 rows> (or 0-length row.names)Step 7: Calculate VW Portfolio Values for 1Q 2013
vw.q1 <- subset(vwport,
vwport$date >= as.Date("2016-12-30") &
vwport$date <= as.Date("2017-04-01"))
vw.q1[c(1:3, nrow(vw.q1)), ]## date AMZN.Close MSFT.Close AAPL.Close TSLA.Close AMZN.ret
## 1 2016-12-30 749.87 62.14 115.82 213.69 NA
## 2 2017-01-03 753.67 62.58 116.15 216.99 1.005068
## 3 2017-01-04 757.18 62.30 116.02 226.99 1.004657
## 63 2017-03-31 886.54 65.86 143.66 278.30 1.011639
## MSFT.ret AAPL.ret TSLA.ret
## 1 NA NA NA
## 2 1.0070809 1.0028492 1.015443
## 3 0.9955257 0.9988807 1.046085
## 63 1.0022828 0.9981242 1.001367vw.q1 <- vw.q1[, c(1, 6:9)]
vw.q1[c(1:3, nrow(vw.q1)), ]## date AMZN.ret MSFT.ret AAPL.ret TSLA.ret
## 1 2016-12-30 NA NA NA NA
## 2 2017-01-03 1.005068 1.0070809 1.0028492 1.015443
## 3 2017-01-04 1.004657 0.9955257 0.9988807 1.046085
## 63 2017-03-31 1.011639 1.0022828 0.9981242 1.001367names(vw.q1)[2:5] <- paste(c("AMZN", "MSFT", "AAPL", "TSLA"))
vw.q1[c(1:3, nrow(vw.q1)), ]## date AMZN MSFT AAPL TSLA
## 1 2016-12-30 NA NA NA NA
## 2 2017-01-03 1.005068 1.0070809 1.0028492 1.015443
## 3 2017-01-04 1.004657 0.9955257 0.9988807 1.046085
## 63 2017-03-31 1.011639 1.0022828 0.9981242 1.001367vw.q1[1, 2:5] <- 1
vw.q1$AMZN <- cumprod(vw.q1$AMZN)
vw.q1$MSFT <- cumprod(vw.q1$MSFT)
vw.q1$AAPL <- cumprod(vw.q1$AAPL)
vw.q1$TSLA <- cumprod(vw.q1$TSLA)
vw.q1[c(1:3, nrow(vw.q1)), ]## date AMZN MSFT AAPL TSLA
## 1 2016-12-30 1.000000 1.000000 1.000000 1.000000
## 2 2017-01-03 1.005068 1.007081 1.002849 1.015443
## 3 2017-01-04 1.009748 1.002575 1.001727 1.062240
## 63 2017-03-31 1.182258 1.066290 1.245751 1.302354vw.q1$AMZN.idx <- vw.q1$AMZN * q1.vw.wgt$AMZN.wgt #Apply the Q-end weights; note
# that q1.vw.wgt$AMZN.wgt is a scalar
vw.q1$MSFT.idx <- vw.q1$MSFT * q1.vw.wgt$MSFT.wgt
vw.q1$AAPL.idx <- vw.q1$AAPL * q1.vw.wgt$AAPL.wgt
vw.q1$TSLA.idx <- vw.q1$TSLA * q1.vw.wgt$TSLA.wgt
vw.q1[c(1:3, nrow(vw.q1)), ]## date AMZN MSFT AAPL TSLA AMZN.idx MSFT.idx
## 1 2016-12-30 1.000000 1.000000 1.000000 1.000000 0.3822358 0.5168934
## 2 2017-01-03 1.005068 1.007081 1.002849 1.015443 0.3841727 0.5205535
## 3 2017-01-04 1.009748 1.002575 1.001727 1.062240 0.3859619 0.5182244
## 63 2017-03-31 1.182258 1.066290 1.245751 1.302354 0.4519014 0.5511585
## AAPL.idx TSLA.idx
## 1 0.06664234 0.03422845
## 2 0.06683222 0.03475704
## 3 0.06675742 0.03635882
## 63 0.08301975 0.04457755#idx = daily gross returns * quarterly weight
#weight is based on market capitalization
#So larger firms would have a greater influence on portfolio returns
q1.vw.val <- data.frame(rowSums(vw.q1[, 6:9])) #Calculate the daily portfolio values
q1.vw.val[c(1:3, nrow(q1.vw.val)), ]## [1] 1.000000 1.006316 1.007303 1.130657names(q1.vw.val) <- paste("port.val")
q1.vw.val$date <- vw.q1$date
q1.vw.val[c(1:3, nrow(q1.vw.val)), ]## port.val date
## 1 1.000000 2016-12-30
## 2 1.006316 2017-01-03
## 3 1.007303 2017-01-04
## 63 1.130657 2017-03-31q2.vw.inv <- q1.vw.val[nrow(q1.vw.val), 1]
q2.vw.inv## [1] 1.130657Step 8: Calculate VW Portfolio Values for 2Q 2013
vw.q2 <- subset(vwport,
vwport$date >= "2017-04-01" &
vwport$date <= "2017-07-03")
vw.q2[c(1:3, nrow(vw.q2)), ]## date AMZN.Close MSFT.Close AAPL.Close TSLA.Close AMZN.ret
## 64 2017-04-03 891.51 65.55 143.70 298.52 1.0056061
## 65 2017-04-04 906.83 65.73 144.77 303.70 1.0171843
## 66 2017-04-05 909.28 65.56 144.02 295.00 1.0027017
## 126 2017-06-30 968.00 68.93 144.02 361.61 0.9918744
## MSFT.ret AAPL.ret TSLA.ret
## 64 0.9952930 1.0002784 1.0726554
## 65 1.0027460 1.0074461 1.0173523
## 66 0.9974135 0.9948194 0.9713533
## 126 1.0064242 1.0023665 1.0023839vw.q2 <- vw.q2[, c(1, 6:9)]
vw.q2[c(1:3, nrow(vw.q2)), ]## date AMZN.ret MSFT.ret AAPL.ret TSLA.ret
## 64 2017-04-03 1.0056061 0.9952930 1.0002784 1.0726554
## 65 2017-04-04 1.0171843 1.0027460 1.0074461 1.0173523
## 66 2017-04-05 1.0027017 0.9974135 0.9948194 0.9713533
## 126 2017-06-30 0.9918744 1.0064242 1.0023665 1.0023839names(vw.q2)[2:5] <- paste(c("AMZN", "MSFT", "AAPL", "TSLA"))
vw.q2[c(1:3, nrow(vw.q2)), ]## date AMZN MSFT AAPL TSLA
## 64 2017-04-03 1.0056061 0.9952930 1.0002784 1.0726554
## 65 2017-04-04 1.0171843 1.0027460 1.0074461 1.0173523
## 66 2017-04-05 1.0027017 0.9974135 0.9948194 0.9713533
## 126 2017-06-30 0.9918744 1.0064242 1.0023665 1.0023839#vw.q2[1, 2:4] <- 1 #difference from Q1
vw.q2$AMZN <- cumprod(vw.q2$AMZN)
vw.q2$MSFT <- cumprod(vw.q2$MSFT)
vw.q2$AAPL <- cumprod(vw.q2$AAPL)
vw.q2$TSLA <- cumprod(vw.q2$TSLA)
vw.q2[c(1:3, nrow(vw.q2)), ]## date AMZN MSFT AAPL TSLA
## 64 2017-04-03 1.005606 0.9952930 1.000278 1.072655
## 65 2017-04-04 1.022887 0.9980261 1.007727 1.091269
## 66 2017-04-05 1.025650 0.9954448 1.002506 1.060007
## 126 2017-06-30 1.091885 1.0526131 1.006644 1.299353vw.q2$AMZN.ind <- (q2.vw.inv * q2.vw.wgt$AMZN.wgt) * vw.q2$AMZN #Apply weight
vw.q2$MSFT.ind <- (q2.vw.inv * q2.vw.wgt$MSFT.wgt) * vw.q2$MSFT
vw.q2$AAPL.ind <- (q2.vw.inv * q2.vw.wgt$AAPL.wgt) * vw.q2$AAPL
vw.q2$TSLA.ind <- (q2.vw.inv * q2.vw.wgt$TSLA.wgt) * vw.q2$TSLA
vw.q2[c(1:3, nrow(vw.q2)), ]## date AMZN MSFT AAPL TSLA AMZN.ind MSFT.ind
## 64 2017-04-03 1.005606 0.9952930 1.000278 1.072655 0.2781398 0.3307206
## 65 2017-04-04 1.022887 0.9980261 1.007727 1.091269 0.2829195 0.3316287
## 66 2017-04-05 1.025650 0.9954448 1.002506 1.060007 0.2836838 0.3307710
## 126 2017-06-30 1.091885 1.0526131 1.006644 1.299353 0.3020037 0.3497671
## AAPL.ind TSLA.ind
## 64 0.4920835 0.03200469
## 65 0.4957475 0.03256004
## 66 0.4931793 0.03162730
## 126 0.4952149 0.03876864q2.vw.val <- data.frame(rowSums(vw.q2[, 6:9]))
q2.vw.val[c(1:3, nrow(q2.vw.val)), ]## [1] 1.132949 1.142856 1.139261 1.185754names(q2.vw.val) <- paste("port.val")
q2.vw.val[c(1:3, nrow(q2.vw.val)), ]## [1] 1.132949 1.142856 1.139261 1.185754q2.vw.val$date <- vw.q2$date
q2.vw.val[c(1:3, nrow(q2.vw.val)), ]## port.val date
## 64 1.132949 2017-04-03
## 65 1.142856 2017-04-04
## 66 1.139261 2017-04-05
## 126 1.185754 2017-06-30#$1.104 at the end of Q1 and $1.056 by the end of Q2
#it doesn't mean that the portfolio grew 5.6% during Q2 but 5.6% during Q1-Q2
#b/c it's a cumulative measureStep 11: Combine Quarterly VW Portfolio Values into One Data Object
vw.portval <- rbind(q1.vw.val, q2.vw.val)
vw.portval[c(1:3, nrow(vw.portval)), ]## port.val date
## 1 1.000000 2016-12-30
## 2 1.006316 2017-01-03
## 3 1.007303 2017-01-04
## 126 1.185754 2017-06-303.3.3 Normalized EW and VW Portfolio Price Chart
Compare the performance of EW and VW portfolio from 12/31/2012 to 12/31/2013
Step 1: Combine the Data
port.val <- merge(vw.portval, ew.portval, by = "date")
port.val[c(1:3, nrow(port.val)), ]## date port.val.x port.val.y
## 1 2016-12-30 1.000000 1.750000
## 2 2016-12-30 1.000000 NA
## 3 2017-01-03 1.006316 1.769192
## 189 2017-06-30 1.185754 2.634692Step 2: Rename the Variables
names(port.val)[2:3] <- paste(c("VW.cum", "EW.cum"))
port.val[c(1:3, nrow(port.val)), ]## date VW.cum EW.cum
## 1 2016-12-30 1.000000 1.750000
## 2 2016-12-30 1.000000 NA
## 3 2017-01-03 1.006316 1.769192
## 189 2017-06-30 1.185754 2.634692Step 3: Plot the Data
par(mfrow = c(1, 1))
y.range <- range(port.val[1, 2:3])
y.range## [1] 1.00 1.75plot(x = port.val$date,
y = port.val$EW.cum,
xlab = "Date",
ylab = "Value of Investment",
ylim = y.range,
type = "l",
lty = 1,
main = "Value of R1 Investment in Equal-Weighted and
Value-Weighted Portfolio of AMZN, AAPL, TSLA, and MSFT
December 30, 2016 - June 30, 2017")
lines(x = port.val$date,
y = port.val$VW.cum,
lty = 2)
abline(h = 1, lty = 1)
legend("topleft",
c("Equal-Weighted Portfolio", "Value-Weighted Portfolio"), #typo in the textbook
lty = c(1, 2))
Interpretation:
1: The gross return on a $100 investment in the equal-weighted portfolio would be $217.59
2: The gross return on a $100 investment in the value-weighted portfolio would be #113.06
3: Out of the 4 stocks, MSFT was the best performing security
4: The equal-weighted portfolio performed the best. In the value-weighted portfolio, Amazon was allocated a larger percentage of the investment. The return for Amazon was -$.81 and thus the portfolio took a bigger hit and underperformed. Having a smaller percentage in Amazon as shown in the equal-weighted portfolio, attributed to the outperformance of the value-weighted portfolio.