2.37 Portfolio Return

A portfolio’s value increases by 18% during a financial boom and by 9% during normal times. It decreases by 12% during a recession. What is the expected return on this portfolio if each scenario is equally likely?

First, we create a data frame object

e <- c("Boom","Normal","Recession")
c <- c(0.333, 0.333, 0.333)
r <- c(0.18, 0.09, -0.12)
data <- data.frame(e,c,r)

names(data) <- c("Economy","Change-Pct","Return")

print(data)
##     Economy Change-Pct Return
## 1      Boom      0.333   0.18
## 2    Normal      0.333   0.09
## 3 Recession      0.333  -0.12

Then, Calculate piecewise expected return. Try to use melt() and cast() from reshape to form a “Pivot” table The grand total of the expected returns would be the portfolio return.

data[,"Expected-Return"] <- 0.0
data["Expected-Return"] <- data["Change-Pct"] * data["Return"]

library(reshape)

data.m <- melt(data,id=c(1:3), measure=c(4))
data.c <- cast(data.m, Economy ~ variable, sum,  margins=c("grand_row"))

Show Result in table format.

library(htmlTable)

htmlTable(data.c)
Economy Expected-Return
1 Boom 0.05994
2 Normal 0.02997
3 Recession -0.03996
4 (all) 0.04995

The Portoflio return is 5%