hw4

Importind data

library(readxl)
hw4 <- read_excel("C:/Users/DELL/Downloads/hw4.xlsx")
head(hw4)

## # A tibble: 6 × 4
##   date                Nordstrom Starbucks Microsoft
##   <dttm>                  <dbl>     <dbl>     <dbl>
## 1 1995-03-01 00:00:00  -0.0362    0.00521   0.121  
## 2 1995-04-01 00:00:00  -0.0568   -0.0211    0.139  
## 3 1995-05-01 00:00:00   0.0782    0.212     0.0353 
## 4 1995-06-01 00:00:00  -0.00302   0.204     0.0650 
## 5 1995-07-01 00:00:00  -0.0276    0.0480    0.00138
## 6 1995-08-01 00:00:00   0.0277    0.0679    0.0219

Computing optimal weight

library(fBasics)
Sigma <- cov(hw4[, 2:4])
ones <- rep(1, 3)
one.vec <- matrix(ones, ncol =1)
a <- inv(Sigma)%*%one.vec
b <- t(one.vec)%*%a
mvp.w <- a / as.numeric(b)
head(mvp.w)

##                [,1]
## Nordstrom 0.3635964
## Starbucks 0.1936574
## Microsoft 0.4427462

For a given portfolio return of 4.5%, compute the optimal weights for the minimum variance portfolio based on the three assets and portfolio risk (standard deviation).

mu <- 0.045/12
return <- hw4[,2:4]
Ax <- rbind(2*cov(return), colMeans(return), rep(1, ncol(return)))
Ax <- cbind(Ax, rbind(t(tail(Ax, 2)), matrix(0, 2, 2)))
b0 <- c(rep(0, ncol(return)), mu, 1)
out <- solve(Ax, b0)
wgt <- out[1:3]
wgt

##   Nordstrom   Starbucks   Microsoft 
##  0.90766134  0.11201674 -0.01967808

sum(wgt)

## [1] 1