Suppose that you want to create a portfolio that consists of stock X and stock Y
ID: 3064814 • Letter: S
Question
Suppose that you want to create a portfolio that consists of stock X and stock Y. For a $1,000 investment, the expected return for stock X is $76.60 and the expected return for stock Y is $122.50. The variance for stock X is 5,000 and the variance for stock Y is 8,350. The covariance of stock X and stock Y is 3,246. a.Compute the portfolio expected return and portfolio risk if the percentage invested in stock X is 30 %. b.Compute the portfolio expected return and portfolio risk if the percentage invested in stock X is 50 %. c.Compute the portfolio expected return and portfolio risk if the percentage invested in stock X is 70 %.
Explanation / Answer
Solution:- Given ,
Total Investment =$1000
Expected return for Stock X = $76.6
Expected return for Stock Y = $122.5
Variance for stock X = 5000
Standard deviation for stock X = (5000)1/2 = 70.71
Variance for stock = 8350
Standard deviation for stock Y = (8350)1/2 = 91.37
Covariance of stock X and stock Y = 3246
if 30%
a) Portfolio expected return
= p*xE(X) + p*yE(Y)
= 0.30*76.60 + (1 - 0.30)*122.50
= 22.98 + 85.75
= $ 108.73 Ans.
Portfolio risk = {(0.3*70.71)2 + (0.7*91.37)2 + 2*0.3*0.7*3246}1/2
= $76.84 Ans.
b) If 50%
Portfolio expected return
= p*xE(X) + p*yE(Y)
= 0.50*76.60 + (1 - 0.50)*122.50
= 38.3 + 61.25
= $ 99.55 Ans.
Portfolio risk = {(0.5*70.71)2 + (0.5*91.37)2 + 2*0.5*0.5*3246}1/2
= $70.43 Ans.
c) If 70%
Portfolio expected return
= p*xE(X) + p*yE(Y)
= 0.70*76.60 + (1 - 0.70)*122.50
=53.62 + 36.75
= $ 90.37 Ans.
Portfolio risk = {(0.7*70.71)2 + (0.3*91.37)2 + 2*0.7*0.3*3246}1/2
= $67.56 Ans.