Question

Problem 7. (15 points) Suppose your investment portfolio consists of three assets: Apple stocks, Walmart stocls, and the risk-free T-bills. The following table lists how many units of each of the three assets you own, along with the price per unit of asset. Number of units owned Price per unit Expected return Asset Apple stocks Walmart stocks T-bills 200 200 12 $70 $1000 0 10-10% 004-4% (a) (5 points) What is the expected return of your investment portfolio? (b) (5 points) Suppose that the variance of each of the two stocks are σ2ppe = 0.12 and σ21 art-0.05, and the covarance between the two stocks is σAppleWi ,--0.1. What is the vanance of your entire investment portfolio? (e) (5 points) What is the Sharpe ratio of your investment portfolio?

Answer 1

a) Apple stocks = 200*$120 = $24000

Expected return = 1.15*$24000 = $27600

Walmart stocks = 200*$70 = $14000

Expected return = 1.1*$14000 = $15400

T Bills = 12*$1000 = $12000

Expected return = 1.04*$12000 = $12480

Expected return of portfolio = ($12480+$15400+$27600)/($12000+$14000+$24000) = 1.1096

So, Return = 10.96%

b) Variance of portfolio = 0.5^2*0.12^2 + 0.5^2*0.05^2 + 2(0.5*0.5*0.12*0.05*-0.1) = 0.2647

c) Sharpe ratio = (Expected return of portfolio - Riskfree rate)/Std deviation of portfolio

= (10.96-4)%/sqrt(26.47%) = 1.353