Question

You have $10,000 to invest in a portfolio containing Stock R, Stock S, and a risk-free asset. You must invest all of your money. Your goal is to create a portfolio that has an expected return of 15% and that has only 120% of the risk of the overall market. If Stock R has an expected return of 25% and a beta of 1.6, Stock S has an expected return of 17.5% and a beta of 1.3, and the risk-free rate is 6%, how much money will you invest in Stock R? Explain your answer.

Please show step by step calculations and formulas

Answer 1

The weighted return of stocks in a portfolio is the expected return of the portfolio.

As the beta of Risk-free asset is 0, it is not considered for the below portfolio.

Also, if W₁ + W₂=1 ,then

W₁ = 1-W₂

The formula is :

Expected Return = W₁R₁ + W₂R_2, where

W₁ is the weight of Stock R

R₁ Expected return of Stock R

W₂ is the weight of Stock S

R₂ Expected return of Stock S

15% = 25%(1-W₂) + 17.5%(W₂)

W₂ = 1.333 or Weight of stock S = 1.333

if W₁ + W₂=1, then W₁ is -0.333, or weight of Stock R = -0.333

The weight of Stock R is -0.333 hence it should be shorted to the extent of 33% and that proceeds should be invested in Stock S in the proportion of 1.33, .33 being proceeds from Short selling of Stock R.