Question

You own a portfolio equally invested in a risk-free asset and two stocks. If one of the stocks has a beta of 1 and the total portfolio is equally as risky as the market, what must the beta be for the other stock in your portfolio?

Multiple Choice

• 1.00

• 2.10

• 1.90

• 1.05

• 2.00

Answer 1

Ans 2.00

Let the Beta of other stock be X.

Beta of Risk free asset is 0. Let Stock 1 be the risk free asset, So its beta = 0.

Since portfolio is equally invested, we take weight of each stock as 1/3

Total Beta = Beta of Stock 1 + Stock 2 + Stock 3

1 = 1/3 * 0 + 1/3* 1 + 1/3 * X

1 - 1/3 = 1/3* X

2/3 = 1/3* X

X = 2

Answer 2

SOLUTION :

bP = 1/3 bF + 1/3 bS1 + 1/3  bS2 

bP = 1 , since it is equal to bM

bF = 0 being risk free.

So,

1 = 0 + 1/3 * 1 + 1/3 bS2 

=> bS2 = (1 - 1/3) * 3 = 2 

=> bS2 (beta of stock 2) = 2 (ANSWER).