Question

A stock has an expected return of 0.13, its beta is 1.44, and the expected return on the market is 0.09. What must the risk-free rate be? (Hint: Use CAPM) Enter the answer in 4 decimals e.g. 0.0123.

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? (Hint: Remember that the market has a Beta=1; also remember that equally invested means that each asset has the same weight- since there are 3 assets, each asset's weight is 1/3 or 0.3333). Enter the answer with 4 decimals (e.g. 1.1234)

Answer 1

1)

Expected return of stock, Rs = 13%

Beta, = 1.44

Expected return on market, Rm = 9%

Using CAPM, Rs = Risk free rate + *(Rm- Rf)

13% = Rf + 1.44* 9% - 1.44 Rf

0.04 = -0.44 Rf

Rf = 0.04/0.44 = -0.091%

2)

Weight of each asset, W1 = W2 = W3 = 1/3

1 = of risk free asset = 0

2 = 1

3 = ?

Portfolio Beta =1= 2 *1/3 + 3*1/3 (since 1 =0)

1= 1/3 + 3 /3

3= 1+ 3

3 = 2.0000