Problem 12-10 A stock has a beta of 1.3 and an expected return of 10 percent. A
ID: 2737421 • Letter: P
Question
Problem 12-10
A stock has a beta of 1.3 and an expected return of 10 percent. A risk-free asset currently earns 3.4 percent.
What is the expected return on a portfolio that is equally invested in the two assets? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)
If a portfolio of the two assets has a beta of .32, what are the portfolio weights? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)
If a portfolio of the two assets has an expected return of 11.50 percent, what is its beta? (Do not round intermediate calculations. Round your answer to 4 decimal places.)
If a portfolio of the two assets has a beta of 1.41, what are the portfolio weights? (Negative values should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)
A stock has a beta of 1.3 and an expected return of 10 percent. A risk-free asset currently earns 3.4 percent.
Explanation / Answer
Answer:a Since the portfolio is equally weighted, we can sum the returns of each asset and divide by the number of assets. The expected return of the portfolio is:
ERP =(0.10+0.034)/2=0.067 or 6.7%
Answer:b Here we need to find the portfolio weights that result in a portfolio with a b of 0.32. We know the b of the risk-free asset is zero. We also know the weight of the risk-free asset is one minus the weight of the stock since the portfolio weights must sum to one, or 100 percent.
So: bp = 0.32 = wS(1.3) + (1 – wS)(0)
0.32 = 1.3wS + 0 – 0wS
wS = 0.32/1.3
wS = 0.25
And, the weight of the risk-free asset is:
wRf = 1 – 0.25
wRf = 0.75
Answer:c We need to find the portfolio weights that result in a portfolio with an expected return of 11.50%. We also know the weight of the risk-free asset is one minus the weight of the stock since the portfolio weights must sum to one, or 100 percent. So:
E(Rp) = 0.115 = 0.10wS + .034(1 – wS)
0.115 = 0.10 wS + 0.034 – 0.034wS
0.115 – 0.034 = 0.066 wS
wS = 0.081/0.066
wS = 1.2272
So, the b of the portfolio will be:
bp = 1.2272(1.3) + (1 – 1.2272)(0)
bp = 1.5954
Answer:d Solving for the b of the portfolio as we did in part b, we find:
bp = 1.41 = wS(1.3) + (1 – wS)(0)
1.41 = 1.3 wS
wS = 1.41/1.3
wS = 1.08
wRf = 1 – 1.08
wRf = –0.08
The portfolio is invested 108% in the stock and –8% in the risk-free asset. This represents borrowing at the risk-free rate to buy more of the stock.