A stock has a beta of 1.55 and an expected return of 15 percent. A risk-free ass
ID: 2784249 • Letter: A
Question
A stock has a beta of 1.55 and an expected return of 15 percent. A risk-free asset currently earns 2.2 percent. a. 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, e.g., 32.16.) Expected return % b. If a portfolio of the two assets has a beta of .93, what are the portfolio weights? (Do not round intermediate calculations. Round your answers to 4 decimal places, e.g., 32.1616.) Weight of stock Risk-free weight c. If a portfolio of the two assets has an expected return of 8 percent, what is its beta? (Do not round intermediate calculations. Round your answer to 3 decimal places, e.g., 32.161.) Beta d. If a portfolio of the two assets has a beta of 3.10, what are the portfolio weights? (Do not round intermediate calculations. Negative amounts should be indicated by a minus sign. Enter your answers as a whole number.) Weight of stock Risk-free weight
Explanation / Answer
a.
Expected return of portfolio = (15% × 50%) + (2.20% × 50%)
= 7.50% + 1.10%
= 8.60%
Expected return of portfolio is 8.60%.
b.
if portfolio beta = 0.93.
Suppose weight of stock = X
weight of risk free securities = 1 - X
0.93 = (1.55 × X) + 0 × (1 - X)
X = 0.93 / 1.55
= 60%
Weight of stock is 60%, so weight of risk free is 40%.
c.
Expected return of portfolio = 8%
Suppose weight of stock = X
weight of risk free securities = 1 - X
8% = (15% × X) + 2.20% × (1 - X)
= 12.80% × X + 2.20%
X = 5.80% / 12.80%
= 45.31%
Weight of stock is 45.31%, so weight of risk free securities is 54.69%.
d.
if portfolio beta = 3.10.
Suppose weight of stock = X
weight of risk free securities = 1 - X
3.10 = (1.55 × X) + 0 × (1 - X)
X = 3.10 / 1.55
= 200%
Weight of stock is 200%, so weight of risk free is -100%. it mean investor should borrow at risk free at invest in stock.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.