A stock has a beta of 1.27 and an expected return of 12.5 percent. A risk-free a
ID: 2757314 • Letter: A
Question
A stock has a beta of 1.27 and an expected return of 12.5 percent. A risk-free asset currently earns 4.15 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 percentage rounded to 2 decimal places (e.g., 32.16).) If a portfolio of the two assets has a beta of 0.87, what are the portfolio weights? (Do not round intermediate calculations. Round your answers to 4 decimal places (e.g., 32.1616).) If a portfolio of the two assets has an expected return of 11.7 percent, what is its beta? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).) If a portfolio of the two assets has a beta of 2.47, what are the portfolio weights? (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 4 decimal places (e.g., 32.1616).)Explanation / Answer
A./
EXPECTED RETURN
= 50% * 12.5% + 50% * 4.15%
= 8.33%
B./
PORTFOLIO BETA
= WEIGHT OF STOCK * BETA OF STOCK + WEIGHT OF RISK REE RATE * BETA OF RISK FREE RATE
0.87 = WEIGHT OF STOCK * 1.27 + 0 [AS BETA OF RISK FREE RATE IS 0]
WEIGHT OF STOCK = 0.87 / 1.27
= 68.50%
C./
LET THE WEIGHT OF STOCK IS W
AND WEIGHT OF RISK FREE RATE IS 1-W
PORTFLOIO EXPECTED RETURN
= WEIGHT OF STOCK * EXPECTED RETURN OF STOCK + WEIGHT OF RISK FREE RATE * RISK FREE RATE
11.7% = W * 12.5% + (1-W) * 4.15%
11.7% = 12.5%W + 4.15% - 4.15%W
8.35%W = 7.55%
W = 0.90
SO WEIGHT OF STOCK IN THE PORTFOLIO IS 0.90
WEIGHT OF RISK FREE RATE IS 0.10
BETA OF PORTFOLIO
= WEIGHT OF STOCK * BETA OF STOCK + WEIGHT OF RISK REE RATE * BETA OF RISK FREE RATE
= 0.90 * 1.27 + 0.10 * 0
= 1.14
D./
LET THE WEIGHT OF STOCK IS W
AND WEIGHT OF RISK FREE RATE IS 1-W
BETA OF PORTFOLIO
= WEIGHT OF STOCK * BETA OF STOCK + WEIGHT OF RISK REE RATE * BETA OF RISK FREE RATE
2.47 = W * 1.27 + (1-W) * 0
W = 1.94
WEIGHT OF STOCK IS 1.94
WEIGHT OF RISK FREE RATE IS -0.94
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