A stock has a beta of 1.28 and an expected return of 12.6 percent. A risk-free a
ID: 2775510 • Letter: A
Question
A stock has a beta of 1.28 and an expected return of 12.6 percent. A risk-free asset currently earns 4.2 percent. Required: (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 percentage rounded to 2 decimal places (e.g., 32.16).) Expected return % (b) If a portfolio of the two assets has a beta of 0.88, what are the portfolio weights? (Do not round intermediate calculations. Round your answers to 4 decimal places (e.g., 32.1616).) Weight of the stock Weight of the risk-free asset (c) If a portfolio of the two assets has an expected return of 11.8 percent, what is its beta? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).) Beta (d) If a portfolio of the two assets has a beta of 2.48, 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).) Weight of the stock Weight of the risk-free asset
Explanation / Answer
a)
RA = 12.6%
RB=4.2%
WA = 0.5
WB= 0.5
Portfolio return = Ra x WA + RB xWB
= 12.6% x0.5 +4.2%x0.50
= 8.40%
Portfolio beta = Beta A x WA + Beta B x WB
0.88 = 1.28 x WA + 0xWB
WA = 0.88/1.28
= 68.75%
WB= 1-WA
= 1-0.6875
= 31.25%
c)
Portfolio return = Ra x WA + RB xWB
11.80% = 12.6% xWA + 4.2% x(1-WA)
11.80% = 8.4% WA +4.2%
WA = 7.6%/8.4%
= 0.9048
WB = 1-WA
= 1-0.9048
= 0.0952
Portfolio beta = Beta A x WA + Beta B x WB
= 1.28 x .9048 + 0x 0.0952
= 1.16
Portfolio beta = Beta A x WA + Beta B x WB
2.48 = 1.28 x WA + 0xWB
WA = 2.48/1.28
= 193.75%
WB= 1-WA
= 1-1.9375
= -93.75%
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