A stock has a beta of 1.21 and an expected return of 11.9
percent. A risk-free asset currently earns 3.85 percent.
a. What is the expected return on a portfolio that
is equally invested in the two assets? (Do not round
intermediate calculations and 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
.81, what are the portfolio weights? (Do not round
intermediate calculations and 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 11.1 percent, what is its beta? (Do not
round intermediate calculations and round your answer to 2 decimal
places, e.g., 32.16.)
Beta
d. If a portfolio of the two assets has a beta of
2.41, what are the portfolio weights? (A negative answer
should be indicated by a minus sign. Do not round intermediate
calculations and round your answers to 4 decimal places, e.g.,
32.1616.)
Weight of the stock | |
Weight of the risk-free asset | |
part A:
Expected Ret = Weighted Avg ret
Partculars | Weight | Ret | Wtd Ret |
Stock | 0.5 | 11.90% | 5.95% |
Rf Asset | 0.5 | 3.85% | 1.93% |
Expected Ret | 7.88% |
Part B:
Portfolio Beta = Weighted in Stock * Stock Beta
Weight in Stock = Portfolio Beta / Stock Beta
= 0.81 / 1.21
= 0.67
Weigt in Risk Free Asset = 1 - 0.67
= 0.33
Part C:
Partculars | Weight | Ret | Wtd Ret |
Stock | X | 11.90% | 0.119X |
Rf Asset | 1-X | 3.85% | 0.0385 - 0.0385X |
Expected Ret | 0.0805X + 0.0385 |
0.0805X + 0.0385 = 0.111
0.0805X = 0.111 - 0.0385
= 0.0725
X = 0.0725/ 0.0805
= 0.90
Portfolio Beta = Weight In Stcok * Stock Beta
= 0.9 * 1.21
= 1.089
Part D:
Weight In stock = Portfolio Beta / Stock Beta
= 2.41 / 1.21
= 2
Weight In stock = 2
Weight is Risk Free Asset = -1
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