Problem 8-13
CAPM, portfolio risk, and return
Consider the following information for three stocks, Stocks A, B, and C. The returns on the three stocks are positively correlated, but they are not perfectly correlated. (That is, each of the correlation coefficients is between 0 and 1.)
Stock | Expected Return | Standard Deviation | Beta | ||
A | 8.30 | % | 16 | % | 0.7 |
B | 9.90 | 16 | 1.1 | ||
C | 12.30 | 16 | 1.7 |
Fund P has one-third of its funds invested in each of the three stocks. The risk-free rate is 5.5%, and the market is in equilibrium. (That is, required returns equal expected returns.)
a |
Using Stock A Data |
As per CAPM |
expected return = risk-free rate + beta * (Market risk premium) |
8.3 = 5.5 + 0.7 * (Market risk premium%) |
Market risk premium% = 4 |
Weight of Stock A = 0.3333 |
Weight of Stock B = 0.3333 |
Weight of Stock C = 0.3333 |
Beta of Fund P = Weight of Stock A*Beta of Stock A+Weight of Stock B*Beta of Stock B+Weight of Stock C*Beta of Stock C |
Beta of Fund P = 0.7*0.3333+1.1*0.3333+1.7*0.3333 |
Beta P = 1.17 |
c |
Weight of Stock A = 0.3333 |
Weight of Stock B = 0.3333 |
Weight of Stock C = 0.3333 |
Expected return of Fund P = Weight of Stock A*Expected return of Stock A+Weight of Stock B*Expected return of Stock B+Weight of Stock B*Expected return of Stock C |
Expected return of Fund P = 8.3*0.3333+9.9*0.3333+12.3*0.3333 |
Expected return of Fund P = 10.17% |
d |
As std dev of all stocks is equal to 16% and the are not perfectly correlated the std dev of Fund P will be less than 16% |
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