CAPM, portfolio risk, and return Consider the following information for three st

Question

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.)

Fund P has one-third of its funds invested in each of the three stocks. The risk-free rate is 6%, and the market is in equilibrium. (That is, required returns equal expected returns.)

What is the market risk premium (rM - rRF)? Round your answer to two decimal places.
%

What is the beta of Fund P? Do not round intermediate calculations. Round your answer to two decimal places.

What is the required return of Fund P? Do not round intermediate calculations. Round your answer to two decimal places.
%

Would you expect the standard deviation of Fund P to be less than 15%, equal to 15%, or greater than 15%?

less than 15%

greater than 15%

equal to 15%

Explanation / Answer

What is the market risk premium (rM - rRF)?

The expected return of fund P = 1/3 * Expected return of stock A + 1/3 * Expected return of stock B +1/3 * Expected return of stock C

= 1/3 * 10% + 1/3* 11.50% + 1/3 * 13.50%

= 11.67%

Beta of fund P = 1/3 * Beta of stock A + 1/3 * Beta of stock B +1/3 * Beta of stock C

= 1/3 * 0.8 + 1/3* 1.1 + 1/3 * 1.5

= 1.13

Now as per Securities Market line (SML)

Required rate of return of Fund P = risk free rate (rRF) + of Fund P *(Expected market return rM – risk free rate rRF)

Where,

Risk free rate (rRF) = 6%

Market is in equilibrium therefore required returns equal expected returns = 11.67%

Therefore

11.67% = 6% +1.13 * market risk premium

Market risk premium = (11.67% -6%)/1.13

=5%

What is the beta of Fund P?

Beta of fund P = 1/3 * Beta of stock A + 1/3 * Beta of stock B +1/3 * Beta of stock C

= 1/3 * 0.8 + 1/3* 1.1 + 1/3 * 1.5

= 1.13

What is the required return of Fund P?

Market is in equilibrium therefore required returns equal expected returns

The expected return of fund P = 1/3 * Expected return of stock A + 1/3 * Expected return of stock B +1/3 * Expected return of stock C

= 1/3 * 10% + 1/3* 11.50% + 1/3 * 13.50%

= 11.67%

The required return of Fund P is 11.67%

Would you expect the standard deviation of Fund P to be less than 15%, equal to 15%, or greater than 15%?

Less than 15%

Because the returns on the three stocks are positively correlated, but they are not perfectly correlated therefore the standard deviation of Fund P will be less than 15%.

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