Question

Question 5 (8 points) a. The expected rates of return for stocks A and B are 16% and 20% respectively. The beta of stock A is 0.7 while that of stock B is 0.8. The T-bill rate is 4% and the expected rate of return on S&P 500 index is 24%. The standard deviation of stock A is 20% while that of B is 32%. If you could invest only in T-bills plus one of these stocks, which stock would you choose?

Answer 1

Part A:

CAPM Ret = Rf + Beta ( Rm - Rf)

Rf = Risk free rate

Beta = Systematic Risk

Rm = Market ret

Stock A:

CAPM Ret = Rf + Beta ( Rm - Rf)

= 4% + 0.7 (24% - 4%)

= 4% + 0.7( 20%)

= 4% +14%

= 18%

Actual Ret = 16%

as Actual ret < CAPM ret, Stock is under performed.

STock B:

CAPM Ret = Rf + Beta ( Rm - Rf)

= 4% + 0.8 (24% - 4%)

= 4% + 0.8( 20%)

= 4% +16%

= 20%

Actual Ret = 20%

as Actual ret = CAPM ret, Stock is perfectly priced.

Hence STock B is selected over STock A.

Part B:

CAPM ret of Stock A:

CAPM Ret = Rf + Beta ( Rm - Rf)

= 5% +1.2 (15% - 5%)

= 5% + 1.2( 10%)

= 5% +12%

= 17%

Actual Ret = 14%

as Actual ret < CAPM ret, Stock is under performed.

IF CAPM is Valid, the situation is not possible.

Pls comment,if any further assistance is required.