Question

is attempting to evaluate 2 possible portfolios consisting of the same 5 assets but held in different proportions. She is particularly interested in using beta to compare the risk of the portfolios and, in this regard, has gathered the following data

:Asset   Asset Beta   Portfolio A   Portfolio B
1   1.28   14%   31%
2   0.72   25%   8%
3   1.26   7%   21%
4   1.09   13%   24%
5   0.95   41%   16%
   Total   100%   100%

.a. Calculate the betas for portfolios A and B.

b. If the risk-free rate is1.9 % and the market return is 6.6 %,

calculate the required return for each portfolio using the CAPM.

c. Then assume you now have the following annual returns

Asset   Returns
1   17.5%
2   10.5%
3   14.0%
4   11.5%
5   8.5%

for each investment:. Using the required return for each portfolio and the additional return data, determine which portfolio you would choose and explain why.

a. The beta of portfolio A is(Round to three decimal places.)

B The beta of portfolio B is

Answer 1

a.

Beta of portfolio A = (1.28*0.14) + (0.72*0.25) + (1.26*0.07) + (1.09*0.13) + (0.95*0.41)

Beta of portfolio A

0.979

Beta of portfolio A is 0.9786

Beta of portfolio B = (1.28*0.31) + (0.72*0.08) + (1.26*0.21)+(1.09*0.24)+(0.95*0.16)

Beta of portfolio B

1.133

b.

Required return using CAPM for portfolio A

Formula to calculate required return using CAPM

Required return = Risk free rate + Beta*(Market return-Risk free return)

Required return = 0.019 + 0.979*(0.066-0.019)

Required return = 0.019 + 0.979*0.047

Required return = 6.50%

Required return using CAPM for portfolio B

Formula to calculate required return using CAPM

Required return = Risk free rate + Beta*(Market return-Risk free return)

Required return = 0.019 + 1.133*(0.066-0.019)

Required return = 0.019 + 1.133*0.047

Required return = 7.22%

c.

Calculation of annual return for Portfolio A

Annual return of portfolio A = (0.175*0.14) + (0.105*0.25) + (0.14*0.07) + (0.115*0.13) + (0.085*0.41)

Annual return of portfolio A

11.04%

Calculation of annual return for Portfolio B

Annual return of portfolio B = (0.175*0.31) + (0.105*0.08) + (0.14*0.21)+(0.115*0.24)+(0.085*0.16)

Annual return of portfolio B

13.33%

Using the annual return data, company should invest in portfolio B as it provides higher annual return than the required return as compared to portfolio A