Question

Jamie Peters invested ?$117,000 to set up the following portfolio one year? ago:

A $33,000 0.81 $1,400 $33,000

B $40,000 0.98 $1,200 $41,000

C $31,000 1.47 $0 $37,500

D $13,000 1.38 $500 $13,500

a.??Calculate the portfolio beta on the basis of the original cost figures.

b.??Calculate the percentage return of each asset in the portfolio for the year.

c.??Calculate the percentage return of the portfolio on the basis of original? cost, using income and gains during the year.

d.??At the time Jamie made his? investments, investors were estimating that the market return for the coming year would be 9 %. The estimate of the? risk-free rate of return averaged 5 % for the coming year. Calculate an expected rate of return for each stock on the basis of its beta and the expectations of market and? risk-free returns.

e.??On the basis of the actual? results, each stock in the portfolio performed differently relative to those? CAPM-generated expectations of performance. What factors could explain these? differences?

Answer 1

a. The portfolio beta equals the weighted sum of the betas of the individual investments

Therefolio the portfolio beta is this case = (0.81*33,000/117,0000) + (0.98*40,000/117,000) +(1.47*31,000/117,000)+(1.38*13,000/117,000) = 1.10

b. The percentage return of asset A = 1,400/33,000= 4.24%

The percentage return of asset B = (1,200+41,000-40,000)/40,000 =5.5%

The percentage return of asset C = 37,500-31,000/31,000=20.97%

The percentage return of asset D = 13,500-13,000/13,000=3.85%

c. The portfolio return equals the weighted sum of the returns of the individual investments

Therefolio the portfolio return is this case = (4.24%*33,000/117,0000) + (5.5%*40,000/117,000) +(20.97%*31,000/117,000)+(3.85%*13,000/117,000) = 9.06%

d. Expected Return = Risk Free Return + (Market Return- Risk-Free Return) * Beta

Therefore,

Expected Return for Investment A= 5 + (9-5) *0.81 =8.24%

Expected Return for Investment B= 5 + (9-5) *0.98 =8.92%

Expected Return for Investment C= 5 + (9-5) *1.47 =10.88%

Expected Return for Investment D= 5 + (9-5) *1.38 =10.52%