Question

Jamie Peters invested ​$120,000 to set up the following portfolio one year​ ago:

Asset	Cost	Beta at purchase	Yearly income		Value today
A	​$31,000	0.78	​$1,400		​$31,000
B	​$37,000	0.99	​$1,100		​$38,000
C	​$39,000	1.56	​$0		​$45,500
D	​$13,000	1.28	​$400		​$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 11%.

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, explain how each stock in the portfolio performed differently relative to those​ CAPM-generated expectations of performance. What factors could explain these​ differences?

Answer 1

a. Calculation of Portfolio beta

1 2A 3 B 4c Asset Cost $31,000 $37,000 $39,000 $13,000 Beta at Yearly purchase Income 0.78 $1,400 0.99 $1,100 1.56 $0 1.28 $400 Value Today $31,000 $38,000 $45,500 $13,500 7 a. Calculation of Potfolio Beta 8 9 Portofolio Beta is the weighted average beta of investments 10 11 Portfolio Beta 1.15 =(B2*C2+B3*C3+B4*C4+B5*C5)/(SUM(B2:B5)) 12

The portflio beta is 1.15

b. Calculation of percentage of return

A B C D 13 b. Calculation of percentage of return Asset Cost Beta at Yearly purchase Income Value Today Gain in value $31,000 $37,000 $39,000 $13,000 0 000 0.78 0.99 1.56 1.28 $1,400 $1,100 $0 $400 $31,000 $38,000 $45,500 $13,500 Percenta Total Gains ge of & Income return $1,400 4.52% $2,100 5.68% $6,500 16.67% $900 6.92% $0 $1,000 $6,500 $500

Percentage of return was calculated by divinding total gains & income with the initial asset cost

c. Calcualation of percentage return on portfolio

A B C D 21 c. Calculation of percentage of return on portfolio $120,000 =SUM(B16:B19) $10,900 ESUM(G16:619) 23 Total cost of Investments 24 Total Gains & Income from investments 25 26 Percentage return on portfolio 27 9.08% =E24/E23

The percentage return on portfolio is 9.08%

d. Calculation of expected rate of return

A B C D 28 d. Calculation of Expected rate of return 29 30 Market Return (Rm) 11% 31 Risk free rate (RF) 5% 32 33 rate of return = Rf + beta * (Rm - Rf) 35 36 A Expected Beta at rate of purchase return 0.78 9.68% =$C$31+(B36*($C$30-$C$31)) 0.99 10.94% =$C$31+(B37*($C$30-$C$31)) 1.56 14.36% =$C$31+(B38*($C$30-$C$31)) 1.28 12.68% =$C$31+(B39*($C$30-$C$31))