Portfolio return and beta Personal Finance Problem Jamie Peters invested 113,000
ID: 2794795 • Letter: P
Question
Portfolio return and betaPersonal Finance ProblemJamie Peters invested 113,000 to set up the following portfolio one year ago:
Asset
Cost
Beta at purchase
Yearly income
Value today
A
$28,000
0.74
$1,100
$28,000
B
$39,000
0.93
$1,000
$40,000 .
C
$31,000
1.41
$0
$37,500
D
$15,000
1.28
$425
$15,500
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 12%. 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?
(Round to two decimal places.)
Asset
Cost
Beta at purchase
Yearly income
Value today
A
$28,000
0.74
$1,100
$28,000
B
$39,000
0.93
$1,000
$40,000 .
C
$31,000
1.41
$0
$37,500
D
$15,000
1.28
$425
$15,500
Explanation / Answer
a) Portfolio beta = Sum of Cost x beta / Sum of cost = 1.06
b) % Returns = (Income + Value today) / Cost - 1
c) % Returns for portfolio = (2,525 + 121,000) / 113,000 - 1 = 9.31%
d) Using CAPM, Expected Returns, E(R) = Rf + beta x (Rm - Rf)
where, Rf = 5%, Rm = 12%
e) Betas are based on historical values, which changes over a period of time. Some stocks might have overvalued at the time of purchase, leading to lower returns this year and vice versa.
Asset Cost Beta Income Value today % Return E(R) A $28,000 0.74 $1,100 $28,000 3.93% 10.18% B $39,000 0.93 $1,000 $40,000 5.13% 11.51% C $31,000 1.41 $0 $37,500 20.97% 14.87% D $15,000 1.28 $425 $15,500 6.17% 13.96% Portfolio $113,000 1.06 $2,525 $121,000 9.31%Related Questions
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