Question

Portfolio return and beta Personal Finance Problem Jamie Peters invested $106,000 to set up the following portfolio one year ago: E 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 3% 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? a. The portfolio beta on the basis of the original cost figures is (Round to two decimal places.) Data Table (Click on the icon located on the top-right corner of the data table below in order to copy its contents into a spreadsheet.) Asset Cost $23,000 $30,000 $38,000 $15,000 Beta at purchase 0.74 0.97 1.57 1.31 Yearly income $1,000 $1,400 Value today $23,000 $31,000 $44,500 $15,500 $0 $425 Print Done

Answer 1

a.	Portfolio beta:
	Asset	Cost	Weight of the cost	Beta	Portfolio beta
			a	b	a*b
	A	23000	0.22	0.74	0.16
			(23000/106000)
	B	30000	0.28	0.97	0.27
			(30000/106000)
	C	38000	0.36	1.57	0.56
			(38000/106000)
	D	15000	0.14	1.31	0.19
			(15000/106000)
		106000			1.18
	Portfolio beta=1.18
b.	Asset	Yearly income	Value today	Cost	Increase in value	Total return	Return %
		a	b	c	d=b-c	e=a+d	f=e/c
	A	1000	23000	23000	0	1000	4.35%
	B	1400	31000	30000	1000	2400	8.00%
	C	0	44500	38000	6500	6500	17.11%
	D	425	15500	15000	500	925	6.17%
c.	Percentage return of portfolio:
	Asset	Cost	Weight of the cost	Return %	Portfolio beta
			a	b	a*b
	A	23000	0.22	4.35%	0.94%
			(23000/106000)
	B	30000	0.28	8%	2.26%
			(30000/106000)
	C	38000	0.36	17.11%	6.13%
			(38000/106000)
	D	15000	0.14	6.17%	0.87%
			(15000/106000)
		106000			10.21%
	Percentage return of portfolio=10.21%
d.	Expected return=Risk-free rate of return+Beta*(Market return-Risk-free rate of return)
	Asset	Risk-free rate of return	Beta	Market return	Expected return
		a	b	c	d=a+b*(c-a)
	A	3%	0.74	11%	8.92%
	B	3%	0.97	11%	10.76%
	C	3%	1.57	11%	15.56%
	D	3%	1.31	11%	13.48%
e.	Stock C performed well since it provides more return (17.11%) than the expected return
	Under performance of other stocks may be due to Unsystematic factors