Question

Junior Sayou, a financial analyst for Chargers Products, a manufacturer of stadium benches, must evaluate the risk and return of two assets, X and Y. The firm is considering adding these assets to its diversified asset portfolio. To assess the return and risk of each asset, Junior gathered data on the annual cash flow and beginning-and end-of-year values of each asset over the immediately preceding 10 years, 2006-2015. These data are summarized in the attached table. Junior’s investigation suggests that both assets, on average, will tend to perform in the future just as they have during the past 10 years. He, therefore, believes that the expected annual return can be estimated by finding the average annual return for each asset over the past 10 years. Junior believes that each asset’s risk can be assessed in two ways: in isolation and as part of the firm’s diversified portfolio of assets. The risk of the assets in isolation can be found by using the standard deviation and coefficient of variation of returns over the past 10 years. The capital asset pricing model (CAPM) can be used to assess the asset’s risk as part of the firm’s portfolio of assets. Applying some sophisticated quantitative techniques, Junior estimated betas for assets X and Y of 1.60 and 1.10, respectively. In addition he found that the risk-free rate is currently 7.0% and that the market return is 10.0%.

Calculate:

1) Expected return on a portfolio XY

2) Risk on a portfolio XY

Weight of each asset is 50%. Average annual return: asset X: 11.74% asset Y: 11.14% Standard deviation: asset X: 8.9 asset Y: 2.78

Asset X
	Value
Year	Cash Flow	Beginning	Ending
2006	$1,000	$20,000	$22,000
2007	1500	22000	21000
2008	1400	21000	24000
2009	1700	24000	22000
2010	1900	22000	23000
2011	1600	23000	26000
2012	1700	26000	25000
2013	2000	25000	24000
2014	2100	24000	27000
2015	2200	27000	30000

Asset Y
	Ending
Year	Cash Flow	Beginning	Ending
2006	$1,500	$20,000	$20,000
2007	1600	20000	20000
2008	1700	20000	21000
2009	1800	21000	21000
2010	1900	21000	22000
2011	2000	22000	23000
2012	2100	23000	23000
2013	2200	23000	24000
2014	2300	24000	25000
2015	2400	25000	25000

Answer 1

1. Expected Return of portfolio = Weight of X * Return of X + Weight of Y * Return of Y

= 0.5 * 11.74% + 0.5 * 11.14%

= 11.14%

2. Asset X

Year	Cashflow	Beginning	Ending	Return	Rate of return (X)	Expected return (x)	(X-x)
2000	1,000	20,000	22,000	3,000	15.00%	11.74%	3.26%
2001	1,500	22,000	21,000	500	2.30%	11.74%	-9.44%
2002	1,400	21,000	24,000	4,400	21.00%	11.74%	9.26%
2003	1,700	24,000	22,000	-300	-1.30%	11.74%	-13.04%
2004	1,900	22,000	23,000	2,900	13.20%	11.74%	1.46%
2005	1,600	23,000	26,000	4,600	20.00%	11.74%	8.26%
2006	1,700	26,000	25,000	700	2.70%	11.74%	-9.04%
2007	2,000	25,000	24,000	1,000	4.00%	11.74%	-7.74%
2008	2,100	24,000	27,000	5,100	21.30%	11.74%	9.56%
2009	2,200	27,000	30,000	5,200	19.30%	11.74%	7.56%

Asset Y

Year	Cashflow	Beginning	Ending	Return	Rate of return (Y)	Expected return (y)	(Y-y)
2000	1,500	20,000	20,000	1,500	7.50%	11.14%	-3.64%
2001	1,600	20,000	20,000	1,600	8.00%	11.14%	-3.14%
2002	1,700	20,000	21,000	2,700	13.50%	11.14%	2.36%
2003	1,800	21,000	21,000	1,800	8.60%	11.14%	-2.54%
2004	1,900	21,000	22,000	2,900	13.80%	11.14%	2.66%
2005	2,000	22,000	23,000	3,000	13.60%	11.14%	2.46%
2006	2,100	23,000	23,000	2,100	9.10%	11.14%	-2.04%
2007	2,200	23,000	24,000	3,200	13.90%	11.14%	2.76%
2008	2,300	24,000	25,000	3,300	13.80%	11.14%	2.66%
2009	2,400	25,000	25,000	2,400	9.60%	11.14%	-1.54%

Calculation of covariance

Year	(X-x)	(Y-y)	(X-x)(Y-y)
2000	3.26%	-3.64%	-0.12%
2001	-9.44%	-3.14%	0.30%
2002	9.26%	2.36%	0.22%
2003	-13.04%	-2.54%	0.33%
2004	1.46%	2.66%	0.04%
2005	8.26%	2.46%	0.20%
2006	-9.04%	-2.04%	0.18%
2007	-7.74%	2.76%	-0.21%
2008	9.56%	2.66%	0.25%
2009	7.56%	-1.54%	-0.12%
Total			1.08%

Risk of portfolio = Std Dev of portfolio

Std Dev of portfolio = (Weight of X^2 * Std Dev of X^2 + Weight of Y^2 * Std Dev of Y^2 + 2 * Weight of X * Weight of Y * Covariance)^1/2

= [(0.5)^2 * (8.9)^2 + (0.5)^2 * (2.78)^2 + 2 * 0.5 * 0.5 * 1.08]^1/2

= (22.2746)^1/2

= 4.72%