Question

Historical Returns: Expected and Required Rates of Return

You have observed the following returns over time:

Year	Stock X	Stock Y	Market
2009	14%	15%	13%
2010	20	7	9
2011	-15	-8	-12
2012	4	2	2
2013	24	13	18

Assume that the risk-free rate is 4% and the market risk premium is 6%. Do not round intermediate calculations.

1. What is the beta of Stock X? Round your answer to two decimal places.
   
   
2. What is the beta of Stock Y? Round your answer to two decimal places.
   
   
3. What is the required rate of return on Stock X? Round your answer to one decimal place.
   %
   
4. What is the required rate of return on Stock Y? Round your answer to one decimal place.
   %
   
5. What is the required rate of return on a portfolio consisting of 80% of Stock X and 20% of Stock Y? Round your answer to one decimal place.
   %

Answer 1

Stock X
Year	Year		Stock		Deviation=Return-Expected return	Deviation^2
2009	1		14.00%		4.600%	0.212%
2010	2		20.00%		10.600%	1.124%
2011	3		-15.00%		-24.400%	5.954%
2012	4		4.00%		-5.400%	0.292%
2013	5		24.00%		14.600%	2.132%
		Total	47.00%		Total	9.712%
	Expected return=	47%/5
	So the expected return is 9.4%
	Variance in return	9.712%/5
	Variance in return	1.9424%
	Standard deviation	'1.9424%^(0.5)
	Standard deviation	13.94%

Stock Y
Year	Year		Stock		Deviation=Return-Expected return	Deviation^2
2009	1		15.00%		9.200%	0.846%
2010	2		7.00%		1.200%	0.014%
2011	3		-8.00%		-13.800%	1.904%
2012	4		2.00%		-3.800%	0.144%
2013	5		13.00%		7.200%	0.518%
		Total	29.00%		Total	3.428%
	Expected return=	29%/5
	So the expected return is 5.8%
	Variance in return	3.428%/5
	Variance in return	0.6856%
	Standard deviation	'0.6856%^(0.5)
	Standard deviation	8.28%

Market
Year	Year		Stock		Deviation=Return-Expected return	Deviation^2
2009	1		13.00%		7.000%	0.490%
2010	2		9.00%		3.000%	0.090%
2011	3		-12.00%		-18.000%	3.240%
2012	4		2.00%		-4.000%	0.160%
2013	5		18.00%		12.000%	1.440%
		Total	30.00%		Total	5.420%
	Expected return=	30%/5
	So the expected return is 6%
	Variance in return	5.42%/5
	Variance in return	1.0840%
	Standard deviation	'1.084%^(0.5)
	Standard deviation	10.41%

Calculation of BETA

Beta Security=	Co-variance with Market/Market Variance
Year	Market deviation	X deviation	Market D * Stock X deviation	Y deviation	Market D * Stock Y deviation
2011	7.00%	4.60%	0.32%		9.20%	0.64%
2012	3.00%	10.60%	0.32%		1.20%	0.04%
2013	-18.00%	-24.40%	4.39%		-13.80%	2.48%
2014	-4.00%	-5.40%	0.22%		-3.80%	0.15%
2015	12.00%	14.60%	1.75%		7.20%	0.86%
		Total	7.00%		Total	4.18%
	Stock X	Stock Y
Co-variance with market=	7%/(5-1)	4.18%/(5-1)
Co-variance with market=	1.75%	1.05%
BETA=	1.75%/1.084%	1.05%/1.084%
BETA=	1.61	0.97

Required return	Risk-free rate + Beta * Market premium
	Stock X	Stock Y
Required return	4%+1.61*6%	4%+0.97*6%
Required return	13.66%	9.82%

Portfolio return
	Stock X	Stock Y	Total
Required return	13.66%	9.82%
Weight	80%	20%
Required return*weight	10.92800%	1.96400%	12.89%
So required return on portfolio will be 12.89%