Question

Stocks X and Y have the following probability distributions of expected returns for four possible economic states.

Economy State	Probability	Stock X	Stock Y
1	0.1	-8%	5%
2	0.4	-10%	8%
3	0.4	9%	-2%
4	0.1	14%	-10%

Suppose you construct a two-stock portfolio that has $3 million invested in Stock X and $1 million invested in Stock Y. The beta of Stock X is 20% higher than the beta of overall stock market. Stock Y’s beta is -0.8. [Show the work leading to your answers]

a. Calculate the expected returns for Stock X and Stock Y.

b. Calculate the standard deviations of returns for Stock X and Stock Y.

c. Calculate the coefficients of variation (CVs) for Stock X and Stock Y. Which stock appears riskier to you?

d. Calculate the two-stock portfolio’s expected return.

e. Calculate the two-stock portfolio’s standard deviation.

f. Calculate the two-stock portfolio’s beta.

g. If the overall market return is 8% and the risk-free rate is 1%, what is the two-stock portfolio’s required return?

h. How can you reallocate t

Answer 1

	Stock X
Economy	Probabilty	Return	Probability* Return	Return- Expected Return[D]	Probability*D*D
1	0.1	-0.08	-0.008	-0.082	0.0006724
2	0.4	-0.1	-0.04	-0.102	0.0041616
3	0.4	0.09	0.036	0.088	0.0030976
4	0.1	0.14	0.014	0.138	0.0019044
	Expected Return = Sum of Probabilty*Return	0.002 = 0.2%	Variance =Sum of [D^2]	0.009836
				Standard Deviation =Variance^1/2	0.09917661 = 9.92%
			Co Efficient of Variation = Standard Deviation/Mean i.e. Expected Return	0.09917661/0.002	49.58830507 = 49.59

	Stock Y
Economy	Probabilty	Return	Probability* Return	Return- Expected Return[D]	Probability*D*D
1	0.1	0.05	0.005	0.031	0.0000961
2	0.4	0.08	0.032	0.061	0.0014884
3	0.4	-0.02	-0.008	-0.039	0.0006084
4	0.1	-0.1	-0.01	-0.119	0.0014161
	Expected Return = Sum of Probabilty*Return	0.019 = 1.9%	Variance =Sum of [D^2]	0.003609
				Standard Deviation =Variance^1/2	0.060074953 = 6.01%
			Co Efficient of Variation = Standard Deviation/Mean i.e. Expected Return	0.060074953/0.019	3.161839641 = 3.16

Co Efficient is Risk per unit of Return. Therefore, Higher the Co Efficient of Variation, Riskier the Stock. Therefore, Stock X appears Riskier.

	X	Y	Portfolio Return [{R(a)*W(a)}+{R(b)*W(b)}]
	Return	Weight	Return	Weight
1	-0.08	0.75	0.05	0.25	-0.0475
2	-0.1	0.75	0.08	0.25	-0.055
3	0.09	0.75	-0.02	0.25	0.0625
4	0.14	0.75	-0.1	0.25	0.08

	Portfolio
Economy	Probabilty	Return	Probability* Return	Return- Expected Return[D]	Probability*D*D
1	0.1	-0.0475	-0.00475	-0.05375	0.000288906
2	0.4	-0.055	-0.022	-0.06125	0.001500625
3	0.4	0.0625	0.025	0.05625	0.001265625
4	0.1	0.08	0.008	0.07375	0.000543906
	Expected Return = Sum of Probabilty*Return	0.00625 = 0.625%	Variance =Sum of [D^2]	0.003599063
				Standard Deviation =Variance^1/2	0.059992187 = 6%

Note: As per Guidelines, we are supposed to answer ONLY 4 Sub-Questions.