Question

4. you are trying to develop a strategy for investing in two different stocks. The anticipated annual return for a $1,000 investment in each stock under four different economic conditions has the following probability distribution:

Probability	Economic Condition	Return Stock X	Return Stock Y
0.1	Recession	−100	50
0.3	Slow growth	0	150
0.3	Moderate growth	80	-20
0.3	Fast growth	150	-100

a. Expected return for stock X and for stock Y.

b. Standard deviation for stock X and for stock Y.

c. Covariance of stock X and stock Y.

d. Would you invest in stock X or stock Y? Explain

Answer 1

Probability Pi	Xi	Yi	xi=Xi/1000	yi=Yi/1000	Pi*xi	Pi*yi	Pi*(xi-Xm)^2	Pi*(yi-ym)^2	Pi*(xi-Xm)*(yi-Ym)
0.1	-100	50	-10.00%	5.00%	-1.00%	0.50%	0.0025281	0.0001296	-0.0005724
0.3	0	150	0.00%	15.00%	0.00%	4.50%	0.0010443	0.0055488	-0.0024072
0.3	80	-20	8.00%	-2.00%	2.40%	-0.60%	0.0001323	0.0003468	-0.0002142
0.3	150	-100	15.00%	-10.00%	4.50%	-3.00%	0.0024843	0.0038988	-0.0031122
Excpected return for X Xm= ∑Pi*xi	5.90%
Excpected return for Y Ym= ∑Pi*yi	1.40%
Variance of X Vx=∑Pi*(xi-Xm)^2	0.006189
Variance of Y Vy=∑Pi*(yi-Ym)^2	0.009924
Standard deviation for X =√Vx	7.87%
Standard deviation for Y =√Vy	9.96%
Covariance Cov(X,Y)= ∑Pi*(xi-Xm)*(yi-Ym)	-0.00631

d) I would invest in stock X because it has higher expected return than Stock Y and also have lower standard deviation than stock Y.