Question

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 probability distribution shown to the right. Complete parts​ (a) through​ (e) below.

		Returns
Probability	Economic Condition	Stock X		Stock Y
0.1	Recession	−40		−170
0.3	Slow growth	20		60
0.4	Moderate growth	90		140
0.2	Fast growth	150		190

a. Whats the expected return for stock X?

b. Whats the expected return for stock Y?

c. Whats the standard deviation for stock X?

d. Whats the standard deviation for stock Y?

e. Compute the covariance of stocks X and Y?

Answer 1

ANSWER

from above:

Probability P	X	Y	P*X	P*Y	P*X^2	P*Y^2	XY*P
0.1	-40	-170	-4	-17	-160	-2,890	-680
0.3	20	60	6	18	120	1,080	360
0.4	90	140	36	56	3,240	7,840	5,040
0.2	150	190	30	38	4500	7,220	5,700
		total	68	95	7,700	13,250	10,420

a)

expected return for stocks X E(X) = =68

b)

expected return for stocks Y = =95

c)

here E(X² )= =7,700

therefore,

standard deviation for stocks X =(E(X² ) -(E(X))²)^1/2 =55.4617

d)

E(Y² )= =13,250

standard deviation for stocks Y =(E(Y² ) -(E(Y))²)^1/2 =65

e)

here E(XY)= =10,420

therefore,

covariance of stocks X and Y =E(XY)-E(X)*E(Y) =3,960