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​ (c) below.

  

		Returns
Probability	Economic Condition	Stock X		Stock Y
0.10.1	Recession	negative 40−40		negative 180−180
0.30.3	Slow growth	2020		5050
0.40.4	Moderate growth	9090		130130
0.20.2	Fast growth	170170		200200

a. Compute the expected return for stock X and for stock Y.

The expected return for stock X is

7272.

​(Type an integer or a​ decimal.)

The expected return for stock Y is

8989.

​(Type an integer or a​ decimal.)

b. Compute the standard deviation for stock X and for stock Y.

The standard deviation for stock X is

____

​(Round to two decimal places as​ needed.)

The standard deviation for stock Y is

____

​(Round to two decimal places as​ needed.)

Answer 1

from above"

x	y	f(x,y)	x*f(x,y)	y*f(x,y)	x^2f(x,y)	y^2f(x,y)
-40	-180	0.1	-4	-18	160	3240
20	50	0.3	6	15	120	750
90	130	0.4	36	52	3240	6760
170	200	0.2	34	40	5780	8000
	Total	1	72	89	9300	18750
	E(X)=ΣxP(x,y)=					72
	E(X2)=Σx2P(x,y)=					9300
	E(Y)=ΣyP(x,y)=					89
	E(Y2)=Σy2P(x,y)=					18750
	Var(X)=E(X2)-(E(X))2=					4116
	Var(Y)=E(Y2)-(E(Y))2=					10829

a)

  expected return for stock X=72

The expected return for stock Y=89

b)

standard deviation for stock X =sqrt(4116)=64.16

standard deviation for stock y =sqrt(10829)=104.06