Question

Consider the following information on the expected return for companies X and Y. Economy Probability X Y

Boom 0.24 38 % 17 %

Neutral 0.49 13 % 29 %

Poor 0.27 −28 % 4 %

a. Calculate the expected value and the standard deviation of returns for companies X and Y. (Round intermediate calculations to at least 4 decimal places. Round your final answers to 2 decimal places.) b. Calculate the correlation coefficient if the covariance between X and Y is 176. (Round your answer to 4 decimal places.)

Answer 1

x	y	f(x,y)	x*f(x,y)	y*f(x,y)	x^2f(x,y)	y^2f(x,y)
38	17	0.24	9.12	4.08	346.56	69.36
13	29	0.49	6.37	14.21	82.81	412.09
-28	4	0.27	-7.56	1.08	211.68	4.32
	Total	1	7.93	19.37	641.05	485.77
	E(X)=ΣxP(x,y)=					7.93
	E(X2)=Σx2P(x,y)=					641.05
	E(Y)=ΣyP(x,y)=					19.37
	E(Y2)=Σy2P(x,y)=					485.77
	Var(X)=E(X2)-(E(X))2=					578.1651
	Var(Y)=E(Y2)-(E(Y))2=					110.5731

from above expected value of X =7.93

expected value of Y =19.37

std deviation of X =sqrt(Var(X))=24.05

std deviation of Y=sqrt(Var(Y))=10.52

correlation coefficient =Cov(X,Y)/(SD(X)*SD(Y))=0.6961