Question

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

Economy	Probability		X				Y
Boom	0.15			25	%			12	%
Neutral	0.56			12	%			27	%
Poor	0.29			−27	%			7	%

    
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.)

	Company X	Company Y
Expected Value	%	%
Standard Deviation	%	%

b. Calculate the correlation coefficient if the covariance between X and Y is 94. (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)
25	12	0.15	3.75	1.8	93.75	21.6
12	27	0.56	6.72	15.12	80.64	408.24
-27	7	0.29	-7.83	2.03	211.41	14.21
	Total	1	2.64	18.95	385.8	444.05
	E(X)=ΣxP(x,y)=					2.64
	E(X2)=Σx2P(x,y)=					385.8
	E(Y)=ΣyP(x,y)=					18.95
	E(Y2)=Σy2P(x,y)=					444.05
	Var(X)=E(X2)-(E(X))2=					378.8304
	Var(Y)=E(Y2)-(E(Y))2=					84.9475

a)

	Company X	Company Y
Expected Value	2.64	18.95
Standard Deviation	19.46	9.22

b)

correlation coefficient =covariance/(SD(X)*SD(Y))=0.5240