Question

Problem #7

Suppose we are deciding between two alternative investments for the coming year. The first investment is a mutual fund that consists of shares which do well when economy is strong. The second investment is a mutual fund that consists of shares that do well when economy is weak. Your estimate of returns per each investment is provided below with a probability of their occurrence. Calculate the correlation between these mutual funds and interpret.

Economy	Prob.(X, Y)	Strong-economy fund ($)	Weak-economy fund ($)
Recession	0.20	-100	200
Stable	0.45	100	50
Progressing	0.35	250	-100

Answer 1

event	x	y	f(x,y)	x*f(x,y)	y*f(x,y)	x^2f(x,y)	y^2f(x,y)
recession	-100	200	0.2	-20	40	2000	8000
stable	100	50	0.45	45	22.5	4500	1125
progressing	250	-100	0.35	87.5	-35	21875	3500
		Total	1	112.5	27.5	28375	12625
		E(X)=ΣxP(x,y)=					112.5
		E(X2)=Σx2P(x,y)=					28375
		E(Y)=ΣyP(x,y)=					27.5
		E(Y2)=Σy2P(x,y)=					12625
		Var(X)=E(X2)-(E(X))2=					15718.75
		Var(Y)=E(Y2)-(E(Y))2=					11868.75
		E(XY)=ΣxyP(x,y)=					-10500
		Cov(X,Y)=E(XY)-E(X)*E(Y)=					-13593.75
		Correlation ρxy=Cov(X,Y)/sqrt(Var(X)*Var(Y))=					-0.9952

since correlation is negative and strong, there appears to be a strong negative relation between these mutual funds . we can predict that on average if Strong-economy fund increases then Weak-economy fund decreases or vice versa,