Question

You have been assigned to examine the following funds with their respective probabilities:

		Stock Fund X	Stock Fund Y
Scenario	Probability	Rate of Return (%)	Rate of Return (%)
Severe recession	0.05	-5	11.2
Mild recession	0.15	-1.6	3.3
Normal growth	0.55	7.7	0.5
Boom	0.25	16.3	-4.1

Calculate the correlation coefficient of a portfolio that invests 55% on stock fund X and 45% on stock fund Y.

Answer 1

Expected Return in severe recession=55%*-5%+45%*11.2%=2.29%
Expected Return in mild recession=55%*-1.6%+45%*3.3%=0.605%
Expected Return in severe recession=55%*7.7%+45%*0.5%=4.46%
Expected Return in severe recession=55%*16.3%+45%*-4.1%=7.12%

Expected Return of Portfolio =0.05*2.29%+0.15*0.605%+0.55*4.46%+0.25*7.12% =4.43825% or 4.44%
Standard Deviation of Portfolio =((0.05*(2.29%-4.43825%)^2+0.15*(0.605%-4.43825%)^2+0.55*(4.46%-4.43825%)^2+0.25*(7.12%-4.43825%)^2)^0.5 =2.0574%

Coefficient of Portfolio =Standard Deviation of Portfolio/Expected Return of Portfolio =2.0574%/4.43825% =0.46