Question

(10%) Question 2: The ABC stock return and the XYZ stock return depend on the state of economy: State of the economy Probability of the state 0.20 0.35 0.45 ABC stock return -0.10 -0.05 0.00 XYZ stock return -0.05 0.00 0.00 What is the correlation between the ABC stock return and the XYZ stock return? a) 0.0625 b) 0.815 c) 1.0 d) 0.0 e) 0.521

Answer 1

Expected Return of ABC =0.20*-0.10+0.35*-0.05+0.45*0.00 =-3.75%
Expected return of XYZ =0.20*-0.05+0.35*0.00+0.45*0.00=-.1%

Standard Deviation of ABC =(0.20*(-0.10+3.75%)^2+0.35*(-0.05+3.75%)^2+0.45*(0.00+3.75%)^2)^0.5 =3.8324%
Standard Deviation of XYZ =(0.20*(-0.05+1%)^2+0.35*(0.00+1%)^2+0.45*(0.00+1%)^2)^0.5 =2.00%

Covariance =0.20*(-0.10+3.75%)*(-0.05+1%)+0.35*(-0.05+3.75%)*(0.00+1%)+0.45*(0.00+3.75%)*(0.00+1%)=0.0625%
Correlation =Covariation/(Standard Deviation of ABC*Standard Deviation of XYZ) =0.0625%/(3.8324%*2%) =0.815

Option b is correct option