Question

1. Two stocks have the following return distributions.

Probability	Stock K return %	Stock Y return %
0.1	-10	30
0.2	5	20
0.4	20	20
0.2	25	10
0.1	30	-15

Do the necessary analysis and determine which stock is a better choice for a risk-averse investor.

Answer 1

Expected returns for Stock K=0.1*(-10%)+0.2*5%+0.4*20%+0.2*25%+0.1*30%=16.0000%

Standard deviation for Stock K=sqrt(0.1*(-10%-16.0000%)^2+0.2*(5%-16.0000%)^2+0.4*(20%-16.0000%)^2+0.2*(25%-16.0000%)^2+0.1*(30%-16.0000%)^2)=11.5758%

Coefficient of variation for Stock K=11.5758%/16%=0.7234875

Expected returns for Stock Y=0.1*30%+0.2*20%+0.4*20%+0.2*10%+0.1*(-15%)=15.5000%

Standard deviation for Stock Y=sqrt(0.1*(30%-15.5000%)^2+0.2*(20%-15.5000%)^2+0.4*(20%-15.5000%)^2+0.2*(10%-15.5000%)^2+0.1*(-15%-15.5000%)^2)=11.5000%

Coefficient of variation for Stock Y=11.5000%/15.5000%=0.741935484

Choose Stock K as it offers better risk adjusted returns (i.e., lower coefficient of variation)