Question

Given the following table:

Probability X Y

20% 15% 30%

60% 25% 18%

20% 30% 20%

Calculate a) the covariance of X and Y, and b) the correlation coefficient.

Select one:

a. a) -20.64% b) -0.90

b. a) -20.18% b) -0.88

c. a) -17.89% b) -0.78

d. a) -19.20% b) -0.84

e. a) -18.35% b)-0.80

Answer 1

Expected return of X =20%*15%+60%*25%+20%*30% =24%
Expected return of Y =20%*30%+60%*18%+20%*20% =20.8%
Covariance of X and Y =20%*(15%-24%)*(30%-20.80%)+60%*(25%-24%)*(18%-20.80%)+20%*(30%-24%)*(20%-20.80%) =-19.20%

Standard Deviation of X =(20%*(15%-24%)^2+60%*(25%-24%)^2+20%*(30%-24%)^2)^0.5 =4.8990%
Standard Deviation of Y =(20%*(30%-20.8%)^2+60%*(18%-20.8%)^2+20%*(20%-20.8%)^2)^0.5 =4.6648%
Correlation =Covariance/(standard Deviation of X*Standard deviation of Y) =-.1920%/(4.8990%*4.6648%)=-0.84

Option d is correct option