Question

1.   Consider the following probability distribution for stocks A and B for questions 1 and 2

STATE   Probability   Return on Stock A   Return on Stock B
          
1 0.10 10% 8%
2 0.30 20% 12%
3 0.60 25% 17%

Calculate the Expected return for Stock A and for Stock B and  calculate the variance for both Stock A and for Stock B.

Answer 1

Stock A:

Expected return of stock A = 0.1*0.1 + 0.3*0.2 + 0.6*0.25

Expected return of stock A = 0.01 + 0.06 + 0.15

Expected return of stock A = 0.22 or 22%

Variance of stock A = [0.1(0.1 - 0.22)² + 0.3(0.2 - 0.22)² + 0.6(0.25 - 0.22)²]

Variance of stock A = [0.00144 + 0.00012 + 0.00054]

Variance of stock A = 0.0021

Stock B:

Expected return of stock B = 0.1*0.08 + 0.3*0.12 + 0.6*0.17

Expected return of stock B = 0.008 + 0.036 + 0.102

Expected return of stock B = 0.146 or 14.6%

Variance of stock B = [0.1(0.08 - 0.146)² + 0.3(0.12 - 0.146)² + 0.6(0.17 - 0.146)²]

Variance of stock B = [0.00044 + 0.0002 + 0.00035]

Variance of stock B = 0.00099