Question

1.The returns on stocks A and B are perfectly negatively correlated (). Stock A has an expected return of 21 % and a standard deviation of return of 40%. Stock B has a standard deviation of return of 20%. The risk-free rate of interest is 11 %. What must be the expected return to stock B?

Answer 1

Since returns on stocks A and B are perfectly negatively correlated, let Wa is invested in Stock A and (1-Wa) is invested in Stock B.

?(p) = Absolute { Wa x ?(a) - Wb x ?(b) }

0 = Wa x 0.40 - (1 - Wa) x 0.20

0.4Wa = 0.20 - 0.2Wa

0.6Wa = 0.2

Wa = 0.33

Thus Wb = 1 - Wa = 1 - 0.33 = 0.67

Now, the expected rate of return of this risk free portfolio is equal to risk free return i.e.

E(p) = E(b)*wb + E(a)*wa

11 = E(b)*0.67 + 21*0.33

33 = 2*E(b) + 21

12 = 2*E(b)

E(b) = 6

Hence, the expected return of Stock B is 6%.