Question

1. Jane Smith has a $500,000 fully diversified portfolio. She inherits XYZ Company common stock worth $60,000. Her financial adviser provided her with the following estimates:

                                                Expected Monthly Returns     Standard deviation of

                                                                                                monthly returns

            Original portfolio                   0.53%                                      2.12%

            XYZ Company                       1.45                                         3.02

The correlation coefficient of XYZ stock returns with the original portfolio is .35. Assuming Jane sells the XYZ stock and replaces it with the government securities yielding 0.3% monthly, calculate the:

1. Expected return of her new portfolio which includes the government securities (8 points)
2. Covariance of the government security returns with the original portfolio returns (3 points)
3. Standard deviation of her new portfolio which includes the government securities. (2 points)

Answer 1

a)Expected return of new portfolio =( 0.53%+0.3%)/2 = 0.415%

b) Weight ( W ) = (S.D of Govt Security)^2- Cov ( Portfolio, Govt Security ) / (SDof portfolio)^2 +(SD of Govt Security)^2- 2 Cov ( Portfolio,Govt Sec)

0.11 = 0^2 - Cov ( Portfolio, Govt Security) / (2.12)^2 + 0^2 - 2 Cov ( Portfolio,Govt Sec)

Cov ( Portfolio,Govt Sec) = 0.6338   

c) When r =0 , Variance of new portfolio = W1*SD of originalportfolio + W2*SD of Govt Security

=0.89*2.12% +0.11*0

= 0.018868

SD = Square root of 0.018868 = 0.1374