Question

Heathcliff has invested 40% of his wealth in stock A and the remainder in stock B. He has

assessed their prospects as follows;

A (15% expected return & 20% Standard deviation)

B (20% expected return & 22% Standard deviation)

The correlation coefficient for these two stocks is ?AB= 0.50.

1. Calculate the expected return (ER) and risk (?) of his portfolio.

2. Is his portfolio better or worse than investing entirely in stock A? Why?

3. If the correlation coefficient of stock A with the market (?Am) is 0.88 and ?m is 12%, calculate

the beta coefficient for stock A

Answer 1

1.the expected return on stock A is = 15%

weight on stock a = 40%

the expected return on Stock B is 20%

weight on stock B = 60%

therefore, the expected return on the portfolio is

= 0.4 * 15 + 0.6 *20

= 6 + 12

= 18%

risk of the portfolio ( standard deviation)

root over ( weight of stock A ^2 * variance of stock A + weight of stock B *variance of B + 2 *weight of A * weight of B * covariance of A and B )

= root over [ 0.4^2 *20^2 + 0.6^2 *22^2 + 2 * 0.4*0.6 * 0.5 *20 * 22

= 64 + 174.24 + 105.6
=343.84

root over (343.84)

= 18.54 %

2. had you only invested in Stock A,you would have recieved a return of 15% and has to bear risk of 20%

,but investing in a combination of risk assets is giving a return of 18 % and a risk of 18.54%.

it is worse, investing enitrely in stock A.

3. beta = covariace of the market with the stock/ variance of the market

correlation of stock with market = covariance of stock with market / standard deviation of stock and standard deviation of market

= 0.88 * 20 * 12 / 12 ^2

= 1.46

therefore, the beta of the stock is 1.46.