Question

1. You are given the option of choosing between three well diversified portfolios to use as the optimal portfolio in a single index model.    Information on them is given below:

Portfolio	Expected Return	Expected Standard Deviation
A	.1	.05
B	.12	.07
C	.14	.08

1. (20 points) If the risk-free rate is .04, which portfolio would you choose? Why?
2. (20 points) How, if at all, does your answer change if the risk-free rate is .06? Explain.

Answer 1

(i) In choosing optimal portfolio We need sharpe Ratio :

Sharpe Ratio measures Risk Premium earned per unit of Total Risk

Sharpe Ratio = ( Return fro Portfolio - Risk free rate) / Standard Deviation of Portfolio

Sharpe Ratio of Portfolio A = (0.10 - 0.04) / 0.05

= 1.2

Sharpe Ratio of Portfolio B = (0.12 - 0.04) / 0.07

= 1.14

Sharpe Ratio of Portfolio C = (0.14 - 0.04) / 0.08

= 1.25

We will choose Portfolio C as it has higher Sharpe Ratio because Higher the sharpe ratio , better the portfolio's Return.

(ii) Calculation of Sharpe ratio when Risk free rate becomes 0.06

Sharpe Ratio of Portfolio A = (0.10 - 0.06) / 0.05

= 0.80

Sharpe Ratio of Portfolio B = (0.12 - 0.06) / 0.07

= 0.86

Sharpe Ratio of Portfolio C = (0.14 - 0.06) / 0.08

= 1

We will choose Portfolio C only as it has higher Sharpe Ratio because Higher the sharpe ratio , better the portfolio's Return.We can see that the result has not been changed due to change in Risk free Rate because return of stock C is more than the return of other two portfolio which still gives more risk premium per unit of Total Risk