Question

A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long- term government and corporate bond fund, and the third is a T-bill money market fund that yields a sure rate of 4.0%. The probability distributions of the risky funds are: Stock fund (S) Bond fund (B) Expected Return 10% 7% Standard Deviation 32% 24% The correlation between the fund returns is 0.1250. What is the Sharpe ratio of the best feasible CAL? (Do not round intermediate calculations. Round your answer to 4 decimal places.) Sharpe ratio

Answer 1

The question asks for calculation of Sharpe ratio for given options and opt for best Sharpe Ratio of the available option over risk free investment.

Sharpe ratio is a tool used for making investments. It helps in making an informed investment decision after understanding additional risk associated with that investment over and above risk free investment. In short, it denotes excess return one can get if one opts for riskier investment over risk free investment. In general, it is difference of expected return earned over and above risk free return discounted by volatility relating to expected return in the investment. Volatility is basically standard deviation of expected return in an investment.

Formula of Sharpe Ratio = (Expected Return of Investment - Risk Free Rate) / Standard Deviation of excess return of investment

It is given in the problem that the risk free T-bill gives 4% sure return. Now, taking the rest of the data from question and plugging the same in the above formula, we can arrive at Sharpe Ratio for each fund as follows :

Sharpe Ratio For Stock Fund (S) = (10% - 4%) / 32% = 0.1875

Sharpe Ratio For Bond Fund (B) = (7% - 4%) / 24% = 0.125

Since Sharpe Ratio of Stock Fund (S) is higher than Sharpe Ratio of Bond Fund (B), investing in Stock Fund (S) is the best option.

Answer to the question is 0.1875

The additional information with respect to CORRELATION between the funds is used when one has already invested in a fund and is comparing whether to add the same fund or invest in other option. In such cases, even if the Sharpe Ratio of the new investment is lower than the Sharpe Ratio of existing investment, still the new investment may be opted if -

Correlation between Funds X Sharpe Ratio of Fund in which investment is made is lesser than Sharpe Ratio of new investment.

For example, consider that the Fund Manager has invested in Stock Fund (S) and now is facing the question whether to add further to Stock Fund (S) or invest in Bond Fund (B).

Then he may consider and opt for investing additional funds in Bond Fund (B), as Sharpe Ratio of Bond (B) (i.e. 0.125) is greater than correlation between funds multiplied by Sharpe Ratio for existing investment in Stock Fund (S) (i.e. 0.1250 X 0.1875 = 0.0234375)