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 rate of 4.3%. The probability distribution of the risky funds is as follows: Expected Return Standard Deviation Stock fund (S) 13% 34% Bond fund (B) 6 27

Answer 1

Question Completion:

What is the Sharpe ratio of the best feasible CAL? (Round your answer to 4 decimal places.)

Answer:

The best feasible CAL (Capital Allocation Line):

The calculated Sharpe Ratio of the Stock Fund (S) is higher than the Sharpe Ratio of the Bond Fund (B).  Therefore, the better option is for the pension fund manager to choose the stock.

Explanation:

a) Data and Calculations:

T-bill money market fund yield rate = 4.3% (This is the Risk Free Rate)

Probability Distribution of the risky funds:

                    Expected    Standard

                      Return      Deviation

Stock fund (S)    13%           34%

Bond fund (B)     6              27

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

Sharpe Ratio For Stock Fund (S) = (13% - 4.3%) / 34% = 0.2559

Sharpe Ratio For Bond Fund (B) = (6% - 4.3%) / 27% = 0.0630

b) The Sharpe Ratio is an important investment decision-making tool.  It creates an understanding of the additional risk of an investment above the comparable risk-free investment by showing the excess return accruable to an investor if she chooses the riskier asset over the risk-free investment.  The Sharpe Ratio formula is given as the difference between the expected return on an investment and the risk-free return, which is then discounted by its volatility. Volatility is the standard deviation of the expected return of the stock fund or the bond fund.