A.) A pension fund manager is considering three mutual funds. The first is a sto

Question

A.) 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 5%. The probability distribution of the risky funds is as follows:

  

  

What is the Sharpe ratio of the best feasible CAL? (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.)

B.) Greta, an elderly investor, has a degree of risk aversion of A = 5 when applied to return on wealth over a 3-year horizon. She is pondering two portfolios, the S&P 500 and a hedge fund, as well as a number of 3-year strategies. (All rates are annual, continuously compounded.) The S&P 500 risk premium is estimated at 5% per year, with a SD of 20%. The hedge fund risk premium is estimated at 12% with a SD of 40%. The return on each of these portfolios in any year is uncorrelated with its return or the return of any other portfolio in any other year. The hedge fund management claims the correlation coefficient between the annual returns on the S&P 500 and the hedge fund in the same year is zero, but Greta believes this is far from certain.

Assuming the correlation between the annual returns on the two portfolios is indeed zero, what would be the optimal asset allocation? (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.)

What is the expected return on the portfolio? (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.)

What should be Greta’s capital allocation? (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.

Expected Return Standard Deviation   Stock fund (S) 19%         32%            Bond fund (B) 12            15            

Explanation / Answer

A.

Coefficient of variation of stock fund = Standard deviation / Expected returns

                                                              = 32% / 19%

                                                              = 1.68

Coefficient of variation of bond fund = Standard deviation / Expected returns

                                                              = 15% / 12%

                                                              = 1.25

The best feasible is stock fund, since it has the highest risk.

Sharpe ratio = (Rate of returns – Risk free returns) / Standard deviation

                      = (19% - 5%) / 32%

                      = 0.4375% (Answer)

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