A portfolio trustee asked a financial consultant to advise on the advantages of investing a portion of the portfolios assets in hedge funds to increase returns, decrease portfolio risk, or both.

Based on the previous 5-year performance for all the currently investable hedge funds that have both been in existence and reported returns for the entire 5-year period, the average annual fund gross return was 17.8% with a standard deviation of returns of 15%. The standard deviation of returns on the S&P 500 Index over the same period was 10%. The Sharpe Ratio for the hedge funds as an asset class was 0.80while the Sharpe Ratio for an investment in the S&P 500 Index was 0.70 for the same 5-year period.

Based on the correlation of hedge fund returns with the returns on the assets currently in the institutional portfolio and the average returns on the hedge funds, the consultant recommends a 30% allocation to hedge funds.

a. From the given Sharpe Ratios and hedge funds data, find the average risk-free rate over the 5-year period. ( 3 marks)

b. What is the average annual return for the S&P 500 Index over the same 5-year period ? ( 3 marks)

c. Discuss any problem(s) from the consultants recommendation, based on the limitations of the 5-year database of performance. Is/are there any other concern(s) if you know that hedge funds use a lot of option-writing investment strategies ? (14 marks)