What would have been the Sharpe ratio for this strategy?

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Derivatives and Liquidity (Collar Strategy & Fixed-Strike)

ASSIGNMENT INSTRUCTIONS:

Section 1: Collar Strategy with at-the-money
Question 1: Construct a collar strategy with at-the-money calls and at-the-money puts using the historical data in case Exhibit 3.
Question 2: Back-test what would have been the growth in value of $1 invested from the start of December 1990 to the end of December 2007 following this strategy. See case Exhibit 2 for details on a collar strategy.
Question 3: Plot it against the monthly growth in value of $1 in the HFRX EH: Equity Market Neutral Index (HFRI EH), the S&P 500 Index, and in one-month Treasury bills (T-bills)
Question 4: What do you conclude?
Question 5: What would have been the Sharpe ratio for this strategy?

Section 2: Collar Strategy with OTM calls
Question 1: Do the same as above (construct a collar strategy) but with OTM calls (with strikes equal to 105% of the current value of the S&P 500 Index) and OTM puts (with strikes equal to 95% of the current value of the S&P 500 Index).
Question 2: What would have been the grown in the value of $1 following this strategy?
Question 3: What do you conclude?
Question 4: What would have been the Sharpe ratio for this strategy?

Section 3: Fixed-Strike Rule
Question 1: Can you get a fixed-strike rule for the “moneyness” of the call and put options on the collar strategy so that you can match the growth in value of $1 experienced by the Fairfield Guard Hedge Fund? A fixed-strike rule means that you should keep the moneyness (the percentage that makes the strikes for the call and put options to be OTM) held constant over time.
Question 2: What are your observations?
Question 3: What do you conclude?