5. Suppose you are an investment manager holding a one million dollars portfolio of a mutual fund in Hong Kong. Let the beta of this fund with respect to the Hong Kong stock market is 1. Suppose you want to hedge against the risk of your portfolio using the Hang Seng Index (HSI) of today as the market index. Assume each future contract on HSI worths $50 times the index level. (a) Determine the number of future contracts you need to short in order to hedge the amount of your portfolio. (b) From a newspaper, figure out the risk-free rate per annum in Hong Kong, say rf . By looking back 3 months ago retroactively to the date of 3 months before today, determine the returns of the market for these three months. Using this rate of return and rf , how much has your portfolio shrunk? (c) Assume the dividend yield for HSI is 1% per annum, suppose you want to hedge against the risk of your portfolio for a period of three months and assume that you want to use a four month HSI future index as the hedging instrument. Calculate F0 and F1 as defined in the notes. You may assume the pass 3-month performance to be the performance of the market 3-month from today in the future. (d) Determine the gain from your future position and the loss from your portfolio. What is your net gain or loss? (e) Can you do the same analysis for the next three months from now? Does the rate of return of the market affect your results?