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A mutual fund currently has $50M in Hang Seng index and $50M in one-year zero-coupon bonds. Assume that the one-year interest rate is 6% (annually compound). Assume that the current quote on the Heng Seng index is 1,125, each futures contract is written on 250 units of the index and the dividend yield on the index is approximately 3% per year, i.e., $1,000 invested in the index yields $30 in dividends at the end of the year.

Suppose you invest $1,125 250 in one-year zero-coupon bonds and at the same time enter into a single futures contract with long position on Heng Seng index with one year to maturity.

a) i)Assume that in one year the index finishes at 1,000. What is the total value of your position? How does this compare with buying 250 units of the index and holding them for a year? ii) Assume that in one year the index finishes at 1,200. Repeat the analysis.