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Relationship for the futures price

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A US fund manager has a portfolio worth $600 million with a beta of 1.10. The manager is concerned about the performance of the S&P500 (SPX) stock market index over the next two months and plans to use three-month futures on the SPX to hedge the risk.

The current level of the S&P500 is 4380, one futures contract is on 250 times the index, the risk-free rate is 1.5% p.a. with continuous compounding, and the dividend yield on the index is 2.0% per annum.

  1. Write out the theoretical relationship for the futures price. Calculate its value in the above case.
  2. What position should the fund manager take to eliminate all exposure to the market over the next two months? 
  3. Suppose that the fund manager wishes to change the portfolio's beta to 0.90. What position should the manager now take?

Reference no: EM133122977

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