It is currently September 20, 2018. Mini-S&P500 Futures contracts are available at the Chicago Mercantile Exchange. These contracts are for $50 multiplied by the S&P index. The contracts have expiry dates of December 17, 2018 and March 17, 2019.

The current spot and futures prices, as well as the 3-and 6-month "risk-free" LIBOR rates (but for simplicity assume continuous compounding and use actual day counts t = Actual/365) are given below.

S&P 500: 2930.80

December Futures:2934.50

March Futures:2937.25

3-month LIBOR2.33%

6-month LIBOR2.54%

a)Estimate the continuous dividend yield (quote it in annual terms) for

a.September - December

b.September - March

c.December - March (you will need to think carefully about this one)

You have a diversified stock fund worth $29,345,000, and you estimate the beta of your fund to be 0.5 (Note that the portfolio beta comes from a regression of returns (DS/S) rather than price changes (DS), and so your hedging equation will need to be slightly adjusted)

b)You wish to hedge your fund entirely against market movements in the next three months, i.e reduce your beta to zero. Calculate how many futures contracts you need to enter into. Do you want to be short or long? Explain your answer.

c)Instead of hedging your portfolio against market movements, you actually wanted to increase the beta to 0.75, how many futures contracts would you have to enter into? Again, explain your answer.