You manage the following S&P 500 portfolio

Market Value: 20 Million, Beta: 1.0, Dividends: 0%, Risk Free Rate: 5%. Futures available on the S&P 500 Index are:

Current Index Level: 1,000, Beta: 1.0, Dividends: 0%, Maturity: 1 Year, Multiplier 250

Assume that the performance of the portfolio follows the capital asset pricing model (CAPM)

a) You want to fully hedge the portfolio for the coming year. Recommend the hedge and show the performance of the hedge if the Index finishes the year at 800 or 1,350.

b) Show the difference in the performance of the hedge between using the Spot Price and the Forward Price in computing the number of contracts used in hedging. For the 800 or 1,350
index scenarios reconcile the performance difference between both hedging outcomes.

c) Assume that instead of a 1 year Futures contact the only contract you can sell is a 3 year contract. However you can buy a Futures contract for any maturity. You also want to target
a portfolio Beta of 0.25 for the upcoming year. Show the performance of the hedged/adjusted portfolio if the Index finishes the year at 500 or 2,000.

d) Assume that instead of a 1 year Futures contact the only contract you can sell or buy are 3 month contracts. You want to target a Beta of -2 for your portfolio for the upcoming year and will therefore need to replace with a new 3 month contract as the existing one expires. Show the performance of the hedged/adjusted portfolio if the Index finishes the first quarter at 800, the second quarter at 900, the third quarter at 950 and finished the year at 850.

e) Outlined two unique benefits of Futures over Forwards, and two unique benefits of Forward over Futures.

f) In 1993 Metallgesellschaft lost $1.3B with speculated on oil prices. Please research and in no more than half a page summarize the problems that Metallgesellschaft encountered in the management of its oil futures.