Scenario: Suppose a fund holds a portfolio of stocks currently trading at $50 million. The Beta of the portfolio is 1.5.

Discuss:

What position in futures contracts on the S&P 500 is necessary to totally hedge the market risk of the portfolio?

What position is necessary to reduce the beta of the portfolio to 0.75?

What position is necessary to increase the beta of the portfolio to 2.0?

What will be the answers above if the S&P 500 is trading at 2,000, and a single index futures contract is 250 times index value?

What will be the factors that will drive the hedging effectiveness of this hedging strategy for such a portfolio, assuming that the index futures contract is always priced exactly in accordance with the cost of carry model?