Part 1. Suppose you need to hedge the risk in a stock portfolio that your company owns in it's pension plan using the E-mini S&P500 futures contracts (which has a multiplier of 50). The current value of the portfolio is $325 million and the S&P500 is currently at 2637.72 while the futures price (for next month delivery) is at 2643.25. You estimate that the "beta" of this portfolio is 1.1 while the beta of the S&P500 is 1. What position do you take in futures?

Part 2. In the above question suppose you want a tailed hedge. Now what position do you take in futures?

Part 3. In part 1 above suppose it is 1 month (1/12 of a year) until delivery of the futures and the 1-month interest rate is 3.5% per annum. Using the S&P500 index level and the futures price what must the dividend yield on the S&P500 be in order to preclude arbitrage?