1- Suppose you have 10,000 shares of the SPY. It is early October and the prices of the SPY and the December e-mini S&P500 futures contract are shown below. Based on the spot-future b estimate (shown below), calculate the number of e-mini S&P 500 futures contracts you need to hedge your portfolio.
SPY = 111.85 and /ESZ9 = 1122
bs,FC = .98
2- Suppose now it is 35 DTM and the risk free rate has stayed constant at 1.48% since you initiated the hedge in October. The SPY are currently priced at 102.5. If the change in the basis is only due to time decay, what is the profit/loss on the un-hedged SPY position and on the hedged position?
3- Now suppose that you want to adjust the risk of the portfolio to have a beta of 0.45. How many futures contracts do you need?