Suppose that you have $1 million invested in an S&P Index. One share of this index has a price of $2552.07. At the start of January, you need to have $900,000 available to invest in a tech startup. You want to keep the money invested in the market for the potential upside, but need to ensure that the value of your account doesnt fall below this threshold.

1.If you keep your money invested in the index fund, how low can the price of the S&P index fall before your account falls below the threshold?

2.To limit your downside potential, you decide to buy a put option. The price of January 2018 put options are listed in the excel sheet S&P Put Prices for various strikes. What is the lowest strike you could choose that would still ensure that the value of your account stays above $900,000?

3.How many shares of this option will you need to be exposed to in order to ensure this lower limit and how much will these shares cost? You may assume that you can fund the purchase of these puts from an outside account. For extra credit, assume that you need to pay for these options by selling shares of your S&P index fund.

4.Draw a payoff diagram that shows the value of your portfolio (shares and puts combined) for S&P prices ranging from 2,000 to 3,000. This diagram should remind you of another kind of derivative. What is it?

5.What is the price of a call option with the same strike as the put option you chose in (b)? Assume a risk-free rate of 1% and a time-to-maturity of .25.

Strike Price 2200 2250 2300 2350 2400 2450 2500 2550 2600 2650106.3.2 2700148.14 2750193.92 2800241.94 2850291.07 2900340.68 2950390.417 3000440.3.2 0.01 0.08 0.37 1.38 4.16 10.5 22.61 42.35 70.48 Strike Price 2200 2250 2300 2350 2400 2450 2500 2550 2600 2650106.3.2 2700148.14 2750193.92 2800241.94 2850291.07 2900340.68 2950390.417 3000440.3.2 0.01 0.08 0.37 1.38 4.16 10.5 22.61 42.35 70.48