Investments Problem Set: Futures and Forwards

Assume, for all problems, that the 1 year risk free interest rate 0.85%

1. Price a 6 month forward on a single security, without a dividend, currently priced at $74.22
2. Price the future on the same security as in problem 1 assuming it has a dividend payment of $0.47 at the end of the second month.
3. Again, using the security in problem 1, price the forward assuming that there is a dividend yield of .04%.
4. You have a portfolio with a value of $1 Million USD. It is comprised of stocks and cash. The overall portfolio is highly correlated with the S&P 500. You believe that the S&P 500 will decline in the following 6 months. How would you hedge your portfolio? Explain in terms of the number and type of contracts you would purchase and the timing of those actions. Assume your cash position is sufficient for hedging and that you will not need to sell securities to finance the hedge. Please note that the S&P 500 futures contract controls the equivalent of 25 S&P Index prices. Assume today is 1 Oct 2021 The spot price for the S&P Index is 75 The contracts for the S&P Futures Prices are as follows (Assume that you may buy or sell at this price): Nov21: 4480 Dec21: 4493 Jan22: 4521 Feb22: 4530 Mar22: 4540
5. Explain the difference between forwards and futures and the reason(s) you would select one or the other instrument.
6. Determine the current value of the margin account for the following scenario: You have two futures contracts purchased one month ago. The underlying instrument was trading at $1000 at the time you entered the futures contract. You are long two $1005 contracts which expire in 3 months. The initial margin for each contract is $200. The maintenance margin is $100. In the month since you entered the contract, the price of the underlying security has risen to $1010 as of today.
   1. What is the value of the margin account today?
   2. Another month passes and the market has crashed. The underlying security is now trading at $850. What is the value of the margin account after the crash (please remember the maintenance margin amount)? Please show the margin account amounts at time 0, 1 and 2 and the cash flows.