Part II Constructed Response Questions

Question 1:

You take a long position in one WTI crude oil contract for future delivery at $62.23 per barrel. The contract size is 1,000 barrels. The initial margin is $5,000 and the maintenance margin is $2,500.

1. In what direction does the futures price has to move so your position loses money?
2. What is the futures price per barrel below or above which you will receive a margin call?
   1. Above $64.73
   2. Above $62.93
   3. Below $59.73
   4. None of the above

Question 2:

An investor wants to minimize market risk on a $50 million stock portfolio by using futures for hedging. The portfolios beta with respect to the S&P 500 equity index is 1.25. The current index futures quote is 2,875 and each contract is for delivery of $250 times the index.

1. What futures position should the investor open to execute the hedge? Long or short?
2. How many index futures contracts does the investor need to use to minimize market risk?
3. To reduce portfolio beta to 0.625, how many contracts does the investor need use?

Question 3:

The Russell 2000 equity index is currently quoted at 1,565. The risk-free interest rate is 2.50% per year, with continuous compounding, and the dividend yield on the index is 1.50% per year.

1. What should the futures price for a six-month contract be?
2. If the six-month Russell 2000 futures contract is currently quoted at 1,600, what futures position should be part of an arbitrage strategy that guarantees a profit? Long or short?

Question 4:

The price of a non-dividend paying stock is now $52, and its annual volatility is 30%. The risk-free interest rate is 4% per annum with continuous compounding.

1. Calculate the BSM value of a three-month European call option with a strike price of $50
2. Calculate the BSM value of a three-month European put option with a strike price of $50
3. Verify that put-call parity holds for the call and the put option