Prepare a time line and a simple spreadsheet to check the numbers in Problem Set 3 about Pyramiding in Gold Futures. Are any of the numbers in the problem set incorrect?

Problem Set 3 Commodity Futures: Pyramiding

NOTE: Data from 2017. This will show you that gold did go up but not straight up!

NOTE: There may be an incorrect number in this problem set. Check each number yourself.

1. Suppose that on July 11, 2017 you observed the December 2017 gold futures contract was trading at $1223 per ounce. You predicted that the price of gold would rise. For purposes of this illustration, assume that the initial margin requirement for gold futures is $2000. In real life, it is much higher (usually in the range of $5,000 - $15,000). This example will show you why it needs to be that high. You open a commodity futures trading account and put $50,000 in the account. Then you buy 25 December 2017 gold futures contracts.

Assume that the opening price the next day is the same as the closing price of the day before. This is not generally true, but it makes this example simpler.

Also assume that gold futures trade seven days a week. This is not true. The futures market closes for part of the weekend.

The initial margin was $2000 per contract, so your broker transferred $50,000 from your account to the clearinghouse, to guarantee that you will perform your commitment to buy gold when the contracts mature. Note that you can sell the contract before it matures, so you will not have to complete the purchase. You are at risk for the price change. Also note that your $2000 makes its way to the clearinghouse via your broker and via the floor broker who buys the contract on your behalf. You can still see the money in your account, but it is frozen to protect the other participants in the market and the clearinghouse.

The next day, July 12, gold goes up $20 per ounce, to $1243 per ounce. That is a $50,000 gain because each contact covers 100 ounces and your 25 contracts cover 2,500 ounces. The profit, although it is only a paper profit, is transferred to your account after the market closes on July 12, 2017. You can take the gain in cash if you wish, but you choose to leave the gain in your account.

The $50,000 gain is enough cash in your account to buy 25 more December 2017 gold futures contracts, so at the opening of the market on July 13, you buy those at $1243 per ounce. The initial margin deposits for buying these contracts come from the previous days paper profit (mark-to-market in the futures market) that has been transferred into your account.

The next day, July 14, gold goes up $30 per ounce. The new price is $1273 per ounce. Your profit is $30 * 50 contracts * 100 ounces per contact = $150,000. That profit is transferred to your account. The next day, July 15, you have enough in your account to buy 75 more December 2017 gold futures contracts, and you do. You buy them early in the trading session, at $1273 per ounce, and later in the session gold goes up. After your most recent purchase you have 125 gold futures contacts. That is 25 contracts at $1223, 25 at $1243, and 75 at $1273.

By the end of the trading session on July 15, gold has gone up $20 more, to $1293 per ounce. Your profit is $20 * 125 contracts * 100 ounces per contract = $250,000. After the market closes on July 15, you now have enough in your account to buy 125 more December 2017 gold futures contracts. You buy 125 more contracts, at $1293 per ounce, so your total position is 250 contracts.

The next day, July 16, gold goes up $50 per ounce, to $1343 per ounce. At that price you sell all 250 contracts and then call your friends to tell them you are giving a party. What was your total gain? Assume that after you sell the 250 contracts, you close your commodity futures account, withdraw all your money, and retire from trading commodities.

Solution: Your gain would be ($1343 - $1223)*100*25 + ($1343 1243)*100*25 + ($1343 - $1273)*100*75 + ($1343 1293)*100*150. That is $1.7 million. Verify if my calculation is correct.

What if gold goes down $50 per ounce on that last day, July 16? Do you lose everything and end up owing money to your broker?

Solution: You would lose. In this scenario, the December gold futures contract goes down on July 16, to from $1293 to $1243. On the final 125 contracts that you bought at the price of $1293, you would lose $50*100*125 = $625,000. That loss would deplete your margin account. Your gain on the positions you bought earlier would be much smaller than it was the day before, and in fact would go negative, because the gain would be computed using the $1243 price of July 16. Using the $1243 price, the purchase of 75 contracts would be under water because you bought those at the price of $1273. So your loss on those would be ($1243 - $1273)*100*75 = -$225,000. On the 25 contracts you bought at $1243 per ounce, you would have neither a gain nor a loss. On the 25 contracts you bought at $1223 per ounce, you have a gain of $20 per ounce, so that small gain still exists, but it is overwhelmed by the big losses you have on the larger positions.

Compute how much your loss would be.

So if you are on Wall Street and someone looks VERY chagrined, this might be what happened.

Now the question for how these markets should be set up: Should the initial margin requirements be $2,000 or $6,000, or some other number? What is your opinion?

To hand in:

1. What annual rate of return would you make on your initial $50,000 if the positive scenario happens? Write a spreadsheet to show what is the value of your margin account after each trading day. Then compute the annual rate of return from your calculations.
2. What annual rate of return would you make on your initial $50,000 if the bad scenario is what happens? Note that you can lose more than what you put in. In other words, your annual rate of return can be WORSE than -100%.
3. If the initial margin deposit requirement were $5,000 per contract instead of $2,000 per contract, how would the two scenarios have worked out? What would have been your annual rate of return in each scenario? Assume that you start with $50,000 as before.