HullFund8eCh02ProblemSolutions
CHAPTER 2
Mechanics of Futures Markets
Practice Questions
Problem 2.8.
The party with a short position in a futures contract sometimes has options as to the precise asset that will be delivered, where delivery will take place, when delivery will take place, and so on. Do these options increase or decrease the futures price? Explain your reasoning.
These options make the contract less attractive to the party with the long position and more attractive to the party with the short position. They therefore tend to reduce the futures price.
Problem 2.9.
What are the most important aspects of the design of a new futures contract?
The most important aspects of the design of a new futures contract are the specification of the underlying asset, the size of the contract, the delivery arrangements, and the delivery months. Problem 2.10.
Explain how margin protect investors against the possibility of default.
Margin is money deposited by an investor with his or her broker. It acts as a guarantee that the investor can cover any losses on the futures contract. The balance in the margin account is adjusted daily to reflect gains and losses on the futures contract. If losses are above a certain level, the investor is required to deposit further margin. This system makes it unlikely that the investor will default. A similar system of margin accounts makes it unlikely that the investor’s broker will default on the contract it has with the clearing house member and unlikely that the clearing house member will default with the clearing house.
Problem 2.11.
A trader buys two July futures contracts on frozen orange juice. Each contract is for the delivery of 15,000 pounds. The current futures price is 160 cents per pound, the initial margin is $6,000 per contract, and the maintenance margin is $4,500 per contract. What price change would lead to a margin call? Under what circumstances could $2,000 be withdrawn from the margin account?
There is a margin call if more than $1,500 is lost on one contract. This happens if the futures price of frozen orange juice falls by more than 10 cents to below 150 cents per lb. $2,000 can be withdrawn from the margin account if there is a gain on one contract of $1,000. This will happen if the futures price rises by 6.67 cents to 166.67 cents per lb.
Problem 2.12.
Show that, if the futures price of a commodity is greater than the spot price during the delivery period, then there is an arbitrage opportunity. Does an arbitrage opportunity exist if the futures price is less than the spot price? Explain your answer.
If the futures price is greater than the spot price during the delivery period, an arbitrageur
buys the asset, shorts a futures contract, and makes delivery for an immediate profit. If the futures price is less than the spot price during the delivery period, there is no similar perfect arbitrage strategy. An arbitrageur can take a long futures position but cannot force immediate delivery of the asset. The decision on when delivery will be made is made by the party with the short position. Nevertheless companies interested in acquiring the asset will find it attractive to enter into a long futures contract and wait for delivery to be made.
Problem 2.13.
Explain the difference between a market-if-touched order and a stop order.
A market-if-touched order is executed at the best available price after a trade occurs at a specified price or at a price more favorable than the specified price. A stop order is executed at the best available price after there is a bid or offer at the specified price or at a price less favorable than the specified price.
Problem 2.14.
Explain what a stop-limit order to sell at 20.30 with a limit of 20.10 means.
A stop-limit order to sell at 20.30 with a limit of 20.10 means that as soon as there is a bid at 20.30 the contract should be sold providing this can be done at 20.10 or a higher price.
Problem 2.15.
At the end of one day a clearing house member is long 100 contracts, and the settlement price is $50,000 per contract. The original margin is $2,000 per contract. On the following day the member becomes responsible for clearing an additional 20 long contracts, entered into at a price of $51,000 per contract. The settlement price at the end of this day is $50,200. How much does the member have to add to its margin account with the exchange clearing house?
The clearing house member is required to provide 20×$2,000 = $40,000 as initial margin for the new contracts. There is a gain of (50,200 - 50,000)? 100 = $20,000 on the existing contracts. There is also a loss of (51,000 – 50,200) × 20 = $16,000 on the new contracts. The member must therefore add
40,000 – 20,000 + 16,000 = $36,000
to the margin account.
Problem 2.16.
On July 1, 2013, a Japanese company enters into a forward contract to buy $1 million with yen on January 1, 2014. On September 1, 2013, it enters into a forward contract to sell $1 million on January 1, 2014. Describe the profit or loss the company will make in dollars as a function of the forward exchange rates on July 1, 2013 and September 1, 2013.
Suppose 1F and 2F are the forward exchange rates for the contracts entered into July 1, 2013 and September 1, 2013, respectively. Suppose further that S is the spot rate on January 1, 2014. (All exchange rates are measured as yen per dollar). The payoff from the first contract is 1()S F - million yen and the payoff from the second contract is 2()F S - million yen. The total payoff is therefore 1221()()()S F F S F F -+-=- million yen.
Problem 2.17.
The forward price on the Swiss franc for delivery in 45 days is quoted as 1.1000. The futures
price for a contract that will be delivered in 45 days is 0.9000. Explain these two quotes. Which is more favorable for an investor wanting to sell Swiss francs?
The 1.1000 forward quote is the number of Swiss francs per dollar. The 0.9000 futures quote is the number of dollars per Swiss franc. When quoted in the same way as the futures price
/.=.. The Swiss franc is therefore more valuable in the
the forward price is11100009091
forward market than in the futures market. The forward market is therefore more attractive for an investor wanting to sell Swiss francs.
Problem 2.18.
Suppose you call your broker and issue instructions to sell one July hogs contract. Describe what happens.
Hog futures are traded by the CME Group. The broker will request some initial margin. The order will be relayed by telephone to your broker’s trading desk on the floor of the exchange (or to the trading desk of another broker). It will be sent by messenger to a commission broker who will execute the trade according to your instructions. Confirmation of the trade eventually reaches you. If there are adverse movements in the futures price your broker may contact you to request additional margin.
Problem 2.19.
“Speculation in futures markets is pure gambling. It is not in the pu blic interest to allow speculators to trade on a futures exchange.” Discuss this viewpoint.
Speculators are important market participants because they add liquidity to the market. However, contracts must be useful for hedging as well as speculation. This is because regulators generally only approve contracts when they are likely to be of interest to hedgers as well as speculators.
Problem 2.20.
Explain the difference between bilateral and central clearing for OTC derivatives.
In bilateral clearing, two market participants enter into an agreement with each other covering all outstanding derivative transactions between the two parties. Typically the agreement covers collateral arrangements, events of default, the circumstances under which one side can terminate the transactions, etc. In central clearing a CCP (central clearing party) stands between the two sides of an OTC derivative transaction in much the same way that the exchange clearing house does for exchange-traded contracts. It absorbs the credit risk but requires initial and variation margin from each side.
Problem 2.21.
What do you think would happen if an exchange started trading a contract in which the quality of the underlying asset was incompletely specified?
The contract would not be a success. Parties with short positions would hold their contracts until delivery and then deliver the cheapest form of the asset. This might well be viewed by the party with the long position as garbage! Once news of the quality problem became widely known no one would be prepared to buy the contract. This shows that futures contracts are feasible only when there are rigorous standards within an industry for defining the quality of the asset. Many futures contracts have in practice failed because of the problem of defining
quality.
Problem 2.22.
“When a futures contract is traded on the floor of the exchange, it may be the case that the open interest increases by one, stays the same, or decreases by one.” Explain this statement.
If both sides of the transaction are entering into a new contract, the open interest increases by one. If both sides of the transaction are closing out existing positions, the open interest decreases by one. If one party is entering into a new contract while the other party is closing out an existing position, the open interest stays the same.
Problem 2.23.
Suppose that on October 24, 2013, a company sells one April 2014 live-cattle futures contract. It closes out its position on January 21, 2014. The futures price (per pound) is 91.20 cents when it enters into the contract, 88.30 cents when it closes out the position and 88.80 cents at the end of December 2013. One contract is for the delivery of 40,000 pounds of cattle. What is the profit? How is it taxed if the company is (a) a hedger and (b) a speculator? Assume that the company has a December 31 year end.
The total profit is
40,000 × (0.9120 – 0.8830) = $1,160
If you are a hedger this is all taxed in 2014. If you are a speculator
40,000 × (0.9120 – 0.8880) = $960
is taxed in 2013 and
40,000 × (0.8880 – 0.8830) = $200
is taxed in 2014.
Problem 2.24
Explain how CCPs work. What are the advantages to the financial system of requiring all standardized derivatives transactions to be cleared through CCPs?
A CCP stands between the two parties in an OTC derivative transaction in much the same way that a clearing house does for exchange-traded contracts. It absorbs the credit risk but requires initial and variation margin from each side. In addition, CCP members are required to contribute to a default fund. The advantage to the financial system is that there is a lot more collateral (i.e., margin) available and it is therefore much less likely that a default by one major participant in the derivatives market will lead to losses by other market participants. There is also more transparency in that the trades of different financial institutions are more readily known. The disadvantage is that CCPs are replacing banks as the too-big-to-fail entities in the financial system. There clearly needs to be careful oversight of the management of CCPs.
Further Questions
Problem 2.25
Trader A enters into futures contracts to buy 1 million euros for 1.4 million dollars in three months. Trader B enters in a forward contract to do the same thing. The exchange (dollars per euro) declines sharply during the first two months and then increases for the third month
to close at 1.4300. Ignoring daily settlement, what is the total profit of each trader? When the impact of daily settlement is taken into account, which trader does better?
The total profit of each trader in dollars is 0.03×1,000,000 = 30,000. Trader B’s profit is realized at the end of the three months. Trader A’s profit is realized day-by-day during the three months. Substantial losses are made during the first two months and profits are made during the final month. It is likely that Trader B has done better because Trader A had to finance its losses during the first two months.
Problem 2.26
Explain what is meant by open interest. Why does the open interest usually decline during the month preceding the delivery month? On a particular day, there were 2,000 trades in a particular futures contract. This means that there were 2,000 buyers (going long) and
2,000 sellers (going short). Of the 2,000 buyers, 1,400 were closing out positions and 600 were entering into new positions. Of the 2,000 sellers, 1,200 were closing out positions and 800 were entering into new positions. What is the impact of the day’s trading on open interest?
Open interest is the number of contract outstanding. Many traders close out their positions just before the delivery month is reached. This is why the open interest declines during the month preceding the delivery month. The open interest went down by 600. We can see this in two ways. First, 1,400 shorts closed out and there were 800 new shorts. Second, 1,200 longs closed out and there were 600 new longs.
Problem 2.27
One orange juice future contract is on 15,000 pounds of frozen concentrate. Suppose that in September 2013 a company sells a March 2015 orange juice futures contract for 120 cents per pound. In December 2013, the futures price is 140 cents. In December 2014, the futures price is 110 cents. In February 2015, the futures price is 125 cents. The company has a December year end. What is the company's profit or loss on the contract? How is it realized? What is the accounting and tax treatment of the transaction is the company is classified as a) a hedger and b) a speculator?
The price goes up during the time the company holds the contract from 120 to 125 cents per pound. Overall the company therefore takes a loss of 15,000×0.05 = $750. If the company is classified as a hedger this loss is realized in 2015, If it is classified as a speculator it realizes a loss of 15,000×0.20 = $3000 in 2013, a gain of 15,000×0.30 = $4,500 in 20104 and a loss of 15,000×0.15 = $2,250 in 2015.
Problem 2.28.
A company enters into a short futures contract to sell 5,000 bushels of wheat for 250 cents per bushel. The initial margin is $3,000 and the maintenance margin is $2,000. What price change would lead to a margin call? Under what circumstances could $1,500 be withdrawn from the margin account?
There is a margin call if $1000 is lost on the contract. This will happen if the price of wheat futures rises by 20 cents from 250 cents to 270 cents per bushel. $1500 can be withdrawn if the futures price falls by 30 cents to 220 cents per bushel.
Problem 2.29.
Suppose that there are no storage costs for crude oil and the interest rate for borrowing or lending is 5% per annum. How could you make money if the June and December futures contracts for a particular year trade at $80 and $86, respectively.
You could go long one June oil contract and short one December contract. In June you take delivery of the oil borrowing $80 per barrel at 5% to meet cash outflows. The interest accumulated in six months is about 80×0.05×0.5 or $2. In December the oil is sold for $86 per barrel and $82 is repaid on the loan. The strategy therefore leads to a profit of $4. Note that this profit is independent of the actual price of oil in June 2010 or December 2009. It will be slightly affected by the daily settlement procedures.
Problem 2.30.
What position is equivalent to a long forward contract to buy an asset at K on a certain date and a put option to sell it for K on that date?
The equivalent position is a long position in a call with strike price K.
Problem 2.31
A company has derivatives transactions with Banks A, B, and C which are worth +$20 million, ?$15 million, and ?$25 million, respectively to the company. How much margin or collateral does the company have to provide in each of the following two situations?
a) The transactions are cleared bilaterally and are subject to one-way collateral agreements where the company posts variation margin, but no initial margin. The banks do not have to post collateral.
b) The transactions are cleared centrally through the same CCP and the CCP requires a total initial margin of $10 million.
If the transactions are cleared bilaterally, the company has to provide collateral to Banks A, B, and C of (in millions of dollars) 0, 15, and 25, respectively. The total collateral required is $40 million. If the transactions are cleared centrally they are netted against each other and the company’s total variation margin (in millions of dollars) is –20 + 15 + 25 or $20 million in total. The total margin required (including the initial margin) is therefore $30 million. Problem 2.32
A bank’s derivatives transactions with a counterparty are worth +$10 million to the bank and are cleared bilaterally. The counterparty has posted $10 million of cash collateral. What credit exposure does the bank have?
The counterparty may stop posting collateral and some time will then elapse before the bank is able to close out the transactions. During that time the transactions may move in the bank’s favor, increasing its exposure. Note that the bank is likely to have hedged the transactions and will incur a loss on the hedge if the transactions move in the bank’s favor. For example, if the transactions change in value from $10 to $13 million after the counterparty stops posting collateral, the bank loses $3 million on the hedge and will not necessarily realize an offsetting gain on the transactions.
Problem 2.33. (Excel file)
The author’s Web page (www.rotman.utoronto.ca/~hull/data) contains daily closing prices
for crude oil futures contract and gold futures contract. You are required to download the
data and answer the following:
a) How high do the maintenance margin levels for oil and gold have to be set so that there is a 1% chance that an investor with a balance slightly above the maintenance margin level on a particular day has a negative balance two days later (i.e. one day after a margin call). How high do they have to be for a 0.1% chance. Assume daily price changes are normally distributed with mean zero. Explain why the exchange might be interested in this calculation.
b) Imagine an investor who starts with a long position in the oil contract at the
beginning of the period covered by the data and keeps the contract for the whole of the period of time covered by the data. Margin balances in excess of the initial margin are withdrawn. Use the maintenance margin you calculated in part (a) for a 1% risk level and assume that the maintenance margin is 75% of the initial margin. Calculate the number of margin calls and the number of times the investor has a negative
margin balance and therefore an incentive to walk away. Assume that all margin calls are met in your calculations. Repeat the calculations for an investor who starts with a short position in the gold contract.
The data for this problem in the 7th edition is different from that in the 6th edition. a) For gold the standard deviation of daily changes is $15.184 per ounce or $1518.4 per contract. For a 1% risk this means that the maintenance margin should be set at 3263.224.1518?? or 4996 when rounded. For a 0.1% risk the maintenance margin should be set at 0902.324.1518?? or 6636 when rounded.
For crude oil the standard deviation of daily changes is $1.5777 per barrel or $1577.7 per contract. For a 1% risk, this means that the maintenance margin should be set at 3263.227.1577?? or 5191 when rounded. For a 0.1% chance the maintenance margin should be set at 0902.327.1577?? or 6895 when rounded. NYMEX might be interested in these calculations because they indicate the chance of a trader who is just above the maintenance margin level at the beginning of the period having a negative margin level before funds have to be submitted to the broker.
b) For a 1% risk the initial margin is set at 6,921 for on crude oil. (This is the
maintenance margin of 5,191 divided by 0.75.) As the spreadsheet shows, for a long investor in oil there are 157 margin calls and 9 times (out of 1039 days) where the investor is tempted to walk away. For a 1% risk the initial margin is set at 6,661 for gold. (This is 4,996 divided by 0.75.) As the spreadsheet shows, for a short investor in gold there are 81 margin calls and 4 times (out of 459 days) when the investor is tempted to walk away. When the 0.1% risk level is used there is 1 time when the oil investor might walk away and 2 times when the gold investor might do so.