Hull_7thEd_CH2_solutions

Hull_7thEd_CH2_solutions - CHAPTER 2 Mechanics of Futures...

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Unformatted text preview: CHAPTER 2 Mechanics of Futures Markets Problem 2.1 . Distinguish between the terms open interest and trading volume. ntract at a particular time is the total number of long it is the total number of short positions outstanding.) time is the number of contracts traded during The open interest of a futures co positions outstanding. (Equivalently, The trading volume during a certain period of this period. Problem 2.2. What is the difl’erence between a A commission broker trades on behalf of a client and charges a commission. A local trades on his or her own behalf. local and a commission broker? Problem 2.3. Suppose that you enter i ounce on the New York Commodity Exchange. The siz 'n is $3,000. What change in the The initial margin is $4,000, and the maintenance margi futures price will lead to a margin call? What happens if you do not meet the margin call? nto a short futures contract to sell July silver for $10.20 per e of the contract is 5,000 ounces. There will be a margin call when $1,000 has been lost from the margin account. This will occur when the price of silver increases by 1,000/ 5,000 = $0.20. The price of silver must therefore rise to $10.40 per ounce for there to be a. margin call. If the margin call is not met, your broker closes out your position. Problem 2.4. Suppose that in September 2009 a company takes along 2010 crude oil futures. It cloSes out its position in March 2010. The futures price (per barrel) is $68.30 when it enters into the contract, $70.50 when it closes out its position, and $69.10 at the end of December 2009. One contract is for the delivery of 1,000 barrels. What is the company’s total profit? When is it realized? How is it taxed if it is (a) a hedger and (b) a speculator? Assume that the company has a December 31 year—end. The total profit is ($70.50 - $68.30) X 1,000 = $2,200. Of this ($69.10 — $68.30) X , 1,000 = $800 is realized on a day-by-day basis between September 2009 and December 31, 2009. A further ($70.50 — $69.10) X 1, 000 = $1,400 is realized on a day-by-day basis between January 1, 2009, and March 2010. A. hedger would be taxed 0n the whole profit : of $2,200 in 2010. A speculator would be taxed on $800 in 2009 and $1,400 in 2010. position in a contract on May 11 -__'e:j Problem 2.5. What does a stop order to sell at 32 mean? When might it be used? What does a limit order to sell at $2 mean? When might it be used? A stop order to sell at $2 is an order to sell at the best available price once a price of $2 or less is reached. It could he used to limit the losses from an existing long position. A limit order to sell at $2 is an order to sell at a price of $2 or more. It could be used to instruct a broker that a short position should be taken, providing it can be done at a price more favorable than $2. Problem 2.6. What is the difference between the operation of the margin accounts administered by a clearinghouse and those administered by a broker? The margin account administered by the clearinghouse is marked to market daily, and the clearinghouse member is required to bring the account back up to the prescribed level daily. The margin account administered by the broker is also marked to market daily. However, the account does not have to be brought up to the initial margin level on a daily basis. It has to be brought up to the initial margin level when the balance in the account falls below the maintenance margin level. The maintenance margin is usually about 75% of the initial margin. Problem 2.7. What differences exist in the way prices are quoted in the foreign exchange fixtures market, the foreign exchange spot market, and the foreign exchange forward market? In futures markets, prices are quoted as the numbei of US. dollars per unit of foreign currency. Spot and forward rates are quoted in this way for the British pound, euro, Austraiian dollar, and New Zealand dollar. For other major currencies, spot and forward rates are quoted as the number of units of foreign currency per U.S. dollar. Problem 2.8. The party with a short position in a futures contract sometimes has options as to the precise asset that will he 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. ' ‘5 ~' 7* ' “ These Options make the contract, Party with the long position and more attractive to the party with the! hurt peeltion. They therefore tend to reduce the futures price. ‘ =7“ 1' - . a. of-a new futures contract? Problem 2.9. _ What are the most importan' W'fatures contract are the specifica- dehvery arrangements, and the The most important tion of the underlying asset_,__t delivery months. :1 l 3 Problem 2.10. Explain how margins protect investors against the possibility of default. A margin is a sum of 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 a further margin. This system makes it unlikely that the investor will default. A similar system of margins makes it unlikely that the investor’s broker will default on the contract it has with the clearinghouse member and unlikely that the clearinghouse member will default with the clearinghouse. Problem 2.11. A trader buys two long July futures contracts on 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 $1,500 is lost on one contract. This happens if the futures price of orange juice falls by 10 cents to 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 1b. Problem 2.12. Show that if the futures price of a commodity is greater than the spot price during the delivery period 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 ar- bitrageur 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 along futures contract and wait for delivery to be made. Problem 2.13. Explain the difl'erence 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 ofi'er at the specified price or at a price less favorable than the specified price. 13 Problem 2. 14. contracts. The member must therefore add 40, 000 — 20, 000 + 16, 000 = $36, 000 to the margin account. Problem 2. 16. Suppose F1 and F2 are the forward exchange rates for the contracts entered into July 1, 2009 and September 1, 2009, and S is the spot rate on January 1, 2010. (All exchange rates are measured as yen per doilar). The payoff from the first contract is (S — F1) million yen and the payofl’ from the second contract is (F2 — S) million yen. The total payoff is therefore (S -— F1) + (F2 — S) 2 (F2 — F1) million yen. Problem 2.17. 14 Problem 2.18. Suppose you call your broker and issue instructions to sell one July hogs contract. Describe what happens. Hog futures are traded on the Chicago Mercantile Exchange. (See Table 2.2). 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 ac- cording 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 public interest to allow speculators to trade on a futures exchange.” Disouss this viewpoint. Speculators are important market participants because they add liquidity to the mar- ket. 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. Identify the centracts that have the highest open interest in Table 2.2. rl‘he table does not show contracts for all maturities. In the Metals and Petroleum category it appears that crude oil has the highest open interest. In the agricultural category it appears that corn has the highest open interest. - , 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 15 The total profit is 40, 000 x (0.9120 — 0.8830) = $1, 160 If you are a hedger this is all taxed in 2009. If you are a speculator 40,000 x (0.9120 — 0.8880) = $960 is taxed in 2009 and 40, 000 x (0.8880 — 0.8830) = $200 is taxed in 2010. Problem 2.24. 3 contracts that have 3 months to maturity. If the price of cattle falls, the gain on the futures contract will ofl‘set If the price of cattle rises, the futures contract. Using cost reduce risk to almost zero. t the farmer no longer gains from favorable movements in cattle prices. total of 3,000 ounces are expected to be produced in January 2009 and February 2009, the price received for this production can be hedged by shorting a. total of 30 February 2009 contracts. 17 ...
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This note was uploaded on 02/23/2011 for the course FBE 459 taught by Professor Matos during the Spring '08 term at USC.

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Hull_7thEd_CH2_solutions - CHAPTER 2 Mechanics of Futures...

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