Option Pricing Unit 5
Give three reasons why the treasurer of a company might not hedge the company's exposure to a particular risk.
(a) If the company's competitors are not hedging, the treasurer might feel that the company will experience less risk if it does not hedge. (See Table 3.1 of the Hull text.) (b) The shareholders might not want the company to hedge because the risks are hedged within their portfolios. (c) If there is a loss on the hedge and a gain from the company's exposure to the underlying asset, the treasurer might feel that he or she will have difficulty justifying the hedging to other executives within the organization.
An investor enters into a short forward contract to sell 100,000 British pounds for US dollars at an exchange rate of 1.5000 US dollars per pound. How much does the investor gain or lose if the exchange rate at the end of the contract is (a) 1.4900 and (b) 1.5200?
(a) The investor is obligated to sell pounds for 1.5000 when they are worth 1.4900. The gain is (1.5000−1.4900) × 100,000 = $1,000. (b) The investor is obligated to sell pounds for 1.5000 when they are worth 1.5200. The loss is (1.5200−1.5000) × 100,000 = $2,000.
A trader enters into a short cotton futures contract when the futures price is 50 cents per pound. The contract is for the delivery of 50,000 pounds. How much does the trader gain or lose if the cotton price at the end of the contract is (a) 48.20 cents per pound; (b) 51.30 cents per pound?
(a) The trader sells for 50 cents per pound something that is worth 48.20 cents per pound. Gain = ($0.5000−$0.4820) × 50,000 = $900. (b) The trader sells for 50 cents per pound something that is worth 51.30 cents per pound. Loss = ($0.5130-$0.5000) × 50,000 = $650.
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.
In the corn futures contract, the following delivery months are available: March, May, July, September, and December. State the contract that should be used for hedging when the expiration of the hedge is in a) June, b) July, and c) January.
A good rule of thumb is to choose a futures contract that has a delivery month as close as possible to, but later than, the month containing the expiration of the hedge. The contracts that should be used are therefore: (a) July (b) September (c) March
Explain how margin accounts 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 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.
Under what circumstances does a minimum-variance hedge portfolio lead to no hedging at all?
A minimum variance hedge leads to no hedging when the coefficient of correlation between the futures price changes and changes in the price of the asset being hedged is zero.
Explain what is meant by a perfect hedge. Does a perfect hedge always lead to a better outcome than an imperfect hedge? Explain your answer.
A perfect hedge is one that completely eliminates the hedger's risk. A perfect hedge does not always lead to a better outcome than an imperfect hedge. It just leads to a more certain outcome. Consider a company that hedges its exposure to the price of an asset. Suppose the asset's price movements prove to be favorable to the company. A perfect hedge totally neutralizes the company's gain from these favorable price movements. An imperfect hedge, which only partially neutralizes the gains, might well give a better outcome.
Under what circumstances are (a) a short hedge and (b) a long hedge appropriate?
A short hedge is appropriate when a company owns an asset and expects to sell that asset in the future. It can also be used when the company does not currently own the asset but expects to do so at some time in the future. A long hedge is appropriate when a company knows it will have to purchase an asset in the future. It can also be used to offset the risk from an existing short position.
Explain what is meant by basis risk when futures contracts are used for hedging.
Basis risk arises from the hedger's uncertainty as to the difference between the spot price and futures price at the expiration of the hedge
What is basis risk? In which of the following cases would you expect basis risk to be most serious? a. A broker owning a large block of Disney common stock hedges by selling index futures. b. An lowa corn farmer hedges the selling price of her crop by selling Chicago corn futures. c. An importer must pay 900 million euros in six months. He hedges by buying euros forward.
Basis risk means that the hedging instrument is imperfectly correlated with the risk to be hedged. It is highest in (a) because Disney stock has considerable nonmarket risk. (b), basis risk is likely to be small and in (c), it should disappear.
A company wishes to hedge its exposure to a new fuel whose price changes have a 0.6 correlation with gasoline futures price changes. The company will lose $1 million for each 1 cent increase in the price per gallon of the new fuel over the next three months. The new fuel's price change has a standard deviation that is 50% greater than price changes in gasoline futures prices. If gasoline futures are used to hedge the exposure what should the hedge ratio be? What is the company's exposure measured in gallons of the new fuel? What position measured in gallons should the company take in gasoline futures? How many gasoline futures contracts should be traded? Each contract is on 42,000 gallons.
Equation (3.1) of the Hull text shows that the hedge ratio should be 0.6 × 1.5 = 0.9. The company has an exposure to the price of 100 million gallons of the new fuel. It should therefore take a position of 90 million gallons in gasoline futures. Each futures contract is on 42,000 gallons. The number of contracts required is therefore 90,000,000 / 42,000 = 2142.9 or, rounding to the nearest whole number, 2143.
When you buy a futures contract, you pay now for delivery at a future date. T or F
False - you pay at time of delivery
Define the following term - Forward vs Futures Contract
Forward vs. futures contract: Forward contracts are contracts to buy or sell at a specified future date at a specified price. Futures contracts are also contracts to buy or sell at a specified future date at a specified price. However, they differ from forward contracts in that they are traded on an exchange and they are marked to market.
"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.
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.
A corn farmer argues "I do not use futures contracts for hedging. My real risk is not the price of corn. It is that my whole crop gets wiped out by the weather." Discuss this viewpoint. Should the farmer estimate his or her expected production of corn and hedge to try to lock in a price for expected production?
If weather creates a significant uncertainty about the volume of corn that will be harvested, the farmer should not enter into short forward contracts to hedge the price risk on his or her expected production. The reason is as follows. Suppose that the weather is bad and the farmer's production is lower than expected. Other farmers are likely to have been affected similarly. Corn production overall will be low and as a consequence the price of corn will be relatively high. The farmer's problems arising from the bad harvest will be made worse by losses on the short futures position. This problem emphasizes the importance of looking at the big picture when hedging. The farmer is correct to question whether hedging price risk while ignoring other risks is a good strategy.
Explain the difference between bilateral and central clearing for OTC derivatives.
In bilateral clearing the two sides enter into an agreement governing the circumstances under which transactions can be closed out by one side, how transactions will be valued if there is a close out, how the collateral posted by each side is calculated, and so on. In central clearing a CCP stands between the two sides in the same way that an exchange clearing house stands between two sides for transactions entered into on an exchange.
Large businesses spend millions of dollars annually on insurance. Why? Should they insure against all risks or does insurance make more sense for some risks than others?
Insurance companies have the experience to assess routine risks and to advise companies on how to reduce the frequency of losses. Insurance company experience and the very competitive nature of the insurance industry result in correct pricing of routine risks. However, BP, for example, has concluded that insurance industry pricing of coverage for large potential losses is not efficient because of the industry's lack of experience with such losses. Consequently, BP has chosen to self-insure against these large potential losses. Effectively, this means that BP uses the stock market, rather than insurance companies, as its vehicle for insuring against large losses. In other words, large losses result in reductions in the value of BP's stock. The stock market can be an efficient risk absorber for these large but diversifiable risks. Insurance company expertise can be beneficial to large businesses because the insurance company's experience allows the insurance company to correctly price insurance coverage for routine risks and to provide advice on how to minimize the risk of loss. In addition, the insurance company is able to pool risks and thereby minimize the cost of insurance. Rarely does it pay for a company to insure against all risks, however. Typically, large companies self-insure against large potential losses.
Define the following term - Long vs Short Position
Investors who are long have agreed to buy the asset. Investors who are short have contracted to sell.
An airline executive has argued: "There is no point in our using oil futures. There is just as much chance that the price of oil in the future will be less than the futures price as there is that it will be greater than this price." Discuss the executive's viewpoint.
It may well be true that there is just as much chance that the price of oil in the future will be above the futures price as that it will be below the futures price. This means that the use of a futures contract for speculation would be like betting on whether a coin comes up heads or tails. But it might make sense for the airline to use futures for hedging rather than speculation. The futures contract then has the effect of reducing risks. It can be argued that an airline should not expose its shareholders to risks associated with the future price of oil when there are contracts available to hedge the risks.
It is now June. A company knows that it will sell 5,000 barrels of crude oil in September. It uses the October CME Group futures contract to hedge the price it will receive. Each contract is on 1,000 barrels of ''light sweet crude.'' What position should it take? What price risks is it still exposed to after taking the position?
It should short five contracts. It has basis risk. It is exposed to the difference between the October futures price and the spot price of light sweet crude at the time it closes out its position in September. It is also possibly exposed to the difference between the spot price of light sweet crude and the spot price of the type of oil it is selling. CHEGG RESPONSE: (1) What position should it take? - The company is going to sell crude oil in September. Therefore, the risk of company is that the price of crude might fall in September and company will have to sell at lower selling price in September. - Since the company's risk is that the price of crude might fall, to hedge it, the company should SELL (SHORT) the October CME Group futures contract, which will help the company lock in the selling price of crude. - Number of contracts to short : = Total selling quantity of company / Quantity per futures contract = 5000 barrels / 1000 barrels = 5.00 (five) Answer: Therefore, the company should sell (short) five futures contract to hedge its risk. (2) What price risks is it still exposed to after taking the position? The company is still exposed to the following price risks after taking the position : (i) Price risk of underlying product difference : The company is expected to sell crude oil in September, while the underlying asset in futures contract is light sweet crude. Therefore, there is risk of price differences between both the products, hence, the futures contract price might not hedge the full transaction amount of spot crude oil selling. (ii) Basis risk : - Basis risk is the risk of price difference between the actual sale transaction that will occur in September, and the futures contract expiry in October. The difference between spot price and futures expiry price is known as basis risk. Due to basis risk, full sale amount may not be 100% hedged.
Suppose you call your broker and issue instructions to sell one July hogs contract. Describe what happens.
Live 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 then 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.
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 2000 buyers (going long) and 2000 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 contracts 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.
Define the following term - Mark to Market
Profits and losses on a position are settled on a regular basis (e.g., daily).
Yesterday you sold six-month futures on the German DAX stock market index at a price of 7,120. Today the DAX closed at 7,100 and DAX futures closed at 7,140. You get a call from your broker, who reminds you that your futures position is marked to market each day. Is she asking you to pay money, or is she about to offer to pay you?
She is asking you to pay money because your sale is showing a loss. You have lost 20 points on your position (7,120 - 7,140 =- 20).
"Speculation in futures markets is pure gambling. It is not in the public 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.
Define the following term - Spot Price
Spot price: Price paid for immediate delivery.
A futures contract is used for hedging. Explain why the daily settlement of the contract can give rise to cash flow problems.
Suppose that you enter into a short futures contract to hedge the sale of an asset in six months. If the price of the asset rises sharply during the six months, the futures price will also rise and you may get margin calls. The margin calls will lead to cash outflows. Eventually the cash outflows will be offset by the extra amount you get when you sell the asset, but there is a mismatch in the timing of the cash outflows and inflows. Your cash outflows occur earlier than your cash inflows. A similar situation could arise if you used a long position in a futures contract to hedge the purchase of an asset at a future time and the asset's price fell sharply. An extreme example of what we are talking about here is provided by Metallgesellschaft (see Business Snapshot 3.2 of the Hull text).
Explain why a short hedger's position improves when the basis strengthens unexpectedly and worsens when the basis weakens unexpectedly.
The basis is the amount by which the spot price exceeds the futures price. A short hedger is long the asset and short futures contracts. The value of his or her position therefore improves as the basis increases. Similarly, it worsens as the basis decreases.
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.
List some of the commodity futures contracts that are traded on exchanges. Who do you think could usefully reduce risk by buying each of these contracts? Who do you think might wish to sell each contract?
The list of commodity futures contracts is long and includes: Gold Buyers include jewelers. Sellers include gold-mining companies Sugar Buyers include bakers. Sellers include sugar-cane farmers. Aluminum Buyers include aircraft manufacturers. Sellers include bauxite miner
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 long forward contract provides a payoff of ST − K where ST is the asset price on the date and K is the delivery price. The put option provides a payoff of max (K−ST, 0). If ST > K the sum of the two payoffs is ST - K. If ST < K the sum of the two payoffs is 0. The combined payoff is therefore max (ST - K, 0). This is the payoff from a call option. The equivalent position is therefore a call option.
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.
Suppose that the standard deviation of quarterly changes in the prices of a commodity is $0.65, the standard deviation of quarterly changes in a futures price on the commodity is $0.81, and the coefficient of correlation between the two changes is 0.8. What is the optimal hedge ratio for a three-month contract? What does it mean?
The optimal hedge ratio is 0.8*(0.65/0.81) = 0.642 This means that the size of the futures position should be 64.2% of the size of the company's exposure in a three-month hedge.
One orange juice future contract is on 15,000 pounds of frozen concentrate. Suppose that in September 2014 a company sells a March 2016 orange juice futures contract for 120 cents per pound. In December 2014 the futures price is 140 cents; in December 2015 the futures price is 110 cents; and in February 2016 it is closed out at 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 if 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 2016, If it is classified as a speculator it realizes a loss of 15,000×0.20 = $3000 in 2014, a gain of 15,000×0.30 = $4,500 in 2015, a loss of 15,000×0.15 = $2,250 in 2016.
Define the following term - Basis Risk
The risk that arises because the price of the asset used to hedge is not perfectly correlated with that of the asset that is being hedged.
"If the minimum-variance hedge ratio is calculated as 1.0, the hedge must be perfect." Is this statement true? Explain your answer.
The statement is not true. The minimum variance hedge ratio is P = Stand Dev S / Stand Dev F It is 1.0 when P = 0.5 & Stand Dev S = 2 * Stand Dev F Since P< 1.0 the hedge is clearly not perfect
**Suppose that in September 2015 a company takes a long position in a contract on May 2016 crude oil futures. It closes out its position in March 2016. The futures price (per barrel) is $88.30 when it enters into the contract, $90.50 when it closes out its position, and $89.10 at the end of December 2015. 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 ($90.50 − $88.30) × 1,000 = $2,200. Of this ($89.10 − $88.30) × 1,000 or $800 is realized on a day-by-day basis between September 2015 and December 31, 2015. A further ($90.50 − $89.10) × 1,000 or $1,400 is realized on a day-by-day basis between January 1, 2016, and March 2016. A hedger would be taxed on the whole profit of $2,200 in 2016. A speculator would be taxed on $800 in 2015 and $1,400 in 2016.
. Trader A enters into futures contracts to buy 1 million euros for 1.3 million dollars in three months. Trader B enters in a forward contract to do the same thing. The exchange rate (dollars per euro) declines sharply during the first two months and then increases for the third month to close at 1.3300. 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.
A company enters into a short futures contract to sell 5,000 bushels of wheat for 750 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 750 cents to 770 cents per bushel. $1500 can be withdrawn if the futures price falls by 30 cents to 720 cents per bushel.
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 pound. $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 pound.
Suppose that you enter into a short futures contract to sell July silver for $17.20 per ounce. The size of the contract is 5,000 ounces. The initial margin is $4,000, and the maintenance margin is $3,000. What change in the futures price will lead to a margin call? What happens if you do not meet the margin call?
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 $17.40 per ounce for there to be a margin call. If the margin call is not met, your broker closes out your position. CHEGG RESPONSE: Diff between Initial Margin & Maintenance Margin = $ 4000 - $ 3000 = $ 1000 Price change required for contract = Diff between Initial margin & Maintenance Margin / No. of Units = $ 1000 / 5000 = $ 0.2 Future Price = Future Sale Price + Price chnage = $ 17.20 + $ 0.20 = $ 17.40 If the Future Price crosses, $ 17.40, we need to call him to restore the account to Initial Margin balance.
Hedging transactions in an active futures market have zero or slightly negative NPVs T or F
True
The holder of a financial futures contract misses out on any dividend or interest payments made on the underlying security T or F
True
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?
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 80×0.05×1/2 or $2. In December the oil is sold for $86 per barrel which is more than the $82 that has to be repaid on the loan. The strategy therefore leads to a profit. Note that this profit is independent of the actual price of oil in June and December. It will be slightly affected by the daily settlement procedures.
A trader enters into a short forward contract on 100 million yen. The forward exchange rate is $0.0090 per yen. How much does the trader gain or lose if the exchange rate at the end of the contract is (a) $0.0084 per yen; (b) $0.0101 per yen?
a) The trader sells 100 million yen for $0.0090 per yen when the exchange rate is $0.0084 per yen. The gain is 100 × 0.0006 millions of dollars or $60,000. (b) The trader sells 100 million yen for $0.0090 per yen when the exchange rate is $0.0101 per yen. The loss is 100 × 0.0011 millions of dollars or $110,000.
A trader owns 55,000 units of a particular asset and decides to hedge the value of her position with futures contracts on another related asset. Each futures contract is on 5,000 units. The spot price of the asset that is owned is $28 and the standard deviation of the change in this price over the life of the hedge is estimated to be $0.43. The futures price of the related asset is $27 and the standard deviation of the change in this over the life of the hedge is $0.40. The coefficient of correlation between the spot price change and futures price change is 0.95. a. What is the minimum variance hedge ratio? b. Should the hedger take a long or short futures position?
a. The minimum variance hedge ratio is 0.95×0.43/0.40=1.02125. b. The hedger should take a short position.
