433 Test 1 (Chapters 1-4), 433 Module 1, 433 Module 2, 433 Module 3

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Firms use derivatives to manage their risk exposer or _____

"Hedge", to protect the firm from an undesirable outcome.

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? (c) What is the optimal number of futures contracts when issues associated with daily settlement are not considered? (d) How can the daily settlement of futures contracts be taken into account?

(a) The minimum variance hedge ratio is 0.95×0.43/0.40=1.02125. (b) The hedger should take a short position. (c) The optimal number of contracts when daily settlement is not considered is 1.02125×55,000/5,000=11.23 (or 11 when rounded to the nearest whole number) (d) The optimal number of contracts is where is correlation between percentage one-day returns of spot and futures, are the standard deviations of percentage one-day returns on spot and futures, VA is the value of the position and VF is the futures price times the size of one contract. In this case VA = 55,000×28 = 1,540,000 and VF =5,000×27=135,000. If we assume that =0.95 and , the optimal number of contracts when daily settlement is considered 0.95×1.075×1,540,000/135,000=11.64 (or 12 when rounded to the nearest whole number). This does not make the interest rate adjustment discussed in the final part of Section 3.4.

Future Contract

- A future contract is an obligation that allows the contract (position) holder to buy/sell the underlying instrument at a predetermined price and date. - If contract terms are not honored, there can be legal implications, be sued or sue

3 broad categories of traders

- Hedgers: use futures, forwards, and options to reduce risks that they face from potential future movements in a market variable - Speculators: use them to bet on the future direction of a market variable - Arbitrageurs take offsetting positions in 2 or more instruments to lock in profit

3 changes to OTC market to the exchange traded market

- standardized OTC derivatives between 2 financial institution in the US (Swap execution facilities) - central counterpart be used for 2 financial institutions transactions - All trades must be reported to a central repository s

Predetermined date refers to

- the futures maturity (expiration) date. Usually 3rd fiday of delivery month. - has predetermined cycles of Jan-April-Jule-Oct. or March-June-Sept.-Dec.

2 types of options:

-Call option: gives the holder the right to buy an asset by a certain date for a certain price - put option: gives holder the right to sell on asset by a certain date for a certain price

Financial derivatives

-financial instruments linked to a specific financial instrument, indicator, or commodity, known as the underlying asset. The value derives from the price of the underlying asset. - exp.) Stock options granted to executives - when price of underlying stock increases (decreases), the value of the option increases (decreases). That is, the value of the option is derived from the value of the stock

2 major things clearing house does

-margin requirements: traders have to admit money to fit initial and maintenance requirements. These are lower than for stock trading. - Daily Settlement: Also known as mark to the market daily. Profit/loss are computed daily, and the margin balance account is credited accordingly.

Closing a futures Position (3 ways)

1. Accept (Make) delivery upon maturity 2. Perform a reverse trade prior to maturity 3. Exchange for physical (exchange of a specified quantity of a cash. Commodity for an equivalent quantity of futures, often done by two traders having opposite futures positions that each want to offset.

Underlying Instruments (3 things)

1. Commodities 2. Financial 3. Non Conventional

Most important objective for firms that hedge

1. minimize fluctuations in cash flow (67%) 2. minimize fluctuation in Accounting Earnings (20%) 3. Protect Appearance of the Balance Sheet (5%)

"When the futures price of an asset is less than its spot price, long hedges are likely to be particularly attractive." Explain this statement.

A company that knows it will purchase a commodity in the future is able to lock in a price close to the futures price. This is likely to be particularly attractive when the futures price is less than the spot price. An illustration is provided by Example 3.2.

In the CME Group's 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 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 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.

On July 1, an investor holds 50,000 shares of a certain stock. The market price is $30 per share. The investor is interested in hedging against movements in the market over the next month and decides to use the September Mini S&P 500 futures contract. The index is currently 1,500 and one contract is for delivery of $50 times the index. The beta of the stock is 1.3. What strategy should the investor follow?

A short position in 1.3*50,000*30/50*1,500 = 26 contracts is required. It will be profitable if the stock outperforms the market in the sense that its return is greater than that predicted by the capital asset pricing model.

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.

Commodities

Agricultural products, energy, and metals

8. Find the profit if the investor buys a Feb futures at 62, sells a March futures at 64 and then reverses the Feb futures at 60 and the March futures at 66.

Answer C: -4 [The investor loses 2 on the Feb contract and 2 on the Mar contract]

5.What happens in a Contango?

Answer: Futures price is above the expected future spot price.

9. What is the convenience yield in the cost-of-carry model?

Answer: It means the convenience enjoyed by holding the spot instrument. it reflects the markets' expectations regarding the future availability of the commodity. If the market expects shortages, the convenience yield is large and no one wants to sell the spot instrument - vice versa. Convenience yield is zero for financial instruments.

Flow of future transactions on future exchanges

Buyer (long futures) to Buyers Broker to Buyers floor Broker to finally futures exchange Sellers (Short future) to sellers broker to sellers floor to finally futures exchange

largest options exchange is the

CBOE

How do you perform the daily settlement of a futures position?

Compute the profit and loss daily and credit (debit) your margin balance account accordingly

date in contract is the expiration date or maturity date

European option can only be exercised on maturity date American option can be exercised at any time

Future trades are 24 hours

Even after futures exchanges are closed, traders can continue to trade using the global computer platform

5 types of financial Derivatives

Futures Options Forward Contracts: Similar to futures, but their contracts characteristics are not standardized and are traded over the counter Options on Futures Swaps

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.

"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.

Suppose that in Table 3.5 the company decides to use a hedge ratio of 1.5. How does the decision affect the way the hedge is implemented and the result?

If the company uses a hedge ratio of 1.5 in Table 3.5 it would at each stage short 150 contracts. The gain from the futures contracts would be 1.50*1.7 = $2.55 per barrel and the company would be $0.85 per barrel better off.

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.

Suppose that in Example 3.4 the company decides to use a hedge ratio of 0.8. How does the decision affect the way in which the hedge is implemented and the result?

If the hedge ratio is 0.8, the company takes a long position in 16 December oil futures contracts on June 8 when the futures price is $8. It closes out its position on November 10. The spot price and futures price at this time are $65 and $62. The gain on the futures position is (62 − 58)×16,000 = $64,000 The effective cost of the oil is therefore 20,000×65 − 64,000 = $1,236,000 or $61.80 per barrel. (This compares with $61.00 per barrel when the company is fully hedged.)

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, 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. The CCP and its members absorb the credit risk, but initial as well as variation margin is required from each side.

Explain how CCPs work. What are the advantages to the financial system of requiring all standardized derivatives transactions to be cleared through CCPs?

In fact it is only standard trades between financial institutions that must 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. The CCP and its members absorb the credit risk, but initial and variation margin is required 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 market participants 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.

Most Common interest rate risk uses swaps

Interest rate swaps

Financial

Interest rates (Eurodollars, treasury notes, treasury bonds), Index related (s&p 100, 500), currency (major currencys only)

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.

Explain how margin protect futures traders against the possibility of default.

Margin is money deposited by a trader with his or her broker, by the broker with the clearing house member, and by the clearing house member with the clearing house. It acts as a guarantee that any losses on the futures contract will be covered. 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 maintenance margin), a trader is required to deposit further margin with the broker. This system makes it unlikely that the trader 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 on its trades with the clearing house.

Does a perfect hedge always succeed in locking in the current spot price of an asset for a future transaction? Explain your answer.

No. Consider, for example, the use of a forward contract to hedge a known cash inflow in a foreign currency. The forward contract locks in the forward exchange rate, which is in general different from the spot exchange rate.

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.

long futures

Position allows you to buy the underlying asset

Non Conventional

Snowfall futures, weather futures, single stock futures (traded on Chicago one platform)

"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.

Explain why collateral requirements will increase in the OTC markets as a result of new regulations introduced since the 2008 credit crisis.

Standard transactions between financial institutions have to be cleared through CCPs. Initial margin and variation margin are therefore required. Nonstandard transactions between financial institutions will continue to be cleared bilaterally, but the credit support annex (CSA) must include a requirement for initial margin from both sides as well as variation margin.

futures contracts are highly

Standardized, they have predetermined maturity cycles. The contracts are also predetermined.

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 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).

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 forward price is. The Swiss franc is therefore more valuable in the forward market than in the futures market. The forward market is therefore more attractive for an investor wanting to sell Swiss francs.

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.

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.

What position is equivalent to a long forward contract to buy an asset at on a certain date and a put option to sell it foron that date?

The equivalent position is a long position in a call with strike price.

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 futures contract is on 42,000 gallons.

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.

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.

One orange juice future contract is on 15,000 pounds of frozen concentrate. Suppose that in September 2016 a company sells a March 2018 orange juice futures contract for 120 cents per pound. In December 2016, the futures price is 140 cents. In December 2017, the futures price is 110 cents. In February 2018, 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 2018, If it is classified as a speculator it realizes a loss of 15,000×0.20 = $3000 in 2016, a gain of 15,000×0.30 = $4,500 in 2017 and a loss of 15,000×0.15 = $2,250 in 2018.

Imagine you are the treasurer of a Japanese company exporting electronic equipment to the United States. Discuss how you would design a foreign exchange hedging strategy and the arguments you would use to sell the strategy to your fellow executives.

The simple answer to this question is that the treasurer should 1. Estimate the company's future cash flows in Japanese yen and U.S. dollars 2. Enter into forward and futures contracts to lock in the exchange rate for the U.S. dollar cash flows. However, this is not the whole story. As the gold jewelry example in Table 3.1 shows, the company should examine whether the magnitudes of the foreign cash flows depend on the exchange rate. For example, will the company be able to raise the price of its product in U.S. dollars if the yen appreciates? If the company can do so, its foreign exchange exposure may be quite low. The key estimates required are those showing the overall effect on the company's profitability of changes in the exchange rate at various times in the future. Once these estimates have been produced the company can choose between using futures and options to hedge its risk. The results of the analysis should be presented carefully to other executives. It should be explained that a hedge does not ensure that profits will be higher. It means that profit will be more certain. When futures/forwards are used both the downside and upside are eliminated. With options a premium is paid to eliminate only the downside.

"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* std. dev. s/ std. dev f. It is 1.0 when and . Since the hedge is clearly not perfect.

"If there is no basis risk, the minimum variance hedge ratio is always 1.0." Is this statement true? Explain your answer.

The statement is true. Suppose for the sake of definiteness that the commodity is being purchased. If the hedge ratio is h, the gain on futures is h(F2 -F1) so that the price paid is S2 − h(F2 -F1) or hb2 + hF1+(1−h)S2. If there is no basis risk, b2 is known. For a given h, there is therefore no uncertainty in the first two terms. For any value of h other than 1, there is uncertainty in the third term. The minimum variance hedge ratio is therefore 1.

Trader A enters into futures contracts to buy 1 million euros for 1.1 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 1.1300. 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 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.

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 120 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 110 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 126.67 cents per lb.

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.

A portfolio manager has maintained an actively managed portfolio with a beta of 0.2. During the last year the risk-free rate was 5% and equities performed very badly providing a return of −30%. The portfolio manage produced a return of −10% and claims that in the circumstances it was good. Discuss this claim.

When the expected return on the market is −30% the expected return on a portfolio with a beta of 0.2 is 0.05 + 0.2 × (−0.30 − 0.05) = −0.02 or -2%. The actual return of -10% is worse than the expected return. The portfolio manager has achieved an alpha of -8%!

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 $60 and $66, respectively.

You could go long one June oil contract and short one December contract. In June you take delivery of the oil borrowing $60 per barrel at 5% to meet cash outflows. The interest accumulated in six months is about 60×0.05×0.5 or $1.50. In December the oil is sold for $66 per barrel and $61.50 is repaid on the loan. The strategy therefore leads to a profit of $4.50. Note that this profit is independent of the actual price of oil in June or December. It will be slightly affected by the daily settlement procedures.

1. A futures contract covers 1000 pounds with a minimum price change of $0.01 is sold for $22.50 per pound. If the initial margin is $2,525 and the maintenance margin is $1,000, at what price would there be a margin call?

[A margin call would come if the escrow balance drops below the maintenance margin of $1000. That is, the initial margin drops from 2525 to below 1000. This drop, 1525 or more, implies an increase in the futures price because the trader has a short position. For a drop of $1525 or more to occur for a 1000-pound of the commodity, the futures price goes up $1525/1000 = $1.525 at least. That is, the futures price = $22.50 + $1.525 = 24.025 or more]

4. Determine the amount by which a stock index futures is mispriced if the stock index is at 105, the futures is at 108, the risk-free rate is 7 percent, the dividend yield is 3 percent, and the contract expires in three months.

[For futures that pay a continuous dividend yield, F = Se^(r-q)*t = 105e^(0.07-0.03)*3/12 = 106.055. Therefore, the contract is overvalued by 108-106.055 = 1.95]

7. A company has a $20 million portfolio with a beta of 1.4. The futures price for a contract on an index is 1000. Futures contracts on $250 times the index can be traded. What trade is necessary to reduce beta to 1.1?

[Price per futures contract = 1000x250 = 250,000. In timing the market, hedge ratio = (beta(desired) - beta(actual)) * So/Fo = (1.4 -1.1) * 20,000,000/(250x1000) = 24 contracts]

6. On March 1 a commodity's spot price is $45 and its August futures price is $47. On July 1 the spot price is $50 and the August futures price is $51. A company entered into futures contracts on March 1 to hedge its purchase of the commodity on July 1. It closed out its position on July 1. What is the effective price (after taking account of hedging) paid by the company?

[The company has to do a long hedge on March 1. That is, it buys futures at Fo = 47. On July 1, it closes the futures position by selling the futures at Ft=51. That is, it has gain 4 on the futures. Only July 1, the firm actually buys the commodity in the spot market for $50, and it is offset by the $4 gain on futures. The effective purchase price = 50 -4 = 46. Or using the equation for effective price = F0 + Bt = F0 + (St - Ft) = 47 + (50 - 51) = 46]

3. Suppose you sell a three-month futures contract at $40. One month later, new futures contracts with similar terms are trading for $36. The continuously compounded risk-free rate is 10 percent. What is the value of your futures contract?

[You can close out the short position by buying back at 36. That is, value of the gain = (40-36)e^-0.1*2/12, =3.933]

2. This morning a company enters into a short futures contract to sell 500 units of a commodity for $40 per unit. The initial margin is $5,000 and the maintenance margin is $3,000. What futures price will allow $1,000 to be withdrawn from the margin account if the account is closed later today?

[You can withdraw from the margin account only if there is a gain. Gain per unit =1000/500 =2. Given that it is a short position, a gain occurs when futures price goes down when the position is closed. Therefore, futures price = 40-2 = 38]

funds deposited after being below a maintenance margin is

a variation margin

It is July 16. A company has a portfolio of stocks worth $100 million. The beta of the portfolio is 1.2. The company would like to use the December futures contract on a stock index to change the beta of the portfolio to 0.5 during the period July 16 to November 16. The index futures price is 2,000, and each contract is on $250 times the index.

a) What position should the company take? b) Suppose that the company changes its mind and decides to increase the beta of the portfolio from 1.2 to 1.5. What position in futures contracts should it take? a) The company should short (1.2 - .5) * 100,000,000 / 2,000 * 250 or 140 contracts. b) The company should take a long position in (1.5 - 1.2) * 100,000,000 / 2,000 * 250 or 60 contracts.

Derivative users

are typically larger firms, and commodity based. The natural resources and manufactured goods industries. (based off survey)

trading floor is divided into

areas, each pit is for trading a specific category of contracts

margin call

bring back to initial margin

forward contracts is an agreement to

buy/sell an asset at a certain time in the future for a certain price. Traded on OTC

4 participants in options markets

buyer of calls sellers of calls buyers of puts sellers of puts -buyers have long positions, sellers are referred to having short positions (selling an option = writing the option)

closing a future position involves

entering into an opposite trade to the original one that opened the position

The expected return on the S&P 500 is 12% and the risk-free rate is 5%. What is the expected return on the investment with a beta of (a) 0.2, (b) 0.5, and (c) 1.4?

equation: rf + beta (Er - rf) a) or 6.4% b) or 8.5% c) or 14.8%

spot price is

for immediate delivery

2 main products trading on exchanges are

futures and options

Derivatives are versatile

instruments

Options contracts, provide

insurance and allows investors to protect themselves against adverse price movements in the future, while benefiting form favorable price movements.

larger firms are more exposed to what

interest rate risks firms dont like risk exposure

Majority of firms are affected by

interest rates and Commodity price risk (fluctuations) Interest rates movements affect a firm's cost of Capital and Commodity price affects a firm's revenue and expenses

most brokers pay investors interest on the balance in a margin account

most brokers pay investors interest on the balance in a margin account

OTC trades are

over a network of computers. Place order with a broker and it goes to the computer network directly

to enter a option contract a trader must

pay an up front price

Short futures

position allows you to sell the underlying asset

settlement price:

price before closing day or average of price before closing

The clearing house of the futures exchange will provide settlements and clearing service so long and short positions are matched. If default....

the clearing house completes process, they assume legal counterpart risk for the trade.

price in contract is known as

the exercise price or strike price

purchase selling price is the predetermined price which is....

the futures price or delivery price. Only payable when future contract matures

when the person with the short position is ready to sell

they file a notice of intention to deliver

price moves down from the previous day by an amount equal to the dialy price limit

this is a limit down and the opposite is a limit up

must be a member of a futures exchange in order to

trade on the floor. You can also lease a month seat on the floor and you can trade for yourself or others.

open-outery systems involve

traders physically meeting on the floor at the exchange

all paper gains and losses on futures positions must be

treated as if they were realized at the end of the year (40% short term, rest is long term gain/loss for tax purposes)

forward contracts are designed to neutralize risk by fixing the price that the hedger will pay or receive for the

underlying asset


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