Tutorial+1+(Chapters+1,2,3)

Tutorial 1

Chapters 1,2 and 3

Hull 7th. Edition

B. B. ChakrabartiProfessor of Finance

B. B. Chakrabarti: [email protected] 2

Multiple Choice Question - 1

• What is the profit from the following portfolio: a long forward contract on an asset and a long European put option on the asset with the same maturity as the forward contract and a strike price that is equal to the forward price of the asset at the time the portfolio is set up.

A. Max (F0 – ST, 0)

B. Max (0, ST – F0)

C. ST – F0

D. F0 – ST


Multiple Choice Question – 1 (Ans.)

• Answer: B. Max (0, ST – F0)

• Explanation:

• The terminal value of long forward contract = ST – F0

• Where,

ST = price of asset at maturity

F0 = forward price of asset when portfolio was set up

• The terminal value of put potion = Max (F0 – ST, 0)

• The terminal value of portfolio therefore = ST – F0 + Max (F0 – ST, 0) = Max (0, ST – F0)

• This is the same as the terminal value of a European call option with the same maturity as forward contract and an exercise price equal to F0.



• Hedgers in the futures market usually:

A. Only trade in futures market

B. Only trade in spot market

C. Trade in neither spot nor futures markets

D. Trade in both spot and futures markets



Answer: D. Trade in both spot and futures markets



• Which of the following statements about options and their underlying assets is FALSE?A. The value of an option, in comparison to its

underlying asset, has the potential of creating an arbitrage opportunity

B. The owner of the option is legally required to engage in a transaction involving the asset

C. The holder of a long position on an option is the only party with the right to initiate a transaction involving the asset

D. The seller of the option is legally required to engage in a transaction involving the asset



• Answer: B. The owner of the option is legally required to engage in a transaction involving the asset

• Explanation:

• The option writer is required to honor the terms of the contract if called upon by the buyer to do so. The option buyer has the discretion to exercise the contract or not.



• Which of the following statements about forward and futures contracts is FALSE?A. A futures contract requires the contract purchaser to

receive delivery of the good at a specified time.

B. A predetermined price is to be paid for a good is a necessary requirement in the terms of a forward contract.

C. The future value of a financial derivative depends on the value of its underlying asset.

D. The primary difference between forwards and futures is that only futures are considered financial derivatives.



• Answer: D. The primary difference between forwards and futures is that only futures are considered financial derivatives.

• Explanation:• Forwards and futures are similar and serve

similar needs. Both are considered as types of financial derivatives in that payoffs depend on another financial instrument or asset. The primary difference is that forwards are designed for the needs of the particular parties entering the contract, where futures are standardized contracts.



• Any rational price for a financial instrument should:

A. Be low enough for most investors to afford.

B. Be always increasing.

C. Provide no opportunity for arbitrage.

D. Provide an opportunity for investors to make a profit.



• Answer: C. Provide no opportunity for arbitrage.


Multiple Choice Question – 6

• Which of the following requires the purchase of the underlying asset at a specified price?

A. Purchasing a call option.

B. Writing a put option.

C. Writing a call option.

D. Purchasing a put option.



• Answer: B. Writing a put option.

• Explanation:

• A put is an option to sell a specified asset at a specified price at the put buyer’s discretion. The writer of a put agrees to purchase the asset if the buyer exercises the option. A call gives the buyer an option to purchase a specified asset and the call writer an obligation to sell the asset if the option is exercised.

Problem No. 1.5 (Hull – 7th Ed.)

An investor enters into a short forward contract to sell 100,000 British pounds for US dollars at an exchange rate of 1.9000 US dollars per pound. How much does the investor gain or loose if the exchange rate at the end of the contract is (a) 1.8900 and (b) 1.9200?

Problem No. 1.5 (Ans.)

a. Gain = $1,000

b. Loss = $2,000

Problem No. 1.5 (Explanation)

Part a:

• The trader sells 100,000 British pounds for 1.9000 US dollar per pound when the exchange rate is 1.8900 US dollar per pound.

• The gain is 100,000*(1.9000 – 1.8900) = $1,000

Part b:

• The trader sells 100,000 British pounds for 1.9000 US dollar per pound when the exchange rate is 1.9200 US dollar per pound.

• The loss is 100,000*(1.9200 – 1.9000) = $2,000


You would like to speculate on a rise in the price of a certain stock. The current stock price is $29, and a three-month call with a strike of $30 costs $2.90. You have $5,800 to invest. Identify two alternative strategies, one involving an investment in the stock and the other involving investment in the option. What are the potential gains and losses from each?


• Strategy 1: Buy 200 shares

• Strategy 2: Buy 2000 options

• If share price does well strategy 2 will give better gain

• If share price does badly strategy 2 will give greater loss


• Example: Suppose share price goes up to $40

– Gain from strategy 1 = 200*($40-$29) = $2,200

– Gain from strategy 2 = [2000*($40 - $30)] - $5800 = $14,200

• Example: Suppose share price goes down to $25

– Loss from strategy 1 = 200*($29 - $25) = $800

– Loss from strategy 2 = Loss of entire investment = $5800


• Suppose that sterling-USD spot and forward exchange rates are as follows:

Spot 2.0080

90-day forward 2.0056

180-day forward 2.0018

• What opportunities are open to an arbitrageur in the following situations?a. A 180-day European call option to buy £1 for $1.97

costs 2 cents.

b. A 90-day European put option to sell £1 for $2.04 costs 2 cents.

Problem No. 1.25 (Ans. – Part A)

• The trader buys a 180-day call option and takes a short position in a 180-day forward contract

• If ST is the terminal spot price,• The profit from the call option is

= max (ST – 1.97,0) – 0.02• The profit from the short forward contract

= 2.0018 – ST

• The profit from the strategy is therefore= max (ST – 1.97,0) – 0.02 +2.0018 – ST

= max (ST – 1.97,0) +1.9818 – ST

• This is1.9818 – ST when ST < 1.970.0118 when ST > 1.97

• Hence profit is always positive

The time value for money has been ignored in these calculations.

Problem No. 1.25 (Ans. – Part B)

• The trader buys a 90-day put option and takes a long position in a 90-day forward contract

• If ST is the terminal spot price,

• The profit from the put option is

= max (2.04 – ST,0) – 0.02

• The profit from the long forward contract

= ST – 2.0056

• The profit from the strategy is therefore

= max (2.04 – S ,0) – 0.02 + S – 2.0056


The price of gold is currently $600 per ounce. The forward price for delivery in one year is $800. An arbitrageur can borrow money at 10% per annum. What should the arbitrageur do? Assume that the cost of storing gold is zero and that gold provides no income.


• The arbitrageur could – Borrow money to buy 100 ounces of gold today and– Short futures contracts on 100 ounces of gold for delivery in one

year

• This means gold– Purchased for $600 per ounce– Sold for $800 per ounce

• The return = 33.3% per annum >> 10% cost of borrowing fund

• The arbitrageur should do this as much he can.• Unfortunately this type of opportunity rarely arise in

practice.– Even if this arises this does not sustain.


A bond issued by Standard Oil worked as follows. The holder received no interest. At the bond’s maturity the company promised to pay $1,000 plus an additional amount based on the price of oil at that time. The additional amount was equal to the product of 170 and the excess (if any) of the price of a barrel of oil at maturity over $25. the maximum additional amount paid was $2,550 (which corresponds to a price $40 a barrel). Show that the bond is a combination of regular bond, a long position in call options on oil with a strike price of $25 , and a short position in call options on oil with a strike price of $40.


• Suppose ST is the price of oil at the bond’s maturity

• In addition to $1,000 the standard oil bond pays:

ST < $25 : 0

$40 > ST > $25 : 170(ST – 25)

ST > $40 : 2,550

• This is the payoff from 170 call options on oil with a strike price of 25 less the payoff from 170 call options on oil with a strike price of 40

• The bond is a combination of regular bond, a long position in 170 call options on oil with a strike price of $25 , and a short position in 170 call options on oil with a strike price of $40



If the balance in a trader’s account falls below the maintenance margin level, the trader will have to deposit additional funds into the account. The additional funds required is called the:A. Initial margin.

B. Margin call.

C. Marking to market.

D. Variation margin.



• Answer: D. Variation margin.



Which of the following statements regarding the relationship between the clearinghouse and the futures exchange is CORRECT? The clearinghouse:

A. Must be a separate corporation.

B. Can be part of the futures exchange or a separate corporation.

C. None of these choices is correct.

D. Must be part of the futures exchange.



• Answer: B. Can be part of the futures exchange or a separate corporation.



If only one transaction occurs today for both a buyer and a seller for a given futures contract, there MUST be:A. One open interest for that futures contract

today.

B. No trading volume today for that futures contract.

C. One contract of trading volume for that contract today.

D. No open interest for that contract today.



• Answer: C. One contract of trading volume for that contract today.



If both the buyer and the seller of a futures contract are opening their position by trading a contract, the:

A. Open interest will decrease by one.

B. Open interest will increase by one.

C. Volume will not be changed.

D. Volume will decrease by one.



• Answer: B. Open interest will increase by one.



All of the following are methods to close out a futures position EXCEPT:

A. Delivery of the underlying commodity.

B. Through an exchange for physicals with another trader.

C. Engaging in an offsetting trade in the futures market.

D. Allowing the contract to expire without taking action.



• Answer: D. Allowing the contract to expire without taking action.

• Explanation:

• A futures contract cannot expire without any action being taken. If the contract has not been closed out through an offsetting trade, then one party must deliver the underlying commodity and the other party must purchase the commodity.



Which type of futures contract does NOT allow for the underlying goods to be delivered?

A. Interest rate.

B. Foreign currency.

C. Index.

D. Agricultural



• Answer: C. Index.• Explanation:• The nature of an index futures realistically

prohibits settlement in the underlying commodity. For example, the Standard and Poor’s 500 stock index would require settlement in 500 different common stocks, in the exact proportion of the total value as exists in the index at expiration of the futures.

• Agriculture, interest rate, and currency futures all involve deliverable commodities.



A trader buys two 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.

a. What price change would lead to a margin call?

b. Under what circumstances could $2,000 be withdrawn from the margin account?



a. If futures price of frozen orange juice falls to 150 cents per lb

b. If futures price of frozen orange juice rises to 166.67 cents per lb



• For margin call reduction required in margin account = $6000 - $4,500 = $1,500 per contract = 10 cents per pound

• So future price should be reduced by 10 cents per pound

• $2,000 can be withdrawn if each contract rises by $1,000 = rise of $1000/15000 per pound = rise of 6.67 cents



At the end of one day a clearinghouse 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 clearinghouse?



The member has to add to its margin account = $36,000



• The clearinghouse 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 from existing contracts

• There is also a loss of ($51,000 - $50,200)*20 = $16,000 from new contracts

• The member must therefore add = 40,000 –20,000 + 16,000 = $36,000


On July 1, 2009, a Japanese company enters into a forward contract to buy $1 million on January 1, 2010. On September 1, 2009, it enters into a forward contract to sell $1 million on January 1, 2010. Describe the profit or loss the company will make in yen as a function of the forward exchange rates on July 1, 2009 and September 1, 2009.


• The total payoff = (F2 – F1), where,

• F1 = forward exchange rate for the contract ended July 1, 2009

• F2 = forward exchange rate for the contract ended September 1, 2009


• Suppose ST is the spot rate on January 1, 2010

• The payoff from 1st contract = (ST – F1) million yen

• The payoff from 2nd contract = (F2 – ST) million yen

• Hence, total payoff = (F2 – F1) million yen



Suppose that on October 24, 2009, a company sells one April 2010 live-cattle futures contract. It closes out its position on January 21, 2010. The futures price (per pound) is 91.20 cents when it enters into the contract, 88.30 cents when it closes out its position, and 88.80 cents at the end of December 2009. One contract is for the delivery of 40,000 pounds of cattle. What is the total profit?



Total profit = $1,160



Total profit

= total no. of cattle/contract * (Futures price when entered – futures price when closed)

= 40000*(0.9120 – 0.8830)

= $1,160



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?


Problem No. 2.28 (Ans.)Payoff from

Long Forward

Price of Underlyingat Maturity, ST

K

Payoff fromLong Put

ST

K

- P

The payoff from a long position in a forward contract on one unit of an asset = ST - K

The payoff from a long position in a European put option = Max (K – ST, 0) - P



Payoff fromLong Call

STK- C

Combining the two positions, we gets a long call.

The payoff from a long position in a European call option

= Max (ST – K, 0) - C

ST

K



Is the following statement TRUE or FALSE?

A perfect hedge always succeeds in locking in the current spot price of an asset for a future transaction.



• Answer: FALSE

• Explanation:

• Consider for example the use of 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




If the minimum variance hedge ratio is calculated as 1.0, the hedge must be perfect.



• Answer: FALSE

• Explanation:

• The minimum variance hedge ratio is

• ρ(σS/σF)

• It is 1.0 when ρ = 0.5 and σS= 2σF

• Since ρ < 1.0, the hedge is not perfect




If there is no basis risk, the minimum variance hedge ratio is always 1.0.



• Answer: TRUE

• Explanation:

• If the hedge ratio is 1.0 the hedger locks in a price of F1 + b2.

• Since both F1 and b2 are known , this has a variance of zero and must be the best hedge



If an oil wholesaler expects to buy some gasoline for his customers in the future and wants to hedge his risk, he needs to:

A. Sell gasoline now.

B. Sell crude oil futures contract.

C. Do nothing.

D. Buy crude oil futures contract.



• Answer: D. Buy crude oil futures contract.



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?



Optimal hedge ratio = 0.642



• All standard deviations are on quarterly basis

• Optimal hedge ratio in 3-month contract

= 0.8*(0.65/0.81) = 0.642

• Meaning:

– The size of the futures position should be 64.2% of the size of the company’s exposure in a 3-month hedge.



A company has a $20 million portfolio with a beta of 1.2. It would like to use futures contracts on the S&P 500 to hedge its risk. The index is currently standing at 1080, and each contract is for delivery of $250 times the index.

a. What is the hedge that minimizes risk?

b. What should the company do if it wants to reduce the beta of the portfolio to 0.6?



a. 89 contracts should be shorted.

b. A short position in 44 contracts is required.



shorted be should contracts 44

position thisof half

0.6, to1 .2 from beta reduce To b.

shorted. be should contracts 89

number, wholenearest the toRounding

shorted be should contracts of no. The a.

9.882501080

000,000,202.1



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 26 contracts is required.



26500,1*50

30*000,50*3.1

shorted be should that contracts of no. The



• The following table gives data on monthly changes in the spot price and the futures price for a certain commodity. Use the data to calculate a minimum variance hedge ratio.

Spot Price Change +0.50 +0.61 -0.22 -0.35 +0.79

Futures Price Change +0.56 +0.63 -0.12 -0.44 +0.60

Spot Price Change +0.04 +0.15 +0.70 -0.51 -0.41

Futures Price Change -0.06 +0.01 +0.80 -0.56 -0.46



• Minimum variance hedge ratio = 0.946



0.946 0.51 1 6

0.49330.981 ratio hedge v ariance minimum The

0.981

1 .30) - 2 .3594(1 00.96) - 2 .447 4(1 0

1 .300.96 - 2 .3521 0 is of estimate An

0.493391 0

1 .30

9

2.3594 is of estimate An

0.51 1 691 0

0.96

9

2.447 4 is of estimate An

2.352 yx 2.3594; y

2 .447 4; x 1 .30; y X Then,

lyrespectiv e price spot and price futures thein

changes theon nsobserv atio th-i thebe y and xDenote

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ii

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;96.0


A fund manager has a portfolio worth $50 million with a beta of 0.87. The manager is concerned about the performance of the market over the next two months and plans to use three-month futures contracts on the $&P 500 to hedge the risk. The current level of the index is 1250, one contract is on 250 times the index, the risk-free rate is 6% per annum, and the dividend yield on the index is 3% per annum. The current 3-month futures price is 1259.

What position should the fund manager take to eliminate all exposure to the market over the next two months?


The no. of contracts to be shorted

= 139


shorted. be should contracts 139

number, olenearest wh the toRounding

139.2 2501250

50,000,0000.87

short shouldmanager fund thecontracts of no. The

Tutorial+1+(Chapters+1,2,3)

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multiple choice

hull 7th ed

forward exchange

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long forward

suppose share

terminal spot

financial