ACCA P4 Advanced Financial Management - 2010 - Study text

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Chapter 14: Futures and hedging with futures

Hedging with bond futures and stock index futures

 Hedging with bond futures

 Hedging with stock index futures

9 Hedging with bond futures and stock index futures

9.1 Hedging with bond futures

Bond futures can be used to hedge against the risk of a change in long-term interest

rates (bond yields) and bond prices. For example, suppose that an investment

institution is holding $200 million of US Treasury bonds, and it wants to protect this

bond portfolio against any rise in bond yields and fall in bond market prices to the end

of December.

It can do this by selling December bond futures for US Treasuries. If the interest

yield goes up before the end of December:

 bond prices in the bond markets will fall

 however, the institution will make an offsetting gain on its position in bond

futures.

The net effect should be to protect the overall value of the institution’s investment

portfolio.

9.2 Hedging with stock index futures

Stock index futures can be used to hedge against the risk of a rise or fall in a stock

market index. Typically, an investment institution might hold a large portfolio of

equity investments that are closely represented by a particular stock market index.

The institution can use futures to hedge against the risk of a fall in the index over

the next few months. It can do this by selling stock index futures.

Example: perfect hedge and basis

An investment institution holds a portfolio of shares in UK companies, and the

portfolio is currently valued at £10 million. The shares in the portfolio are closely

represented by the composition of the FTSE100 stock market index.

The institution can hedge against the risk of a fall in the stock market using stock

index futures. For the FTSE100 futures contract, one point of the index has a tick

value of £10. The institution should sell futures to hedge its position, and the

number of contracts it should sell is:

valueTick price Futures

portfolio the of valueCurrent

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For example, if the futures price for the FTSE100 index is 6000, to hedge a portfolio

worth £15 million, the institution would sell £15 million/(6000 × £10) = 250 futures.

If the actual index fell by 1 point to 5999, the value of the portfolio would fall by

1/6,000 or £2,500. There would be an offsetting gain on the futures position of 250

contracts × 1 tick × £10 per tick = £2,500.

The position has been successfully hedged.

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Advanced Financial Management

CHAPTER

Options and hedging

with options

Contents

1 Features of options

2 Buying options and selling (writing) options

3 Exercising options

4 Factors influencing option values

5 Hedging with options

6 Currency options

7 Interest rate options

8 Caps, floors and collars

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Features of options

 Definition of an option

 Financial options, commodity options and real options

 Call options and put options

 Expiry date: American-style and European-style options

 OTC and exchange-traded options

1 Features of options

1.1 Definition of an option

An option is something that gives its holder the right, but not the obligation, to take

a particular course of action at sometime in the future. Typically, an option gives its

holder the right, but not the obligation, either to buy or to sell a quantity of a

particular item on or before a specified date in the future, at a price that is fixed in

the contract.

1.2 Financial options, commodity options and real options

There are different types of option.

 A financial option is a contract that gives its holder the right, but not the

obligation, either to buy or to sell a quantity of a financial item on or before a

specified date in the future, at a price that is fixed in the contract. There are

financial options in currencies, interest rates, share prices and stock index values.

For example, an option in shares of company Z might give its holder the right to

sell 1,000 shares in company Z on 31st March at a price of $10 per share.

 With a commodity option, the option holder has the right to buy or sell a

quantity of a specified commodity, such as a quantity of wheat, or a quantity of a

metal such as gold or copper.

Real options are somewhat different. Real options relate to the choices facing a

company when it is considering whether to invest in a new capital project. The

company has the following choices (which are not obligations):

 to make a further investment or additional investment if the project is a success

 to abandon the investment after it has been started, if it now appears that it will

not be successful

 to wait before investing, instead of investing immediately.

These types of option are called real options, which were described in an earlier

chapter.

Chapter 15: Options and hedging with options

1.3 Call options and put options

Financial options are either call options or put options.

 A call option gives its holder the right to purchase the underlying item in the

option agreement.

 A put option gives its holder the right to sell the underlying item in the option

agreement.

For example, a call option on 1,000 shares in company Z gives its holder the right to

buy 1,000 shares in company Z at the price agreed in the option contract, and a put

option on 1,000 shares in company Z would give its holder the right to sell 1,000

shares in company Z at the agreed price.

1.4 Expiry date: American-style and European-style options

An option agreement has an expiry date, after which the option lapses and the

agreement comes to an end.

 An American-style option can be exercised by its holder at any time on or before

the expiry date.

 A European-style option can be exercised only at the expiry date for the option

and not before.

The terms ‘American’ and ‘European’ do not refer to the countries where these

types of option are available. Both types of option agreement are made throughout

the world.

For example, if a company holds an American-style call option to buy US$500,000 in

exchange for euros at a rate of 1.2000 (US$/€1) with an expiry date of 20 September,

the company can exercise its right to buy the $500,000 at the agreed rate at any time

up to and including 20th September. However, if the option is not exercised by that

date, it will lapse (cease to exist).

1.5 OTC and exchange-traded options

Some financial options are arranged directly between buyer and seller. Directly-

negotiated options are called over-the-counter options or OTC options. Examples of

OTC options include borrowers’ and lenders’ options, caps, floors and collars.

Currency options might also be arranged in OTC agreements.

Some options are traded on an exchange. Traded share options and some currency

options are exchange-traded. In addition, there are options on futures contracts, and

all options on futures are traded on the futures exchange where the underlying

futures are traded.

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Buying options and selling (writing) options

 Exercise price or strike price

 Rights and obligations of buyer and seller

 Option premium = option price

 Options: a zero-sum game

2 Buying options and selling (writing) options

2.1 Exercise price or strike price

The exercise price for an option is the price at which the holder can:

 buy the underlying item, in the case of a call option, or

 sell the underlying item, in the case of a put option.

With OTC options, the exercise price is agreed between the option buyer and the

option seller. With exchange-traded options, options are available for buying or

selling at a limited range of fixed strike prices, and buyers and sellers agree on the

price at which they will make a transaction in the options at one of these prices.

For example, the following table shows exercise prices that might be available on

the CME exchange for US dollar/euro currency options on a day in August, and the

prices of the most recent transactions in those options.

CALLS PUTS

Expiry: Sep Dec Mar Sep Dec Mar

Strike price:

12200 0.34 2.03 3.22 1.62 3.15 3.91

12300 0.18 1.62 2.81 2.16 3.53 4.49

12400 0.09 1.33 2.44 3.06 4.20 5.12

12500 0.04 1.18 2.11 3.66 4.90 -

Notes

(a) A strike price of 12200 indicates an exchange rate of €1 = $1.2200.

(b) At this date, currency options were being traded at just four strike prices, for

expiry dates in September, December and March.

2.2 Rights and obligations of buyer and seller

Options are bought and sold. The seller of an OTC option is often called the option

writer. Selling an OTC option is often called ‘writing an option’. For exchange-

traded options, it is more usual to refer to ‘sellers’ of options, who have a short

position in the options.

 The option buyer or option holder has the right to exercise the option but is not

obliged or contractually required to do so.

 On the other hand, the seller or writer of the option is contractually obliged to

sell or buy the underlying item if the option is exercised by its holder.

Chapter 15: Options and hedging with options

2.3 Option premium = option price

Options are bought and sold at a price, which is called the option premium. This is

paid by the buyer of the option to the option seller/writer when the option

agreement is made. The option writer therefore receives the premium no matter

whether the option is subsequently exercised or not.

The table of currency options above shows current prices for US dollar/euro traded

currency options. For example, September call options in $/€ were being traded at a

price of 0.34. In this particular example, this premium price is stated in US cents per

euro. Each traded option on the CME exchange is for 125,000 euros in exchange for

US dollars, and the cost of one September call option was therefore $425 (125,000 ×

$0.0034).

Similarly, the premium for a December put option at a strike price of $1.25 was

$6,125 (125,000 × $0.0490).

2.4 Options: a zero-sum game

Options can be described as a zero-sum game between the option buyer and the

option seller. Any gain for the buyer is matched by an equal loss for the seller.

Similarly, any gain for the seller is matched by an equal loss for the buyer. The

combined sum of their profits and losses is always zero.

Example

A company buys a European-style call option on 1,000,000 euros at a strike price of

1.2500 (US$/€1). The option premium is 2.4 US cents per euro, therefore the cost of

the option is $24,000.

What would be the net gain or loss for the option buyer and the option writer if the

exchange rate at expiry is:

(a) $1.2350 = €1,

(b) $1.2670 = €1, and

Answer

(a) The option will not be exercised, because it is cheaper to buy the 1 million

euros at the spot market price of $1.2350. The option will lapse.

(b) The option will be exercised, because it is cheaper to buy euros at the strike

price of $1.2500 than the spot rate of $1.2670.

price of $1.2500 than the spot rate of $1.2930.

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Option buyer

(a) spot price

1.2350

(b) spot price

1.2670

1.2930

Spot price Not

1.2670

1.2930

Exercise price exercised

1.2500

Gain from exercising option (per

€

0.0170

0.0430

Total gain on option (€1,000,000) 0

17,000

43,000

Cost of option (24,000)

(24,000)

(Loss)/gain to the buyer (24,000)

(7,000)

19,000

The option writer would make a gain of $24,000 if the spot rate at expiry is $1.2350,

a net gain of $7,000 if the spot rate is 1.2670 and a net loss if the spot rate is 1.2930.

Chapter 15: Options and hedging with options

Exercising options

 In-the-money, out-of-the-money and at-the-money options

 Exercising call options

 Exercising put options

3 Exercising options

3.1 In-the-money, out-of-the-money and at-the-money options

Options are in-the-money, at-the-money or out-of-the-money.

 An option is in-the-money when its exercise price (strike price) is more

favourable to the option holder than the current market price of the underlying

item.

 An option is at-the-money when its exercise price (strike price) is exactly equal

to the current market price of the underlying item.

 An option is out-of-the-money when its exercise price (strike price) is less

favourable to the option holder than the current market price of the underlying

item.

When an option is first written, it might be in-the-money, at-the-money or out-of-

the-money.

 An in-the-money option is worth more than an out-of-the-money option, and so

it has a higher premium.

 An at-the-money option or an out-of-the-money option should still have some

value, because there is some possibility that the market price of the underlying

item will move in the option holder’s favour before the expiry date, and so there

is a possibility that the option will be in-the-money at expiry.

However, an option that is deeply out-of-the-money, with an exercise price that is

very much worse than the current market price of the underlying item (from the

option holder’s point of view) is most unlikely to be exercised, and so will have a

value of 0 or close to 0.

An option will only be exercised if it is in-the-money.

When an option is exercised, the value of the option is the difference between the

exercise price and the current market price of the underlying item.

3.2 Exercising call options

A call option will only be exercised if the market price of the underlying item is

higher than the exercise price for the option. For example, a European call option on

1,000 shares in company Z with a strike price of $10 per share will only be exercised

if the market price of the share is above $10 at expiry.

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3.3 Exercising put options

Similarly, a put option will only be exercised if the market price of the underlying

item is lower than the exercise price for the option. For example, a European put

option on 2,000 shares in company XY with a strike price of $8 per share will only be

exercised if the market price of the share is below $8 at expiry.

ACCA P4 Advanced Financial Management - 2010 - Study text - Emile Woolf Publishing

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