investment analysis and portfolio management lecture 9 gareth myles

Investment Analysis and Portfolio Management

Lecture 9

Gareth Myles

Revision Lecture

The revision lecture is scheduled for 2nd May 2-4pm in Amory Moot Room

OptionsCall Expire at close Fri, Put Expire at close Fri,

Dec 15, 2006 Dec 15, 2006Strike Symbol Last Strike Symbol Last

15 GMLC.X 20.5 10 GMXB.X 0.0517.5 GMLT.X 18.1 12.5 GMXS.X 0.05

20 GMLD.X 11.6 15 GMXC.X 0.0522.5 GMLX.X 8.7 17.5 GMXT.X 0.08

25 GMLE.X 6.5 20 GMXD.X 0.0527.5 GMLY.X 4 22.5 GMXX.X 0.05

30 GMLF.X 1.9 25 GMXE.X 0.1532.5 GMLZ.X 0.55 27.5 GMXY.X 0.25

35 GMLG.X 0.14 30 GMXF.X 0.6537.5 GMLU.X 0.05 32.5 GMXZ.X 1.75

40 GMLH.X 0.05 35 GMXG.X 3.942.5 GMLV.X 0.04 37.5 GMXU.X 6.3

45 GMLI.X 0.05 40 GMXH.X 8.642.5 GMXV.X 11.2

An option is a contract that either gives: The right to buy an asset at a specific price within a

specific time period but no obligation to buy This is a call option

Or gives: The right to sell an asset at a specific price within a

specific time period but no obligation to sell This is a put option

Options

Call Options

A call option is the right to buy The contract specifies

1. The company whose shares are to be bought

2. The number of shares that can be bought3. The purchase (or exercise or strike) price4. The date when the right to buy expires

(the expiration date)

Call Options

European call: can only be exercised at the expiration date

American call: can be exercised at any date up to the expiration date

The premium is the price paid to buy the contract

Exercise of the option does not imply that the asset is actually traded

Because of transactions costs it is better for both parties to just transfer cash equal in value to what would happen if the asset were traded

Call Options

A call option is purchased in expectation that it may be exercised Exercise depends on the exercise price and the

price of the asset Will not exercise if the asset price is below the

exercise price A European call is exercised if asset price is

above exercise price at expiration date Purchase for less than its trading price

With an American call when to exercise is a choice

Call Options

Example A sells B the right to “buy 100 shares for £50 per share at any time in the next six months” If current price is £45 B must expect a price rise

If price rises above £50 B will exercise the option and obtain assets with a value in excess of £50 If the price rises to £60 B purchases assets worth

£6000 for £5000 If price falls below £50 B will not exercise the

option

Call Options

The return to A is the premium paid by B for the option If this is £3 per share B pays A £300 for the contract

Final price £60Profit of B is £6000 – £5000 – £300 = £700Profit of A is £300 – £1000 = – £700

Final price £40Profit of B is – £300Profit of A is £300

The loss of A (or profit for B) is potentially unlimited The loss of B (profit for A) is limited to the premium

Call Options

A profit is made on a call option if the underlying stock prices rises sufficiently above the exercise price to offset the premium

Example Call options on Boeing stock with a strike price

of $30.00 were trading at $5.20 on June 23, 2003 If a contract for 100 stock were purchased this

would cost $520 In order to make a profit form this, the price on the

exercise date must be above $35.20

Call Options

Call options with lower exercise prices are always preferable and trade at a higher price A lower exercise price raises the possibility of

earning a profit Profit is greater for any price of the underlying

Example On June 23, 2003 IBM stock were trading at

$83.18 Call options with expiry after the 18 July and a

strike price of $80 traded at $4.70 Options with a strike price of $85 traded at $1.75

Put Options

A put option is the right to sell The contract specifies

1. The company whose shares are to be sold 2. The number of shares that can be sold 3. The selling (or strike) price 4. The date when the right to sell expires (expiration

date) European put: can only be exercised at the

expiration date American put: can be exercised at any date up

to the expiration date

Put Options

An American put must be at least as valuable as the European given the flexibility in exercise

Example On July 11 2003 Walt Disney Co. stock were

trading at $20.56 Put options with an exercise price of $17.50 traded

with a premium of $0.10 These will only be exercised if the price of Walt

Disney Co. stock falls below $17.50

Put Options

A put option is profitable if the price of the underlying asset falls far enough It must fall enough to cover the premium

Example Put options on Intel stock with a strike price of

$25.00 were trading at $4.80 on June 23, 2003 A contract for 100 stock would cost $480 To make a profit from this option the price of the

underlying asset must be below $20.20

Put Options

Example A sells B the right to sell 300 shares for £30

per share at any time in the next six months A must believe that the price will not fall below £30 B believes it will

If the price falls below £30, B will exercise the option and obtain a payment in excess of the value of the assets

Put Options

If the price goes to £20 B will receive £9000 for assets worth £6000

If price stays above £30 B will not exercise the option

The return to A is the premium paid by B for the option If this is £2 per share B pays A £600 for the contract

Put Options

Final price £20Profit of B is £9000 – £6000 – £600 = £2400Profit of A is £6000 + £600 – £9000 = – £2400

Final price £40Profit of B is – £600Profit of A is £600

The loss to A (or profit to B) is limited to the exercise price

The loss of B (profit to A) is limited to the premium

Put Options

The higher is the strike price the more desirable is a put option

This is because a greater profit will be made upon exercise

Example On June 23, 2003 General Dynamics stock

were trading at $73.83 Put options with expiry after the 18 July and a strike

price of $70 traded at $1.05 Those with a strike price of $75 traded at $2.95

Trading Options

Options are traded on a range of exchanges Chicago Board Options Exchange, the Philadelphia

Stock Exchange, the American Stock Exchange and the Pacific Stock Exchange

Eurex in Germany and Switzerland and the London International Financial Futures and Options Exchange

Options contracts are for a fixed number of stock An options contract in the US is for 100 stock

Trading Options

Exercise prices are set at discrete intervals $2.50 interval for stock with low prices Up to $10 for stock with high prices

On introduction of an option two contracts are written One with an exercise prices above the stock price One with an exercise price below the stock price If the stock price goes outside this range new

contracts can be introduced As each contract reaches its date of expiry

new contracts are introduced for trade

Trading Options

Quotes of trading prices for options contracts can be found in The Wall Street Journal and the Financial Times Quote the call and put contracts with exercise

prices just above and just below the closing stock price of the previous day

Price quoted is for a single share More detailed information can also be found

on Yahoo Lists the prices for a range of exercise values, the

volume of trade, the number of open contracts

Trading Options

Market makers can be found on each exchange to ensure that there is a market for the options

The risk inherent in trading options requires that margin payments must be must in order to trade

Valuation of Options

The value of an option is related to the value of the underlying security

At expirationConsider a call option, exercise price £100Asset price below £100: option worthlessAsset price above £100: can profit from

owning option, so valuable


The value (which is equal to the "fair" price) at expiration is given by

Vc = max{S – E, 0} Vc is the value of the

call option, S the price of the underlying asset and E the exercise price

Vc

SE


Example On June 26 2003 GlaxoSmithKline stock was trading at $41

The exercise prices for the option contracts directly above and below this price were $40 and $42.50

The table displays the value at expiry for these contracts for a selection of prices of GlaxoSmithKline stock at the expiration date

S 37.50 40 41 42.50 45 47.50

max{S-40,0} 0 0 1 2.50 5 7.50

max{S-42.50,0} 0 0 0 0 2.50 5


The profit, c, from holding the option is

c = Vc – V0

= max{S – E, 0}- V0

= max{S – E - V0, -V0}

V0 is the price (premium) paid for the call option

c

SEcV0


Consider a put option, exercise price £100This is worthless if the price of the asset is

greater than £100 It is valuable if the price of the asset is less

than £100


The value or fair price at expiration is given

Vp = max{E – S, 0} The value is

whichever is larger of 0 and E – S

Vp

SE

E


Shares in Fox Entertainment Group Inc. traded at $29.72 on 7 July 2003

The expiry value of put options with exercise prices of $27.50 and $30.00 are given in the table for a range of prices

pIV

S 20 22.50 25 27.50 30 32.50

max{27.50-S,0} 7.50 5 2.50 0 0 0

max{30-S,0} 10 7.50 5 2.50 0 0


The profit from purchasing it is

p = Vp - V0p

= max{E - S, 0}- V0p

= max{E – S - V0p, -V0

p}

V0p is the purchase price

of the put option

p

SE pV0

pVE 0

Combining Puts and Calls

Combinations of puts and calls engineer different structures of payoffs

The straddle involves buying a put and a call on the same stock

If these have the same exercise price, the profit is

= max{E - S, 0}

+ max{S - E, 0} - V0p - V0

c

P

S

Ecp VV 00