investment analysis and portfolio management
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Investment Analysis and Portfolio Management. Lecture 9 Gareth Myles. Revision Lecture. The revision lecture is scheduled for 2 nd May 2-4pm in Amory Moot Room. Options. Options. An option is a contract that either gives: - PowerPoint PPT PresentationTRANSCRIPT
Investment Analysis and Portfolio Management
Lecture 9Gareth 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
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
Valuation of Options
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
Valuation of Options 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
Valuation of Options
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
Valuation of Options
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
Valuation of Options
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
Valuation of Options
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
Valuation of Options
The profit from purchasing it is
p = Vp - V0p
= max{E - S, 0}- V0p
= max{E – S - V0p, -V0
p} V0
p 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} - V0
p - V0c
P
SE
cp VV 00