Investment Analysis and Portfolio Management

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

Options

Options • 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

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 bought • 3. The purchase (or exercise or strike) price • 4. 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 Bwill 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 £60 Profit of B is £6000 – £5000 – £300 = £700 Profit of A is £300 – £1000 = – £700 • Final price £40 Profit of B is – £300 Profit 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 • Asells 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 £20 Profit of B is £9000 – £6000 – £600 = £2400 Profit of A is £6000 + £600 – £9000 = – £2400 • Final price £40 Profit of B is – £600 Profit 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 expiration Consider a call option, exercise price £100 • Asset price below £100: option worthless • Asset 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, Sthe price of the underlying asset and E the exercise price

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

Valuation of Options • The profit, Pc, from holding the option is Pc = Vc – V0 = max{S–E, 0}- V0 = max{S –E - V0, -V0} • V0 is the price (premium) paid for the call option

Valuation of Options • Consider a put option, exercise price £100 • This 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

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

Valuation of Options • The profit from purchasing it is Pp = Vp - V0p = max{E - S, 0}- V0p = max{E – S - V0p, -V0p} • V0p is the purchase price of the put option

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 - V0c

Investment Analysis and Portfolio Management