Chapter 11 (M13)

AN INTRODUCTION TO DERIVATIVE SECURITIES

Chapter 11 Questions

What are the basic features of forward contracts, futures contracts, and options contracts?

Why do derivative securities exist? How do they help meet investor needs and increase market efficiency?

What are the similarities and differences between forward contracts and futures contracts?

Chapter 11 Questions

What terminology do we use to describe option contracts?

What does a payoff diagram show?

What are the risks and potential returns from option positions such as buying and writing calls; buying and writing puts; owning long and short positions in spreads, straddles, strangles, or butterfly spreads?

Chapter 11 Questions

What are the relationships among the prices of puts, calls, and futures?

What are some uses of derivatives in investment analysis and portfolio management?

Derivative Instruments

Value is determined by, or derived from, the value of another instrument vehicle, called the underlying asset or securityForward contracts are agreements between two parties - the buyer agrees to purchase an asset, the seller agrees to sell the asset, at a specific date at a price agreed upon nowFutures contracts are similar, but are standardized and traded on an organized exchange

Derivative Instruments

Options offer the buyer the right, but not the obligation, to buy or sell and underlying asset at a fixed price up to or on a specific dateBuyer is long in the contractSeller or “writer” is short the contractThe price at which the transaction would we made is the exercise or strike priceThe profit or loss on an option position depends on the market price

Why Do Derivatives Exist?

Assets are traded in the cash or spot marketSometimes have one’s fortunes dependent on spot price movements leads to considerable riskVarious derivatives markets have evolved

that allow some investors to manage these risks, while also creating opportunities for speculators to invest in the same contracts

Potential Benefits of Derivatives

Risk shifting Especially shifting the risk of asset price changes

or interest rate changes to another party willing to bear that risk

Price formation Speculation opportunities when some investors

may feel assets are mis-priced

Investment cost reduction To hedge portfolio risks more efficiently and less

costly than would otherwise be possible

Forward Contracts

An agreement between two parties to exchange an asset at a specified price on a specified dateBuyer is long, seller is short; symmetric gains and losses as price changes, zero sum gameContracts are OTC, have negotiable terms, and are not liquidSubject to credit risk or default riskValue realized only at expirationPopular in currency exchange markets

Futures Contracts

Like forward contracts… Buyer is long and is obligated to buy Seller is short and is obligated to sell

Unlike forward contracts… Standardized – traded on exchange More liquidity - can “reverse” a position and offset

the future obligation, other party is the exchange Less credit risk - initial margin required Additional margin needs are determined through a

daily “marking to market” based on price changes

Futures Contracts

Chicago Board of Trade (CBOT) Grains, Treasury bond futures

Chicago Mercantile Exchange (CME) Foreign currencies, Stock Index futures, livestock

futures, Eurodollar futures

New York Mercantile Exchange (NYMEX) Crude oil, gasoline, heating oil futures

Development of new contracts Futures exchanges look to develop new contracts

that will generate significant trading volume

Futures Contracts

Futures Quotations One contract is for a fixed amount of the

underlying asset 5,000 bushels of corn (of a certain grade) $250 x Index for S&P 500 Index Futures (of a certain

maturity) Prices are given in terms of the underlying asset

Cents per bushel (grains) Value of the index

Value of one contract is price x contract amount Settle is the closing price from the previous day

Futures Contracts

Example: Suppose you bought (go long) the most recent (Sept.) S&P 500 contract at the settle price (see Exhibit 11.5).What was the original contract value?

Value = $250 x 1180.80 = $295,200What is your profit if you close your position (sell a contract) for 1250.00?

Value = $250 x 1250.00 = $312,500Profit = $312,500 - $295,200 = $17,300

Options

Option TerminologyOption to buy is a call optionOption to sell is a put optionOption premium – price paid for the optionExercise price or strike price – the price at which the asset can be bought or sold under the contract

Options

Option TerminologyExpiration date European: can be exercised only at expiration American: exercised any time before expiration

In-the-money: the option has intrinsic value, and would be exercised if it were expiringOut-of-the-money: the option has no intrinsic value, would not be exercised if expiring If not expiring, could still have value since it could

later become in-the-money

Options

Example: Suppose you own a call option with an exercise (strike) price of $30.If the stock price is $40 (in-the-money): Your option has an intrinsic value of $10 You have the right to buy at $30, and you can

exercise and then sell for $40.

If the stock price is $20 (out-of-the-money): Your option has no intrinsic value You would not exercise your right to buy

something for $30 that you can buy for $20!

Options

Example: Suppose you own a put option with an exercise (strike) price of $30.If the stock price is $20 (in-the-money): Your option has an intrinsic value of $10 You have the right to sell at $30, so you can buy

the stock at $20 and then exercise and sell for $30

If the stock price is $40 (out-of-the-money): Your option has no intrinsic value You would not exercise your right to sell

something for $30 that you can sell for $40!

Options

Chicago Board Options Exchange (CBOE) Centralized facility for trading standardized option

contracts Clearing Corporation is the opposite party to all

trades, allowing buyers and sellers to terminate positions prior to expiration with offsetting trades

Standardized expiration dates, exercise prices, and contract sizes

Secondary market with standardized contracts Offer options on almost 1,400 stocks and also

index options

Options

Stock Option Quotations One contract is for 100 shares of stock Quotations give:

Underlying stock and its current price Strike price Month of expiration Premiums per share for puts and calls Volume of contracts

Premiums are often small A small investment can be “leveraged” into high

profits (or losses)

Options

Example: Suppose that you buy a January $60 call option on Microsoft (see Exhibit 11.10).What is the cost of your contract?

Cost = $9 x 100 = $900Is your contract in-the-money?

Yes. The current stock price is $63.20, so the intrinsic value is $3.20 per share.

Options

Example (cont.):

What is your dollar profit (loss) if, at expiration, Microsoft is selling for $50?

Out-of-the-money, so Profit = ($900)

Is your percentage profit with options?

Return = (0-9)/9 = (100%)

What if you had invested in the stock?

Return = (50-63.20)/63.20 = (20.89%)

Options

Example (cont.):

What is your dollar profit (loss) if, at expiration, Microsoft is selling for $65?

Profit = 100(65-60) – 900 = ($400)

Is your percentage profit with options?

Return = (65-60-9)/9 = (44.44%)

What if you had invested in the stock?

Return = (65-63.20)/63.20 = 2.85%

Options

Example (cont.):

What is your dollar profit (loss) if, at expiration, Microsoft is selling for $85?

Profit = 100(85-60) – 900 = $1,600

Is your percentage profit with options?

Return = (85-60-9)/9 = 177.78%

What if you had invested in the stock?

Return = (85-63.20)/63.20 = 34.49%

Options

Payoff diagrams Show payoffs at expiration for different stock prices

(V) for a particular option contract with a strike price of X

For calls: if the V<X, the payoff is zero If V>X, the payoff is V-X Payoff = Max [0, V-X]

For puts: if the V>X, the payoff is zero If V<X, the payoff is X-V Payoff = Max [0, X-V]

Option Trading Strategies

There are a number of different option strategies:

Buying call options

Selling call options

Buying put options

Selling put options

Option spreads

Buying Call Options

Position taken in the expectation that the price will increase (long position)Profit for a purchasing a Call Option:

Per Share Profit =Max [0, V-X] – Call PremiumNote that profits on an option strategy include option payoffs and the premium paid for the optionThe following diagram shows different total dollar profits for buying a call option with a strike price of $70 and a premium of $6.13

Buying Call Options

40 50 60 70 80 90 100

1,000

500

0

1,500

2,000

2,500

3,000

(500)

(1,000)

Exercise Price = $70

Option Price = $6.13

Profit from Strategy

Stock Price at Expiration

Selling Call Options

Bet that the price will not increase greatly – collect premium income with no payoffCan be a far riskier strategy than buying the same optionsThe payoff for the buyer is the amount owed by the writer (no upper bound on V-X)Uncovered calls: writer does not own the stock (riskier position)Covered calls: writer owns the stock

Selling Call Options

40 50 60 70 80 90 100

(1,000)

(1,500)

(2,000)

(500)

0

500

1,000

(2,500)

(3,000)

Exercise Price = $70

Option Price = $6.13

Stock Price at Expiration

Profit from Uncovered Call Strategy

Buying Put Options

Position taken in the expectation that the price will decrease (short position)Profit for purchasing a Put Option:

Per Share Profit = Max [0, X-V] – Put PremiumProtective put: Buying a put while owning the stock (if the price declines, option gains offset portfolio losses)The following diagram shows different total dollar profits for buying a put option with a strike price of $70 and a premium of $2.25

Buying Put Options

40 50 60 70 80 90 100

1,000

500

0

1,500

2,000

2,500

3,000

(500)

(1,000)

Exercise Price = $70

Option Price = $2.25

Profit from Strategy

Stock Price at Expiration

Selling Put Options

Bet that the price will not decline greatly – collect premium income with no payoff

The payoff for the buyer is the amount owed by the writer (payoff loss limited to the strike price since the stock’s value cannot fall below zero)

Selling Put Options

40 50 60 70 80 90 100

(1,000)

(1,500)

(2,000)

(500)

0

500

1,000

(2,500)

(3,000)

Exercise Price = $70

Option Price = $2.25

Stock Price at Expiration

Profit from Strategy

Option Spreads

Many other option strategies can be crafted using combinations of option positions

Price spread (vertical spread) Buying and selling options on the same stock with

the same expiration, but with different strike prices

Time spread (horizontal or calendar spread) Buying and selling options on the same stock with

the same strike price, but with different expirations

Option Spreads

Bullish spreads Buy a higher priced option and sell a lower priced

option on the same stock

Bearish spreads Sell a higher priced option and buy a lower priced

option on the same stock

Straddle Combination of a purchasing (long) or selling (short)

a put and a call on the same expiration Betting on a large price movement (long straddle) or

little price movement (short straddle)

Option Spreads

Strangle Combination of a call and put with the same

expiration but different exercise prices (long or short)

Similar to straddle strategies

Butterfly spread Combination strategy with 4 options, similar to

straddles and strangles, but with less risk of large losses

The number of different strategies is potentially limitless

Put/Call Parity

Premiums for puts and calls are not completely independent otherwise arbitrage opportunities would exist

Two investments with equally risky payoffs should have similar costs

Parity relationships exist between options, also between options and futures, options and spot prices, and futures and spot prices