Futures and Options Econ71a: Spring 2007 Mayo, chapters Section 4.6.1, 4.6.2

Goals Definitions Futures Options –Call option –Put option Option strategies

Derivatives: Definition Derivative: Any security whose payoff depends on any other security

Types Futures Options Swaps SPDR (S+P 500 Depository Receipts) –GM page 565 WEBS (World Equity Benchmark Shares) –GM page 510

Goals Definitions Futures Options –Call option –Put option Option strategies

Futures Contract allowing delivery at a specified future data (delivery date) at a certain price Price is decided on today Used for: –Commodities Wheat, Soy, Oil –Financial Treasury Bills S+P 500 Foreign Exchange

Mechanics Buy or sell contracts for a specified delivery date Price is agreed on today for payment at the delivery date Essentially, no money changes hands today Margin (often 10%) is paid today to guarantee parties will hold to contract

Mechanics (more) Contracts: –Traded in organized exchanges Most in Chicago –Uniform time periods Contracts ending in March, June, Sept, December

Usage: Insurance vs. Speculation Insurance (Hedging) –Farmer has 100 bushels of soy that will be harvested in Sept. –What should he do? Wait until Sept. and sell on the spot market Sell futures contracts today (short position) –In the first case he is open to risk in the price movement –In the second, he has no risk since the futures contract sets price today

Speculation Oil market: –You think that oil prices will go up in the future –How can you try to “bet” on this idea? Buy (go long) oil futures for some month in the future You have no intention of buying oil You hope that the spot price will rise and, –Buy with your (now lower) futures price –Turn around and sell for the (now higher) spot price

Winning and Losing with Speculation Winning –Oil price goes up Since the margins are low, you can make many more times the money you actually put in when you purchased the future Losing –Oil price goes down Can end up in big trouble You must purchase oil for what your contract price says, and sell on the spot market You can now lose a lot of money this way

Example of Losing Money in a Futures Contract It is April, oil sells for $50 a barrel The June futures contract sells at $48 Buy (go long) the June futures for 1 barrel –Pay margin amount now (10% = $4.80) June arrives and the price of oil falls to $30 You have to buy oil at the futures price of $48, and then sell for $30, losing $18 You get your margin back, so you end up with a net value of –4.8– = -18 Nothing (except the margin) to stop you from taking big positions and losing big money

Settlement Actual –Take delivery of the actual stuff Pork bellies in your driveway Cash –Cash value of the good is transferred to your account –More common for financial futures –Example S+P futures

Goals Definitions Futures Options –Call option –Put option Option strategies

Options Two types –Call: Option to buy –Put: Option to sell Parts: –Option price –Strike price –Expiration

Call Option Option to purchase asset at the strike price Horizon:(two types) –American: Anytime between now and the expiration date –European: On the expiration date only Strike price: Price at which the security can be purchased

Example: Buying a call option on Amazon Amazon share price = $100 Purchase American call option –Option price = $5 –Strike price = $120 –Expiration = 2 months from now Case A: price goes to $150 –Exercise option Buy at $120, sell at $150 Total = = +$25 Case B: price goes to $50 Don’t exercise option Total = -5 (lose entire investment)

Example: Writing (selling) a call option on Amazon Amazon share price = $100 Write American call option –Option price = $5 –Strike price = $120 –Expiration = 2 months from now Case A: price goes to $150 –Purchaser exercises option Buy at $150, sell at $120 Total = = -25 Case B: price goes to $50 Purchaser doesn’t exercise option Total = +5

Options and Insurance The writer is kind of selling insurance to the buyer As long as the price doesn’t go up by too much ($20) the writer gets to pocket the $5 Like an insurance premium Danger: If price rises by large amount, option writer can lose lots of money

How do you lose big money with options? Write (sell) a naked call on Amazon.com (p = 100), strike price = 150 –Sell for $5 You feel very happy (+5) Then Amazon goes to $250 The other side of your option trade exercises the option You must buy Amazon at $250, and sell it for $150

Option Terms In-the-money Stock price > call option strike price At-the-money Stock price = call option strike price Out-of-the-money Stock price < call option strike price

Contingency Graph Plot of net $ gain as a function of stock price Strike price = $100 Option price = $4 Net Gain Stock Price

Option Pricing Is it as easy as (Price – strike price) when strike < stock price 0 if strike is > stock price Why does this get more complicated? Have to consider today plus all days to the expiration date Even though the price is in the zero value range today (out-of-the-money, it might move into the positive value range tomorrow

General Properties of an option price Option value will be higher: –When the expiration date is farther in the future –When the stock price moves around more (This is known as higher volatility)

Option Pricing There are different formulas that try to take account of all this stuff Black/Scholes is the most famous of these Techniques used –Arbitrage –Stochastic calculus

Goals Definitions Futures Options –Call option –Put option Option strategies Real options

Put Option Same as Call –Price –Strike price –Expiration Difference: Option to Sell

Example: Put Value Option price = $4 Strike price = $100 Net Gain Stock Price

Goals Definitions Futures Options –Call option –Put option Option strategies

Options+Stocks Holding option alone is known as holding a “naked option” Holding option with the stock is known as a “covered option”

Example 1: Insuring gains by buying a put option Purchasing a put option on stock you already own sets a floor on what you can sell Buy stock at 75, price rises to 100 Lock in gains, buy put at strike = 100 Gains will be at least Cost = price of the put option

Example 1: Buy Stock + Put Strike price = $100 How much would your portfolio (option + stock) be worth for different prices? Total Value Stock Price

Example 2: Writing a covered call option Own stock Write a covered call option, strike = 100, sell for $5 Price goes below 100, nothing happens Price goes above 100, option may get exercised Puts a ceiling on your gains

Writing a Covered Call Option Value of stock + written (sold) call Stock Price Total Value 100 If the option is exercised, Then stock must be sold for $100

Why do this? Trading “upside potential” for $5

Example 3: Option Straddle Purchase a put and call at the same strike price Strategy makes money when stock price moves a lot (volatility is high)

Straddle Example Current stock price = 100 Purchase at-the-money call (strike = 100) for $2 Purchase at-the-money put (strike = 100) for $3 What is the total value of your option portfolio for different stock prices?

Straddle Performance Lose money when no change in price Price goes up: Call makes money Price goes down: Put makes money Strategy makes money when price moves a lot (depends on option prices)

Straddle Contingency Graph Plot of net $ gain as a function of stock price Strike price = $100 Option prices: call = $2, put = $3 Net Gain Stock Price

Other Combinations Many other combinations are possible As with futures, you can use options to reduce risk or increase risk if you want

Option + Future Summary Both can be used to either reduce, or increase risk Have insurance like characteristics Derivatives as fire

Goals Definitions Futures Options –Call option –Put option Option strategies