1 Today Options Risk management: Why, how, and what? Option payoffs Reading Brealey and Myers,...

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Today

Options

•Risk management: Why, how, and what?

• Option payoffs

Reading

•Brealey and Myers, Chapter 20, 21

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Types of questions

•Your company, based in the U.S., supplies machine tools to manufacturers in Germany and Brazil. Prices are quoted in each country’s currency, so fluctuations in the € / $ and R / $ exchange rate have a big impact on the firm’s revenues. How can the firm hedge these risks? Should it? •Your firm is thinking about issuing 10-year convertible bonds. In the past, the firm has issued straight debt with a yield-to-maturity of 8.2%. If the new bonds are convertible into 20 shares of stocks, per $1,000 face value, what interest rate will the firm have to pay on the bonds? Why? •You have the opportunity to purchase a mine that contains 1 million kgs of copper. Copper has a price of $2.2 / kg, mining costs are $2 / kg, and you have the option to delay extraction one year. How much is the mine worth?

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Exchange rates, 1995 – 2003

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Example

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$ exchange rate, 1980 – 2000

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Risk management

What is the goal?

How can firms create value through risk management?

•View 1: Hedging is irrelevant (M&M)

Purely financial transaction Diversified shareholders don’t care about firm-specific risks

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Risk management

What is the goal?

How can firms create value through risk management?

•View 2: Hedging creates value

Reduces probability of financial distress Improves performance evaluation and compensation Other benefits: reduce taxes, undiversified shareholders

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Why hedge?Three gold producers

•Homestake Mining Does not hedge because “shareholders will achieve maximum benefit from such a policy.”

•American Barrick Hedges aggressively to give the company “extraordinary financial stability… offering investors a predictable, rising earnings profile in the future.”

•Battle Mountain Gold Hedges up to 25% because “a recent study indicates that there may be a premium for hedging.”

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Derivative use

Evidence

•Random sample of 413 large firms

Average cashflow from operations = $735 million Average PP&E = $454 million Average net income = $318 million

•How much hedging?

57% of firms use derivatives in 1997

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Financial derivatives

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Financial derivatives

Assets

•Financial assets Stocks, bonds, stock indices, Tbonds (interest rates), foreign exchange

•Commodities Oil, gold, silver, corn, soybeans, OJ, pork bellies, coffee

•Other events and prices Electricity, weather, etc.

•Imbedded options Convertible bonds, warrants, real options, mortgages

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Futures contract

On Thursday, 5th May 2004, the NYM traded natural gas futures with delivery in August 2004 at a price of 4.900 $ / MMBtu.

•Buyer has a ‘long’ position Wins if prices go up

•Seller has a ‘short’ position Wins if prices go down

•The price of the contract is zero No cash changes hands today

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Futures contract: Payoff diagram

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Option Contract

• Contract between two parties

• Buy - Long

• Sell - Short

• For buyer: it is “right” rather than “obligation”

• Premium: the purchase price of the option

• Write a call option: option writer

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Option Contract

• Call option: the right to buy an asset at a specified exercise price (strike price) on or before a specified expiration date– February call option on Microsoft stock with exercise price

$80.• Put option: the right to sell an asset at a specified exercise

price on or before a specified expiration date– February put option on IBM stock with exercise price $90.

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Option Contract

• Open interest:

– The number of contracts currently outstanding

• Key Elements

– Underlying asset

– Exercise or Strike Price

– Premium or Price

– Maturity or Expiration

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Different Types of Options-by exercise timing

• American vs European Options– American: the option can be exercised at any

time on or before the expiration or maturity date

– European: the option can only be exercised on the expiration or maturity date

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Different Types of Options-by underlying asset

• Stock Options– Each option contract provides for the right to buy and

sell 100 shares of stock in the US

– Each option contract provides for the right to buy and sell 5,000 shares of stock in Taiwan

• Index Options: cash settlement• Futures Options:

– Foreign exchange futures options

• Foreign Currency Options• Interest Rate Options: Treasury bills (bond)

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Payoffs and Profits on Options at Expiration - Calls

• Example– You buy an European Call, February Microsoft

stock with x=$70 for $14– Price on 2/28:

1) $90 2) $80 3) $70 4) $60– What is your payoff?– What is your profit?

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St 90 80 70 60

exercise Yes Yes No No

payoff 20 10 0 0 profit 20-14= 6 10-14= -4 0-14= -14 0-14= -14

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Payoffs and Profits on Options at Expiration - Calls

Notation

Stock Spot Price = ST ， Exercise Price = X

Payoff to Call Holder

(ST - X) if ST >X

0 if ST < X

Profit to Call Holder

=Payoff - Purchase Price (premium)

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Payoffs and Profits on Options at Expiration - Calls

Payoff to Call Writer

- (ST - X) if ST >X

0 if ST < X

Profit to Call Writer=Payoff + Premium

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PayoffPayoff

Stock PriceStock Price

0

Call WriterCall Writer

Call HolderCall Holder

Payoff Profiles for CallsPayoff Profiles for Calls

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ProfitProfit

Stock PriceStock Price

0

Call WriterCall Writer

Call HolderCall Holder

Profit Profiles for CallsProfit Profiles for Calls

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Payoffs and Profits at Expiration - Puts

• Example– You buy an European Put, February IBM stock

with x=$90 for $15– Price on 2/28:

1) $60 2) $80 3) $90 4) $100– What is your payoff?– What is your profit?

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St 60 80 90 100

exercise Yes Yes No No

payoff 30 10 0 0

profit 30-15= 15 10-15= -5 0-15= -15 0-15= -15

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Payoffs and Profits at Expiration - PutsPayoffs to Put Holder

0 if ST > X

(X - ST) if ST < X

Profit to Put Holder

Payoff - Premium

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Payoffs and Profits at Expiration - PutsPayoffs to Put Writer

0 if ST > X

-(X - ST) if ST < X

Profits to Put Writer

Payoff + Premium

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Payoff Profiles for PutsPayoff Profiles for Puts

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Payoff

Stock Price

Put Writer

Put Holder

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Profit Profiles for PutsProfit Profiles for Puts

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Profits

Stock Price

Put Writer

Put Holder

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Market and Exercise Price Relationships

• In the Money - exercise of the option would be profitableCall: market price>exercise pricePut: exercise price>market price

• Out of the Money - exercise of the option would not be profitableCall: market price < exercise pricePut: exercise price < market price

• At the Money - exercise price and asset price are equal

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Option-like Securities

• Callable Bonds

Issuer hold a call option• Convertible Bonds

Bond holders long a call • Warrants

An option issued by a firm.

When exercised, number of shares outstanding will increase and there are cash inflows to the firm.

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WSJ option quotes

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Option payoffs (strike = $50)

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Options

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Returns, stock vs. option

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Option strategies

Financial engineering

Options can be mixed in various ways to create an unlimited number of payoff profiles.

Examples

•Buy a stock and a put •Buy a call with one strike price and sell a call with another •Buy a call and a put with the same strike price

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Option strategies: Stock + put

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Option strategies: Call1 – call2

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Option strategies: Call + Put

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Option Strategies

Straddle• When a stock will move a lot in price but are

uncertain about the direction of the move• Long straddle : Buy both a call and a put on a stock,

each with the same exercise price and the same expiration date

• Write straddle: Sell both a call and a put on a stock, each with the same exercise price and the same expiration date

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多頭跨式部位• 採取多頭跨式部位的原因在於未來標的物價格的波動太大，投資人無法判斷標的物價格的趨勢，因此採取多頭跨式部位，當標的物價格有劇烈波動時，將可獲得利潤。

損益

買進買權

買進賣權

ST

多頭跨式部位K

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空頭跨式部位• 空頭跨式部位則是投資人同時賣出到期日期和履約價格相同的買權與賣權所組成的。

損益

ST

賣出賣權

賣出買權

放空跨式部位K

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股價指數選擇權

股價指數選擇權（ Stock-Index Option ）之標的物為股價指數，不同於股票選擇權，履約時採現金交割的方式。

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Index-Options

台指選擇權 (TXO)Buy a callX=5700 ， C=400 點Multiplier( 契約乘數 =50 元 )到期 :TXO=6200權利金 :400 x $50=20,000Payoff:(6200-5700)x50=25,000 Profit ( 利得 ):$25,000-20,000=5,000

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Index-Options: Risk Management

Portfolio:P

• Vp=5 million, βp=1, when Index=250

• Buy 200 index put option (each put:100 multiplier)

X=235

IT=225 ， Vp=5*(225/250)=4.5 million

﹝100x(235-225) x ﹞ 200 =200,000=0.2 million

Total loss:5-(4.5+0.2)=0.3 million