Options (1)

Class 19 Financial Management, 15.414 MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 18

Today

Options

• Risk management: Why, how, and what?

• payoffs

Reading

• Brealey and Myers, Chapter 20, 21

• Sally Jameson

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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 these risks? Should it?

Your firm is thinking about issuing 10-year convertible bonds. In the past, the firm has issued straight with a -to-maturity of 8.2%. If the new bonds are convertible into 20 shares of , per $1,000 face value, what 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

4.0 1.6

3.5 1.4

3.0 1.2

2.5 1.0

2.0 0.8

1.5 0.6

1.0 0.4 Real / $ (left scale) 0.5 0.2 Euro / $ (right scale) 0.0 0.0 Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan-03

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Example

Caterpillar

Global leader, construction and mining equipment Sales in nearly 200 countries

In 1980s, dollar up, then down 50%

Year 1980 1984 1988 Sales $8,598 $6,576 $10,435 Net income 565 -428 616 Cap exp 749 234 793

$ millions

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$ exchange rate, 1980 – 2000

145 Trade-weighted exchange rate 130

115

100

85

70 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 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

View 2: Hedging creates value

Helps ensure that is available for positive NPV investments Reduces dependence on external finance 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

For users, if 3σ event, then cashflows up by $15 million and market value up by $31 million

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Financial derivatives

Options

Gives the holder the right to buy (call option) or sell () an asset at a specified price. Buyer has the choice Forwards and futures

A contract to exchange an asset in the future at a specified price and time. Obligation for both

Swaps

An agreement to exchange a series of cashflows at specified prices and times. Obligation for both

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Financial derivatives

Assets

Financial assets Stocks, bonds, 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, the NYM traded natural gas futures with delivery in August 2004 at a price of 4.900 $ / MMBtu.

Buyer has a ‘’ Wins if prices go up

Seller has a ‘’ 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

1.5 Long position (buy) Short position (sell) 1

0.5

Gas price, Aug04 0 4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8 -0.5

-1

-1.5

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Option contract

Thursday, the CBOE traded 4,258 call option contracts (100 shares each) on Cisco stock with a of $20.00 and an date in October. The option price is $0.30.

Buyer has the right to buy Cisco at $20 Option will be exercised if Cisco > $20

Seller is said to ‘write’ the option

American options can be exercised anytime on or before the maturity date.

European options can be exercised only on the maturity date.

Out of the money if the stock price is lower than the strike price. In the money if the stock price is greater than the strike price.

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WSJ option quotes

Call Put Option/Strike Exp Vol Last Vol Last Cisco 15 Jan 4128 3.60 25 0.70 17.83 17.50 Aug 5307 0.40 4410 0.15 17.83 20 Oct 4258 0.30 100 2.60

Stock price Call price Put price

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Call option: Payoff diagram

12 Buy a call 10 Strike price = $20

8 Payoff = max(0, S - X)

6

4 Option payoff Option payoff 2

Stock price 0 10 15 20 25 30 -2

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Option payoffs (strike = $50)

25 25

20 20 Buy a call Buy a put 15 15

10 10

5 5

0 0 30 40 50 60 70 30 40 50 60 70 -5 -5 Stock price Stock price

5 5 Stock price Stock price 0 0 30 40 50 60 70 30 40 50 60 70 -5 -5

-10 -10 Sell a call Sell a put -15 -15

-20 -20

-25 -25

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Options

Option payoffs

Asset price = S, strike price = X

Buyer of the option

S < X S > X Call 0 S – X Risky if used Put X – S 0 alone

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Returns, stock vs. option

150% Stock price = $50 100% Call option, strike = $50 with 1-year to expiration

50% Stock return

0% Stock in 1 year 30 34 38 42 46 50 54 58 62 66 70 -50% Option return Price ≈ $9 -100%

-150%

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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

70 25 65 20 60 Buy stock 55 15 Buy put 50 10 45 40 5 35 0 30 30 40 50 60 70 30 40 50 60 70 -5 Stock price Stock price

70 65 60 55 50 45 40 Stock + put 35 30 30 40 50 60 70 Stock price

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Option strategies: Call1 – call2

25 25 20 20 15 15 10 Buy call with 10 Write call with 5 X = 50 5 X = 60 0 0 30 40 50 60 70 -5 30 40 50 60 70 -5 -10 -10 -15 -15 -20 -20 Stock price Stock price

20

16

12 call1 – call2

8

4

0 30 40 50 60 70 Stock price

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Option strategies: Call + Put

25 25

20 20

15 Buy call with 15 Buy put with

10 X = 50 10 X = 50

5 5

0 0 30 40 50 60 70 30 40 50 60 70 -5 -5 Stock price Stock price

25

20 15 Call + put 10

5

0 30 40 50 60 70 -5 Stock price

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Option pricing

What is an option worth?

How can we estimate the expected cashflows? How risky is an option? What is the appropriate discount rate?

Two formulas to know

Put-call parity

Black-Scholes formula

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Put-call parity

Relation between put and call prices

P + S = C + PV(X)

S = stock price P = put price C = call price X = strike price PV(X) = present value of $X = X / (1+r)t r = riskfree rate

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Option strategies: Stock + put

70 25 65 20 60 55 Buy stock 15 50 Buy put 10 45 40 5 35 0 30 30 40 50 60 70 30 40 50 60 70 -5 Stock price Stock price

70 65 60 55 50 45 40 Stock + put 35 30 30 40 50 60 70 Stock price

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Option strategies: Tbill + call

70 25 65 20 60 Buy Tbill with 55 FV = 50 15 50 Buy call 10 45 40 5 35 0 30 30 40 50 60 70 30 40 50 60 70 -5 Stock price Stock price

70 65 60 55 50 45 40 Tbill + call 35 30 30 40 50 60 70 Stock price

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Example

On Thursday, call options on Cisco stock with an expiration date in October and a strike price of $20 sold for $0.30. The current price of Cisco is $17.83. How much should put options with the same strike price and expiration date sell for?

Put-call parity

P = C + PV(X) – S

C = $0.30, S = $17.83, X = $20.00

r = 1% annually → 0.15% over the life of the option

Put option = 0.30 + 20 / 1.0015 – 17.83 = $2.44

(WSJ price = $2.60)

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Option pricing

Factors affecting option prices

Option prices depend on S, X, T, σ2, r, D

Call option Put option Stock price (S) + – price (X) – + Time-to-maturity (T) + + Stock (σ) + + Interest rate (r) + – (D) – +

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