Options (1)

Class 19Financial Management, 15.414

MIT SLOAN SCHOOL OF MANAGEMENT

15.414 Class 18

Today

Options

• Risk management: Why, how, and what?

• Option payoffs

Reading

• Brealey and Myers, Chapter 20, 21

• Sally Jameson

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MIT SLOAN SCHOOL OF MANAGEMENT

15.414 Class 18

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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MIT SLOAN SCHOOL OF MANAGEMENT

15.414 Class 18

Exchange rates, 1995 – 2003

4.0

Real / $ (left scale) Euro / $ (right scale)

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

0.5 0.2

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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MIT SLOAN SCHOOL OF MANAGEMENT

15.414 Class 18

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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MIT SLOAN SCHOOL OF MANAGEMENT

15.414 Class 18

$ exchange rate, 1980 – 2000

145

130

115

100

85

70 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000

Trade-weighted exchange rate

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MIT SLOAN SCHOOL OF MANAGEMENT

15.414 Class 18

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 cash 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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MIT SLOAN SCHOOL OF MANAGEMENT

15.414 Class 18

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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MIT SLOAN SCHOOL OF MANAGEMENT

15.414 Class 18

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

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MIT SLOAN SCHOOL OF MANAGEMENT

15.414 Class 18

Financial derivatives

Options

Gives the holder the right to buy (call option) or sell (put option) an asset at a specified price.

Buyer has the choice

Forwards and futures

and time. Obligation for both

A contract to exchange an asset in the future at a specified price

Swaps

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

Obligation for both

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MIT SLOAN SCHOOL OF MANAGEMENT

15.414 Class 18

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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MIT SLOAN SCHOOL OF MANAGEMENT

15.414 Class 18

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 ‘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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MIT SLOAN SCHOOL OF MANAGEMENT

15.414 Class 18

Futures contract: Payoff diagram

1.5

1

0.5

0

-0.5

-1

-1.5

Long position (buy) Short position (sell)

4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8

Gas price, Aug04

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MIT SLOAN SCHOOL OF MANAGEMENT

15.414 Class 18

Option contract

Thursday, the CBOE traded 4,258 call option contracts (100 shares each) on Cisco stock with a strike price of $20.00 and an expiration 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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MIT SLOAN SCHOOL OF MANAGEMENT

15.414 Class 18

WSJ option quotes

2.601000.304258Oct20

0.1544100.405307

0.70253.604128Jan15Cisco LastVolLastVolExp

PutCall

17.83

Aug 17.50 17.83

Option/Strike

Stock price Call price Put price

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MIT SLOAN SCHOOL OF MANAGEMENT

15.414 Class 18

Call option: Payoff diagram

-2

0

2

4

6

8

10

12

10 15 20 25 30

Opt

ion

payo

ff

Buy a call Strike price = $20

Payoff = max(0, S - X)

Stock price

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MIT SLOAN SCHOOL OF MANAGEMENT

15.414 Class 18

Option payoffs (strike = $50) 25 25

20 20

1515

1010

55

00

-5-5 30 40 50 60 70 30 40 50 60 70

Buy a call Buy a put

Stock price Stock price

-5

0

5

30 40 50 60 70 -5

0

5

30 40 50 60 70

Sell a call Sell a put

-25

-20

-15

-10

Stock price

-25

-20

-15

-10

Stock price

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MIT SLOAN SCHOOL OF MANAGEMENT

15.414 Class 18

Options

Option payoffs

Asset price = S, strike price = X

Buyer of the option

S < X S > X Risky if usedCall 0 S – X alonePut X – S 0

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MIT SLOAN SCHOOL OF MANAGEMENT

15.414 Class 18

Returns, stock vs. option

-150%

-100%

-50%

0%

50%

100%

150%

30 34 38 42 46 50 54 58 62 66 70

Stock return

Option return Price ≈ $9

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

Stock in 1 year

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MIT SLOAN SCHOOL OF MANAGEMENT

15.414 Class 18

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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MIT SLOAN SCHOOL OF MANAGEMENT

15.414 Class 18

Option strategies: Stock + put

30 35 40

45 50 55 60

65 70

30 40 50 60 70 -5

0

5

10

15

20

25

30 40 50 60 70

30 35 40 45 50 55 60 65 70

30 40 50 60 70

Buy stock Buy put

Stock + put

Stock price Stock price

Stock price

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MIT SLOAN SCHOOL OF MANAGEMENT

15.414 Class 18

Option strategies: Call1 – call2

-20

-15

-10

-5

0

5

10

15

20

25

30 40 50 70 -5

0

5

10

15

20

25

30 40 50 60 70

0

4

8

12

16

20

30 40 50 60 70

Buy call with X = 50

Write call with X = 60

call1 – call2

60

Stock price -20

-15

-10

Stock price

Stock price

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MIT SLOAN SCHOOL OF MANAGEMENT

15.414 Class 18

Option strategies: Call + Put

-5

0

5

10

15

20

25

30 40 50 60 70 -5

0

5

10

15

20

25

30 40 50 60 70

-5

0

5

10

15

20

25

30 40 50 60 70

Buy call with X = 50

Buy put with X = 50

Call + put

Stock price Stock price

Stock price

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MIT SLOAN SCHOOL OF MANAGEMENT

15.414 Class 18

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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MIT SLOAN SCHOOL OF MANAGEMENT

15.414 Class 18

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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MIT SLOAN SCHOOL OF MANAGEMENT

15.414 Class 18

Option strategies: Stock + put

30

35

40

45

50

55

60

65

70

30 40 50 60 70 -5

0

5

10

15

20

25

30 40 50 60 70

30 35

40 45

50 55 60 65

70

30 40 50 60 70

Buy stock Buy put

Stock + put

Stock price Stock price

Stock price

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MIT SLOAN SCHOOL OF MANAGEMENT

15.414 Class 18

Option strategies: Tbill + call

30 35 40 45 50 55 60 65 70

30 40 50 60 70 -5

0

5

10

15

20

25

30 40 50 60 70

30 35

40 45

50 55 60 65

70

30 40 50 60 70

Buy Tbill with FV = 50

Buy call

Tbill + call

Stock price Stock price

Stock price

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MIT SLOAN SCHOOL OF MANAGEMENT

15.414 Class 18

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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MIT SLOAN SCHOOL OF MANAGEMENT

15.414 Class 18

Option pricing

Factors affecting option prices

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

Call option Put option Stock price (S) Exercise price (X) Time-to-maturity (T) Stock volatility (σ) Interest rate (r) Dividends (D)

+ – – + + + + + + – – +

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