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?
•
Option payoffs
Reading
•
Brealey and Myers, Chapter 20, 21
•
Sally Jameson
2
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?
3
MIT SLOAN SCHOOL OF MANAGEMENT
15.414
Class 18
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)
Euro / $ (right scale)
0.5
0.0
0.2
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
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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
Sales
Net income
Cap exp
1980
1984
1988
$8,598
565
749
$6,576
-428
234
$10,435
616
793
$ millions
5
MIT SLOAN SCHOOL OF MANAGEMENT
15.414
Class 18
$ exchange rate, 1980 – 2000 145
Trade-weighted exchange rate
130
115
100
85
70
1980
1982
1984
1986
1988
1990
6
1992
1994
1996
1998
2000
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
7
MIT SLOAN SCHOOL OF MANAGEMENT
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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.”
8
MIT SLOAN SCHOOL OF MANAGEMENT
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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 derivative users, if 3σ event, then cashflows up by $15
million and market value up by $31 million
9
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
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
10
MIT SLOAN SCHOOL OF MANAGEMENT
15.414
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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
11
MIT SLOAN SCHOOL OF MANAGEMENT
15.414
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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 ‘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
12
MIT SLOAN SCHOOL OF MANAGEMENT
15.414
Class 18
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
-0.5
-1
-1.5
13
5.2
5.4
5.6
5.8
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. 14
MIT SLOAN SCHOOL OF MANAGEMENT
15.414
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WSJ option quotes Call
Put
Option/Strike
Exp
Vol
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
Last
Call price
15
Vol
Last
Put price
MIT SLOAN SCHOOL OF MANAGEMENT
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Class 18
Call option: Payoff diagram 12
Buy a call
Strike price = $20
10
Payoff = max(0, S - X)
Option payoff
8
6
4
2
Stock price
0
10
15
20
-2
16
25
30
MIT SLOAN SCHOOL OF MANAGEMENT
15.414
Class 18
Option payoffs (strike = $50)
25
25
20
20
Buy a call
15
10
10
5
5
0
0
-5
30
40
Buy a put
15
50
60
70
Stock price
-5
5
30
40
-5
-10
-15
60
70
60
70
Stock price
5
Stock price
Stock price
0
50
0
30
40
Sell a call
50
60
70
-5
-10
-15
-20
-20
-25
-25
17
30
40
50
Sell a put
MIT SLOAN SCHOOL OF MANAGEMENT
15.414
Class 18
Options
Option payoffs
Asset price = S, strike price = X
Buyer of the option
Call
Put
S<X
0
X–S
S>X
S–X
0
18
Risky if used
alone
MIT SLOAN SCHOOL OF MANAGEMENT
15.414
Class 18
Returns, stock vs. option 150%
Stock price = $50
Call option, strike = $50 with 1-year to expiration
100%
50%
Stock return
Stock in 1 year
0%
30
34
38
42
46
50
-50%
54
58
62
66
Option return
Price ≈ $9
-100%
-150%
19
70
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
20
MIT SLOAN SCHOOL OF MANAGEMENT
15.414
Class 18
Option strategies: Stock + put 25
70
65
20
60
Buy stock
55
15
50
Buy put
10
45
5
40
35
0
30
30
30
40
50
Stock price
60
40
50
-5
70
Stock price
70
65
60
55
50
45
40
Stock + put
35
30
30
40
50
Stock price
21
60
70
60
70
MIT SLOAN SCHOOL OF MANAGEMENT
15.414
Class 18
Option strategies: Call1 – call2 25
25
20
20
15
10
5
15
Buy call with
X = 50
5
0
0
-5 30
Write call with
X = 60
10
40
60
50
70
-5 30
-10
-10
-15
-15
-20
-20
40
Stock price
50
Stock price
20
16
call1 – call2
12
8
4
0
30
40
50
Stock price
22
60
70
60
70
MIT SLOAN SCHOOL OF MANAGEMENT
15.414
Class 18
Option strategies: Call + Put
25
25
20
20
Buy call with
X = 50
15
10
10
5
5
0
0
30
-5
40
Buy put with
X = 50
15
50
60
30
70
40
-5
Stock price
50
Stock price
25
20
Call + put
15
10
5
0
-5
30
40
50
Stock price
23
60
70
60
70
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 24
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
25
MIT SLOAN SCHOOL OF MANAGEMENT
15.414
Class 18
Option strategies: Stock + put 70
25
65
20
60
Buy stock
55
15
50
Buy put
10
45
5
40
35
0
30
30
40
50
60
30
70
40
50
-5
Stock price
Stock price
70
65
60
55
50
45
Stock + put
40
35
30
30
40
50
Stock price
26
60
70
60
70
MIT SLOAN SCHOOL OF MANAGEMENT
15.414
Class 18
Option strategies: Tbill + call 70
25
65
Buy Tbill with
FV = 50
60
55
20
15
50
Buy call
10
45
40
5
35
0
30
30
40
50
60
30
70
40
-5
Stock price
50
Stock price
70
65
60
55
50
45
Tbill + call
40
35
30
30
40
50
Stock price
27
60
70
60
70
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
Stock price (S)
Exercise price (X)
Time-to-maturity (T)
Stock volatility (σ)
Interest rate (r)
Dividends (D)
Call option
+
–
+
+
Put option
–
+
+
+
+
–
–
+
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