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Options (1) Class 19 Financial Management, 15.414 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) 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 4 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 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 1992 1994 1996 1998 2000 6 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 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.” 8 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 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 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 11 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 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 5.2 5.4 5.6 5.8 -0.5 -1 -1.5 13 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 Class 18 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 15 MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 18 Call option: Payoff diagram 12 Buy a call 10 Strike price = $20 8 Payoff = max(0, S - X) 6 4 Option payoff 2 Stock price 0 10 15 20 25 30 -2 16 MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 18 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 17 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 Call 0 S – X Risky if used Put X – S 0 alone 18 MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 18 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% 19 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 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 21 MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 18 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 22 MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 18 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 23 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 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 26 MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 18 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 27 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.
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