Today

1. Today • Options • Risk management: Why, how, and what? • Option payoffs • Reading • Brealey and Myers, Chapter 20, 21

2. 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. Exchange rates, 1995 – 2003

4. Example

5. $ exchange rate, 1980 – 2000

6. 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

7. 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

8. 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.”

9. 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

10. Financial derivatives

11. 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

12. 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

13. Futures contract: Payoff diagram

14. 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

15. 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.

16. Option Contract • Open interest: • The number of contracts currently outstanding • Key Elements • Underlying asset • Exercise or Strike Price • Premium or Price • Maturity or Expiration

17. 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

18. 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)

19. 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?

21. 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)

22. 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

23. Payoff Profiles for Calls Payoff Call Holder 0 Call Writer Stock Price

24. Profit Profiles for Calls Profit Call Holder 0 Call Writer Stock Price

25. 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?

27. Payoffs and Profits at Expiration - Puts Payoffs to Put Holder 0 if ST> X (X - ST) if ST < X Profit to Put Holder Payoff - Premium

28. Payoffs and Profits at Expiration - Puts Payoffs to Put Writer 0 if ST > X -(X - ST) if ST < X Profits to Put Writer Payoff + Premium

29. Payoff Profiles for Puts Payoff Put Holder 0 Put Writer Stock Price

30. Profit Profiles for Puts Profits Put Writer 0 Put Holder Stock Price

31. Market and Exercise Price Relationships • In the Money - exercise of the option would be profitable Call: market price>exercise price Put: exercise price>market price • Out of the Money - exercise of the option would not be profitable Call: market price < exercise price Put: exercise price < market price • At the Money - exercise price and asset price are equal

32. 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.

33. WSJ option quotes

34. Option payoffs (strike = $50)

35. Options

36. Returns, stock vs. option

37. 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

38. Option strategies: Stock + put

39. Option strategies: Call1 – call2

40. Option strategies: Call + Put

41. 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

42. 損益 買進買權 多頭跨式部位 K ST 買進賣權 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。

43. 損益 賣出賣權 ST K 放空跨式部位 賣出買權 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。

44. 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。

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

46. 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