1. 2-1 Faculty of Business and Economics University of Hong Kong Dr. Huiyan Qiu MFIN6003 Derivative Securities Lecture Note Two

2. 2-2 Outline Basic derivatives contracts Forward contracts; Call options; Put options Types of positions and payoff / profit diagrams Long / Short position Risk management From producer’s and buyer’s perspective Empirical evidence on hedging Reasons to hedge or not to hedge

3. 2-3 Today Expiration date Forward Contracts Forward contract : a binding agreement (obligation) to buy/sell an underlying asset in the future, at a price set today

4. 2-4 Forward Contracts A forward contract specifies The features and quantity of the asset to be delivered The delivery logistics, such as time, date, and place The price (forward price) the buyer will pay at the time of delivery Two parties sign the contract Long forward: agree to pay THE price to buy Short forward: agree to sell for THE price

5. 2-5 Payoff and Profit Payoff for a contract is its value at expiration. Profit for a position in a contract is net value at expiration of all relevant cash flows. We can use diagrams to show the value of a position at expiration. Forward: (1) zero cash flow at initiation, (2) pay forward price at expiration, (3) get asset (value S T ) at expiration For forward contract, payoff = profit

6. 2-6 Payoff on a Forward Contract Example: S&R (special and rich) index Today: Spot price = $1,000 6-month forward price = $1,020 In six months at contract expiration: Case 1: Spot price = $1,050 Long position payoff = $1,050 – $1,020 = $30 Short position payoff = $1,020 – $1,050 = – $30 Case 2: Spot price = $1,000 Long position payoff = $1,000 – $1,020 = – $20 Short position payoff = $1,020 – $1,000 = $20

7. 2-7 Payoff Diagram for Forwards X-axis: S&R index level 6-month later. Y-axis: payoff for 6- month forward 6-month forward price = $1,020 Long: y = x – 1,020 Short: y = 1,020 – x

8. 2-8 Futures Contracts Futures contracts are the same as forwards in principle except for some institutional and pricing differences. Forward contracts are OTC products. Futures contracts exist in exchange market.

9. 2-9 Reading Price Quotes Index Futures Expiration month The open price High of the day Low of the day Settlement price Daily change Open interest

10. Hang Seng Index Futures 2-10 Hang Seng Index Futures Daily market report on August 22, 2012. Source: www.hkex.com.hkwww.hkex.com.hk

11. 2-11 Forward vs. Outright Purchase Outright purchase: Invest $1,000 in index and own the index. Forward: Invest zero, sign the contract Invest $1,020 at expiration and own the index. Same outcome: own the index at expiration. Why investing $1,000 now results in the same outcome as investing $1,020 later? Price indication?

12. 2-12 Forward payoffBond payoff Forward vs. Outright Purchase Forward + bond = Spot price at expiration – $1,020 + $1,020 = Spot price at expiration Figure Summing the value of the long forward plus the bond at each S&R Index price gives the line labeled “ Forward + Bond ”.

13. 2-13 Additional Considerations Type of settlement Cash settlement: less costly and more practical Physical delivery: often avoided due to significant costs Credit risk of the counter party Major issue for over-the-counter contracts Credit check, collateral, bank letter of credit Less severe for exchange-traded contracts Exchange guarantees transactions, requires collateral

14. 2-14 TodayExpiration date or at buyer’s choosing Call Option and Put Option A call option ( put option ) gives the owner the right but not the obligation to buy ( to sell ) the underlying asset at a predetermined price during a predetermined time period The seller of a call option is obligated to sell if asked The seller of a put option is obligated to buy if asked

15. 2-15 Terminology Strike (or exercise) price: predetermined price Call: the amount paid by the option buyer for the asset if he/she decides to exercise Put: the amount the option buyer receives for selling the asset if he/she decides to exercise Exercise: the act of paying the strike price to buy (for call) or selling the asset for the strike price (for put) Expiration: the date by which the option must be exercised or become worthless

16. 2-16 Exercise Style Exercise style: specifies when the option can be exercised European-style: can be exercised only at expiration date American-style: can be exercised at any time before expiration Bermudan-style: Can be exercised during specified periods Focus: European-style options.

17. Reading Price Quotes Hang Seng Index options 2-17 Hang Seng Index Options Daily market report on top-10 traded options on August 22, 2012. Source: www.hkex.com.hk www.hkex.com.hk

18. 2-18 Call Option on S&R Index A 1000-strike call on S&R Index Underlying asset: S&R Index with current (spot) price of $1,000 Strike price: $1,000 Expiration date: 6 months later Today: call buyer acquires the right to pay $1,000 in six months for the index, but is not obligated to do so call seller is obligated to sell the index for $1,000 in six months, if asked to do so

19. 2-19 Payoff for the Buyer Six months later at contract expiration: If the spot price S T is higher than $1,000, the call buyer will exercise the option: pay $1,000, get S T. Payoff = spot price – 1,000 If the spot price S T is lower than $1,000, the option buyer will walk away and do nothing. Payoff = 0. Payoff = Max [0, spot price – strike price]

20. 2-20 Call Option on S&R Index Call option preserves the upside potential ( ), while at the same time eliminating the unpleasant ( ) downside (for the buyer) Why would anyone agree to be on the seller side? The option buyer must pay the seller an initial premium of $93.81 (option pricing)

21. 2-21 Payoff and Profit for the Buyer Payoff = Max [0, spot price at expiration – strike price] Profit = Payoff – future value of option premium Suppose effective 6-month risk-free rate is 2% If index value in six months = $1,100 Payoff = max [0, $1,100 – $1,000] = $100 Profit = $100 – ($93.81 x 1.02) = $4.32 If index value in six months = $900 Payoff = max [0, $900 – $1,000] = $0 Profit = $0 – ($93.81 x 1.02) = – $95.68

22. 2-22 Diagrams for Purchased Call Payoff at expirationProfit at expiration y = max [0, x – 1,000] – (93.81 x 1.02)

23. 2-23 Payoff/Profit of a Written Call Call writer: the option seller To receive the premium for option sold To have the obligation to sell if requested Seller ’ s payoff and profit is opposite to the buyer Payoff = - max [0, spot price at expiration – strike price] Profit = Payoff + future value of option premium The payoff and profit diagram of a written call is the mirror image of a purchased call, symmetric with regard to the X-axis

24. 2-24 Profit Diagram for a Written Call Figure Profit for writer of 6-month S&R call with strike of $1000 versus profit for short S&R forward. y = (93.81 x 1.02) – max [0, x – 1,000]

25. 2-25 Put Options Payoff/profit of a purchased (i.e., long) put Payoff = max [0, strike price – spot price at expiration] Profit = Payoff – future value of option premium Payoff/profit of a written (i.e., short) put Payoff = – max [0, strike price – spot price at expiration] Profit = Payoff + future value of option premium

26. 2-26 Put Option Examples S&R Index 6-month Put Option Strike price = $1,000, Premium = $74.20, effective 6-month risk-free rate = 2% If index value in six months = $1,100 Payoff = max [0, $1,000 – $1,100] = $0 Profit = $0 – ($74.20 x 1.02) = – $75.68 If index value in six months = $900 Payoff = max [0, $1,000 – $900] = $100 Profit = $100 – ($74.20 x 1.02) = $24.32

27. 2-27 Profit Diagram for a Long Put Position Figure Profit on a purchased S&R index put with strike price of $1000 versus a short S&R index forward. y = max [0, 1,000 – x] – (74.20 x 1.02)

28. 2-28 A Few Items to Note A call option becomes more profitable when the underlying asset appreciates in value A put option becomes more profitable when the underlying asset depreciates in value Moneyness of option: In-the-money : positive payoff if exercised immediately At-the-money : zero payoff if exercised immediately Out-of-the money : negative payoff if exercised immediately

29. 2-29 Summary on Forward & Option Table Maximum possible profit and loss at maturity for long and short forwards and purchased and written calls and puts.

30. 2-30 Summary on Forward & Option Figure Profit diagrams for the three basic long positions: long forward, purchased call, and written put. (Long w.r.t. the underlying asset.)

31. 2-31 Summary on Forward & Option Figure Profit diagrams for the three basic short positions: short forward, written call, and purchased put. (Short w.r.t. the underlying asset.)

32. 2-32 Summary on Forward & Option Table Forwards, calls, and puts at a glance: a summary of forward and option positions.

33. 2-33 Basic Risk Management In general, to hedge against price increase in the future: Take derivatives positions with positive payoff when price is high Long forward, long call, short put To hedge against price decrease in the future: Take derivatives positions with positive payoff when price is low Short forward, short call, long put

34. 2-34 Basic Risk Management Firms convert inputs into goods and services output input commodity producer buyer A firm is profitable if the cost of what it produces exceeds the cost of its inputs A firm that actively uses derivatives and other techniques to alter its risk and protect its profitability is engaging in risk management

35. 2-35 Empirical Evidence on Hedging Half of nonfinancial firms report using derivatives Among firms that do use derivatives, less than 25% of perceived risk is hedged, with firms more likely to hedge short-term risk Firms with more investment opportunities are more likely to hedge Firms that use derivatives have a higher market value and more leverage

36. 2-36 The Producer and the Buyer A producer selling a risky commodity has an inherent long position in this commodity When the price of the commodity , the firm’s profit  (assuming other costs are fixed) A buyer that faces price risk on an input has an inherent short position in this commodity When the price of the input , the firm’s profit  (assuming other costs are fixed)

37. 2-37 Producer: Hedging With Forwards A short forward contract allows a producer to lock in a price for his output Example: the firm enters into a short forward contract, agreeing to sell gold at a price of $420/oz. in 1 year.

38. 2-38 Producer: Hedging With a Put Option Buying a put option allows a producer to have higher profits at high output prices, while providing a floor on the price Example: the mining firm purchases a 420- strike put at the premium of $8.77/oz

39. 2-39 Producer: Insuring by Selling a Call A written call reduces losses through a premium, but limits possible profits by providing a cap on the price Example: the mining firm sells a 420-strike call and receives an $8.77 premium

40. 2-40 Adjusting the Amount of Insurance Insurance is not free!…in fact, it is expensive How to reduce the cost of insurance (at the same time, reducing the benefit of insurance)? In the case of hedging against a price decline by purchasing a put option, one can using a put with a lower strike price instead  lower the price in addition, sell a call  reduce the total price

41. 2-41 Gold Options Call and put premiums for gold options with one year until expiration.

42. 2-42 Figure Comparison of profit for Golddiggers using three different put strikes.

43. 2-43 Figure Comparison of Golddiggers hedged with 420- strike put versus hedged with 420-strike put and written 440-strike call (420–440 collar).

44. 2-44 Buyer: Hedging With Forwards A long forward contract allows a buyer to lock in a price for his input Example: a firm, which uses gold as an input, purchases a forward contract, agreeing to buy gold at a price of $420/oz. in 1 year (revenue after other cost adjusted: $460/oz)

45. 2-45 Buyer: Hedging With a Call Option Buying a call option allows a buyer to have higher profits at low input prices, while being protected against high prices Example: a firm, which uses gold as an input, purchases a 420-strike call at the premium of $8.77/oz

46. 2-46 Why Do Firms Manage Risk? Hedging changes the distribution, not the value, of cash flows. Golddiggers’ example: the hedging strategies shift dollars from more profitable states (when gold prices are high) to less profitable states (when gold prices are low). Hedging can be optimal for a firm when an extra dollar of income received in times of high profits is worth less than an extra dollar of income received in times of low profits.

47. 2-47 An Example How hedge adds value Consider a firm with cost per unit of $10 The selling price is either $11.20 or $9, with 50% probability Thus, the firm has either a $1.20 profit or $1 loss The expected profit per unit = ____$0.10__________ If the tax rate on profit is 40%, after-tax profit is either $0.72 or – $1 After-tax expected profit = ______-$0.14__________

48. 2-48 An Example (cont ’ d) If the firm sells forward at strike $10.10 The profit is fixed at $0.10 with certainty After-tax profit per unit is $0.06 After-tax profit Selling price Slope = 1 Slope = 1-tax rate A B C D -$0.14 $0.06

49. 2-49 Why Do Firms Manage Risk? Concave profits can arise from - Taxes: differential taxation treatment on gains or losses, capital or ordinary incomes, across countries - Bankruptcy and distress costs: avoid huge loss - Costly external financing: smooth cash reserves in the firm - Preservation of debt capacity: reduce riskiness of cash flows - Managerial risk aversion: reduce firm risk

50. 2-50 Reasons Not to Hedge Reasons why firms may elect not to hedge Transaction costs of dealing in derivatives (such as, commissions and the bid-ask spread) The requirement for costly expertise The need to monitor and control the hedging process Complications from tax and accounting considerations Potential collateral requirements

51. 2-51 What can Go Wrong? One of the risks faced by a company that trades derivatives: an employee who has a mandate to hedge or to look for arbitrage opportunities may become a speculator. Barings Bank Case (more detail in Appendix): One of the most infamous tales of financial demise The 200-year-old British bank was wiped out in 1995 by the activities of one trader, Nick Leeson, in Singapore

52. 2-52 End of the Notes!

53. 2-53 Appendix: Barings Bank Case One of the most infamous tales of financial demise The 200-year-old British bank was wiped out in 1995 by the activities of one trader, Nick Leeson, in Singapore

54. 2-54 In 1993, Nick Leeson was appointed general manager of the bank's Barings Futures subsidiary in Singapore. The mandate is to look for arbitrage opportunities between the Nikkei 225 futures price on the Singapore exchange and the Osaka exchange. Over time, Leeson moved from being an arbitrageur to being a speculator: bets on the future direction of the Nikkei 225 using futures and options. When incurring losses, he began to take bigger speculative positions. By the time Leeson’s activities were uncovered, the total loss was close to one billion dollars.

55. 2-55 Barings Bank Case One trading strategy Leeson used: written straddle – selling put and call options on the Nikkei 225 Index. A written straddle is a bet on the volatility being low. Hence it will produce positive earnings when markets are stable but can result in large losses if markets are volatile. When an earthquake in Japan caused a steep drop in the Nikkei 225 equity index, Leeson's unauthorized trading positions suffered huge losses and his operation unraveled.

56. 2-56 Barings Bank Case Leeson managed both the trading and back office function as the general manager. Thus he was able to conceal his unauthorized trading activities for over a year. The senior managers at Barings came primarily from a merchant banking background and knew very little about trading. In March 1995, Dutch banking group ING bought Barings for one British pound, assumed its debts, took over operations and renamed it ING Barings.

57. 2-57 Leeson Afterwards Leeson pleaded guilty to fraud and was sentenced to six and a half years in prison. (He was released from prison in July 1999 for good behavior.) During his detention, he was diagnosed as suffering from colon cancer which he survived. When in prison, Leeson wrote a book “ Rogue Trader ”, which was made into a movie. Nick Leeson now is CEO of Galway United Football Club (Ireland) In June of 2005, Leeson released a new book “ Back from the Brink: Coping with Stress”.