Faculty of Business and Economics University of Hong Kong Dr. Huiyan Qiu

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

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

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. 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 ST) at expiration • For forward contract, payoff = profit

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. 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. 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. Reading Price QuotesIndex Futures Low of the day Settlement price High of the day Daily change The open price Open interest Expiration month

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

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. Forward vs. Outright Purchase Forward payoff Bond payoff • 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. 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. Today Expiration date or at buyer’s choosing Call Option and Put Option • A call option (put option)gives the owner the right but not the obligationto 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. 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. 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 QuotesHang Seng Index options Hang Seng Index Options Daily market report on top-10 traded options on August 22, 2012. Source: www.hkex.com.hk

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

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

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

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. Basic Risk Management • Firms convert inputs into goods and servicesoutput input commodityproducerbuyer • 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. 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. 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. 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. 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: themining firm purchases a 420-strike put at the premium of $8.77/oz

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: themining firm sells a 420-strike call and receives an $8.77 premium

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

42. Figure Comparison of profit forGolddiggers using three different put strikes.

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. 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. 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. 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. 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. 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 B After-tax profit Slope = 1-tax rate C $0.06 D Selling price Slope = 1 -$0.14 A

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. 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