Derivatives

1. Derivatives Fin 119 Spring 2009

2. Derivatives • Basic Definition • Any Asset whose value is based upon (or derived from) an underlying asset. • The performance of the derivative is dependent upon the performance of the underlying asset. • Risk Management • Since a derivatives performance is based on an underlying asset they can often be used to decrease the risk associated with changes in the spot price of an asset.

3. Basic Types of Derivative Contracts • Forward Contracts • Agreement between two parties to purchase or sell something at a later date at a price agreed upon today • Futures Contract • Same idea as a forward, but the contract trades on an exchange and the counter party is not set. • Options • Buying or selling the right but not obligation to purchase or sell something in the future at a price agreed upon today • Swaps • Exchange of Cash flow Streams based on a notional value.

4. Brief History • Organized Exchanges in US • Chicago Board of Trade Established in 1848 to bring farmers and merchants together. Futures Contracts were first traded on the CBOT1865. Developed the first standard contract • Chicago Mercantile Exchange Started as the Chicago Produce Exchange in 1874 for trade in perishable agricultural products. In 1919 it became the Chicago Mercantile Exchange (CME). Introduced a contract for S&P 500 futures in 1982. • NYMEX 1872 KCBOT 1876

5. Other US Exchanges • NYBOT • Coffee Sugar and Cocca Exchange • New York Futures Exchange • Minneapolis Grain Exchange • Philadelphia Board of Trade

6. Payoff on Forward Contracts • Long Position • Agreeing to buy a specified amount (The Contract Size) of a given commodity or asset at a set point in time in the future (The Delivery Date) at a set price (The Delivery Price) • Payoff • The payoff will depend upon the spot price at the delivery date. • Payoff = Spot Price – Delivery Price

7. Example • Assume you have agreed to buy €1,000,000 in 3 months at a rate of €1 = $1.6196 Spot RateSpot – Delivery PricePayoff $1.65 $1.65-$1.6196=$0.0304 $30,400 $1.6169 $1.6196-$1.6196=0 0 $1.55 $1.55-$1.6196=$0.0696 -$69,600

8. Example Graphically Payoff .0304 1.6196 1.650 1.55 Spot Price -.0696

9. Payoff: Short Position • Agreeing to sell a specified amount (The Contract Size) of a given commodity or asset at a point of time in the future (The Delivery Date) at a set price (The Delivery Price). • Payoff on Short position • Since the position is profitable when the price declines the payoff becomes: • Payoff = The Delivery Price – The Spot Price

10. Long vs. Short • For a long position to exist (someone agreeing to buy) there must be an offsetting short position (someone agreeing to sell). • Assume that you held the short position for the previous example: sell € 1,000,000 in 3 mos at a rate of €1 = $1.6196 Spot RateSpot – Delivery PricePayoff $1.65 $1.6196-$1.65=-$0.0304 -$30,400 $1.6169 $1.6196-$1.6196=0 0 $1.55 $1.6196-$1.55= $0.0696 $69,600

11. Example Graphically Payoff .0304 1.6196 1.650 1.55 Spot Price -.0696

12. Contract Goals • The goal of the contract is to decrease risk, assume that you had to pay €1,000,000 in 3 months for the shipment of an input. You are afraid that the $ price will increase and you will pay a higher price. • Similarly the other party may be afraid that the $ price will decrease (maybe they are receiving a payment in 3 months)

13. Determining the delivery price • The delivery price will be determined by the participants expectations about the future price and their willingness to enter into the contract. (Today’s spot price most likely does not equal the delivery price). • What else should be considered? • They should both also consider the time value of money

14. Future and Forward contracts • Both Futures and Forward contracts are contracts entered into by two parties who agree to buy and sell a given commodity or asset (for example a T- Bill) at a specified point of time in the future at a set price.

15. Futures vs. Forwards • Future contracts are traded on an exchange, Forward contracts are privately negotiated over-the-counter arrangements between two parties. • Both set a price to be paid in the future for a specified contract. • Forward Contracts are subject to counter party default risk, The futures exchange attempts to limit or eliminate the amount of counter party default risk.

16. Other Forward Contract Risks • One goal of the negotiation is to specify exactly the type, quantity, and means of delivery of the underlying asset. • The chance that an asset different than anticipated might be delivered should be eliminated by the contract. • Futures contracts attempt to account for this problem via standardization of the contract.

17. Futures Contracts • Long Position: Agreeing to purchase a specified amount of a given commodity or asset at a point in time in the future at a set price (the futures price) • Short Position: Agreeing to sell a specified amount of a given commodity or asset at a point of time in the future for a set price (the futures price).

18. Standardization of Futures Contracts • To promote confidence in the system and eliminate counter party default risk, future contracts are highly standardized.

19. Specifications of Futures Contract • The Asset • The Contract Size • Delivery Arrangements • Delivery Months • Price Quotes • Price Limits • Position Limits

20. Contract Specifications • Asset • Quality and type of asset are specified to guarantee specific product is delivered. • Contract Size • The amount of asset that is to be delivered for one contract • Delivery Arrangements • More important for commodities than financial assets. Specify how delivery occurs and location.

21. Contract Specifications • Delivery Months • When delivery will occur (and during what part of the month delivery can occur) • Price Quotes • Contract must specify the units for the price quote (1/32 of a dollar etc) Also implicitly establishes the minimum fluctuation for the price of the contract.

22. Contract Specifications • Price Limits • Designed to add stability to the market, limits on the maximum fluctuation in price that can occur during a trading day. • Position Limits • Limits the number of contracts that can be entered into by a speculator. • Speculator –attempting to profit from a movement in the market • Hedger – attempting to offset an underlying spot position.

23. Does Delivery need to take place? • No – most contracts will be closed out. • Closing out a contract is simply taking the opposite (short if you are long or vice versa) position. The change in the futures price will be your gain or loss. • With a futures contract your counter party does not remain the same. It does not matter who takes the opposite position. This is not the case for a forward contract.

24. Summary Forward ContractsFutures Contracts Private contract between Traded on two parties an exchange Not Standardized Standardized Usually a single delivery date Range of delivery dates Settled at the end of contract Settled daily Delivery or final cash Contract is usually closed settlement usually takes place out prior to maturity

25. Important Terminology • Open Interest • The number of contracts that are currently open (both a short and long position exist). • What happens to open interest if a new long position is taken out? • It could Increase • It could decrease • It might not change. The answer depends on whether both the long and short positions are new, or closing out, or one of each.

26. Margin Requirements • To limit counter party default risk, the futures exchange requires participants to place funds in a margin account when the contract is taken out. • Some Terminology: • Initial Margin: The original amount deposited in the margin account • Maintenance margin: The amount that must remain in the margin account • Margin call – Notice that the margin account has dropped below the maintenance margin, more money must be added to the account

27. Margin Example • Example: • An investor has taken a long position in gold (agreed to buy gold at some date in the future). • Assume that the agreement is for 2 gold contracts each contract consists of 100 ounces of gold. The futures price is $400 per ounce. • This implies that the participant would need 200*400 = $80,000 to purchase gold at the expiration of the contract.

28. Margin Example • If the futures price for gold decreases to $398, the investor would suffer a loss if the contract is closed out. • The loss would total (400 - 398)200 = $400. • The fear is that if at the expiration of the contract the price is 398, the participant will not honor the contract since it would result in a loss of $400.

29. Margin Example • To counteract this the investor is ask to put a sum of money into a margin account lets assume $2,000 per contract or $4000 total. • When the futures price declines the loss of $400 is taken from the margin account of the investor and given to a participant that took a short position.

30. Margin Example • The value of the contract is marked to market each day, and the margin account is adjusted. The margin is effectively guaranteeing that the position is covered. • If the level of the account falls below the maintenance margin the investor is required to put more funds into the account this is known as a margin call. The extra funds provided are the variation margin, if they are not provided the broker will close out the account.

31. Margin Account

32. Note: • You can withdraw any amount above the initial margin • Most accounts pay a money market rate of interest • Some accounts allow deposit of securities, but valued at less than face value. (treasures valued at 90% other at 50%)

33. Role of Clearinghouse • The clearinghouse serves as an intermediary that guarantees the contract. • The clearinghouse is an independent corporation whose shareholders are comprised of its member firms. Each member firm maintains a margin account (similar to the traders) with the clearinghouse. • In essence the clearinghouse guarantees the long and the short trader that the other side will honor the contract

34. Patterns of Futures Prices • Basis = Spot Price – Futures Price • The Basis moves toward zero as the spot price matures. • This eliminates arbitrage possibilities. • If futures is greater than spot, you could enter short in the futures market and make a profit by buying in the spot and then delivering in futures • Since everyone will attempt this demand for short positions increases and futures price decreases, also spot price would increase….

35. Other Patterns • The Futures Price over time • Normal Market: The futures price increase as the time to maturity increases • Inverted Market: the futures price is a decreasing function of the time to maturity • Comparing the futures price to the expected future spot price. • Normal Backwardation: The futures price is below the expected future spot price. • Contango: The futures price is above the expected futures price.

36. Theoretical Explanations of Backwardation • Keynes and Hicks-- Speculators will only enter the market if they expect to have a positive profit. If more speculators are holding a long position, it implies that the futures price is less than the expected spot price • A second explanation can be found by looking at the relationship between risk and return in the market. If thee is systematic risk involved with holding the security then the investor should be compensated for accepting the risk (nonsystematic risk can be diversified away).

37. Option Terminology • Call Option – the right to buy an asset at some point in the future for a designated price. • Put Option – the right to sell an asset at some point in the future at a given price

38. Review of Option Terminology Expiration Date The last day the option can be exercised (American Option) also called the strike date, maturity, and exercise date Exercise Price The price specified in the contract American Option Can be exercised at any time up to the expiration date European OptionCan be exercised only on the expiration date

39. Review of Option Terminology • Long position: Buying an option • Long Call: Bought the right to buy the asset • Long Put: Bought the right to sell the asset • Short Position: Writing (Selling) the option • Short Call: Agreed to sell the other party the right to buy the underlying asset, if the other party exercises the option you deliver the asset. • Short Put: Agreed to buy the underlying asset from the other party if they decide to exercise the option.

40. Review of Terminology • In - the - money options • when the spot price of the underlying asset for a call (put) is greater (less) than the exercise price • Out - of - the - money options • when the spot price of the underlying asset for a call (put) is less (greater) than the exercise price • At - the - money options • when the exercise price and spot price are equal.

41. Interest Rate Options • Traded on Chicago Board of Options Exchange (CBOE) • Interest rate Options are traded on 13 Week, 5 year, 10 year and 30 year treasury securities

42. Call Option Profit • Call option – as the price of the asset increases the option is more profitable. • Once the price is above the exercise price (strike price) the option will be exercised • If the price of the underlying asset is below the exercise price it won’t be exercised – you only loose the cost of the option. • The Profit earned is equal to the gain or loss on the option minus the initial cost.

43. Profit Diagram Call Option(Long Call Position) Profit Spot Price Cost S-X-C S X

44. Call Option Intrinsic Value • The intrinsic value of a call option is equal to the current value of the underlying asset minus the exercise price if exercised or 0 if not exercised. • In other words, it is the payoff to the investor at that point in time (ignoring the initial cost) the intrinsic value is equal to max(0, S-X)

45. Payoff Diagram Call Option Payoff Spot Price S-X X S

46. Example: Naked Call Option • Assume that you can purchase a call option on an 8% coupon bond with a par value of $100 and 20 years to maturity. The option expires in one month and has an exercise price of $100. • Assume that the option is currently at the money (the bond is selling at par) and selling for $3. • What are the possible payoffs if you bought the bond and held it until maturity of the option?

47. Five possible results • The price of the bond at maturity of the option is $100. The buyer looses the entire purchase price, no reason to exercise. • The price of the bond at maturity is less than $100 (the YTM is > 8%). The buyer looses the $3 option price and does not exercise the option.

48. Five Possible Results continued • The price of the bond at maturity is greater than $100, but less than $103. The buyer will exercise the option and recover a portion of the option cost. • The price of the bond is equal to $103. The buyer will exercise the option and recover the cost of the option. • The price of the bond is greater than $103. The buyer will make a profit of S-$100-$3.

49. Profit Diagram Call Option(Long Call Position) Profit Spot Price -3 S-100-3 S 103 100

50. Price vs. Rate • Note buying a call on the price of the bond is equivalent to buying a put on the interest rate paid by the bond. • As the rate decreases, the price increases because of the time value of money.