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The Nature of Derivatives

DERIVATIVES IN TREASURY MANAGEMENT Parikshit Jain 08 EM-028 Sushan rungta 08EM-048 Nilesh Baid 08EM-024. The Nature of Derivatives. A derivative is an instrument whose value depends on the values of other more basic underlying variables. Examples of Derivatives. Swaps Options

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The Nature of Derivatives

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  1. DERIVATIVES IN TREASURY MANAGEMENTParikshit Jain 08 EM-028Sushanrungta 08EM-048NileshBaid 08EM-024

  2. The Nature of Derivatives A derivative is an instrument whose value depends on the values of other more basic underlying variables

  3. Examples of Derivatives • Swaps • Options • Forward Contracts • Futures Contracts

  4. Derivatives Markets • Exchange Traded • standard products • trading floor or computer trading • virtually no credit risk • Over-the-Counter • non-standard products • telephone market • some credit risk

  5. Ways Derivatives are Used • To hedge risks • To reflect a view on the future direction of the market • To lock in an arbitrage profit • To change the nature of a liability • To change the nature of an investment without incurring the costs of selling one portfolio and buying another

  6. Forward Contracts • A forward contract is an agreement to buy or sell an asset at a certain time in the future for a certain price (the delivery price) • It can be contrasted with a spot contract which is an agreement to buy or sell immediately

  7. How a Forward Contract Works • The contract is an over-the-counter (OTC) agreement between 2 companies • The delivery price is usually chosen so that the initial value of the contract is zero • No money changes hands when contract is first negotiated and it is settled at maturity

  8. The Forward Price • The forward price for a contract is the delivery price that would be applicable to the contract if were negotiated today (i.e., it is the delivery price that would make the contract worth exactly zero) • The forward price may be different for contracts of different maturities

  9. Terminology • The party that has agreed to buyhas what is termed a long position • The party that has agreed to sell has what is termed a short position

  10. Example • On January 20, 1998 a trader enters into an agreement to buy £1 million in three months at an exchange rate of 1.6196 • This obligates the trader to pay $1,619,600 for £1 million on April 20, 1998 • What are the possible outcomes?

  11. Profit Price of Underlying at Maturity, ST Profit from aLong Forward Position K

  12. Profit Price of Underlying at Maturity, ST Profit from a Short Forward Position K

  13. Futures Contracts • Agreement to buy or sell an asset for a certain price at a certain time • Similar to forward contract • Whereas a forward contract is traded OTC a futures contract is traded on an exchange

  14. 1. Gold: An Arbitrage Opportunity? • Suppose that: • The spot price of gold is US$300 • The 1-year forward price of gold is US$340 • The 1-year US$ interest rate is 5% per annum • Is there an arbitrage opportunity?

  15. 2. Gold: Another Arbitrage Opportunity? • Suppose that: • The spot price of gold is US$300 • The 1-year forward price of gold is US$300 • The 1-year US$ interest rate is 5% per annum • Is there an arbitrage opportunity?

  16. The Forward Price of Gold If the spot price of gold is S & the forward price for a contract deliverable in T years is F, then F = S (1+r )T where r is the 1-year (domestic currency) risk-free rate of interest. In our examples, S=300, T=1, and r=0.05 so that F = 300(1+0.05) = 315

  17. 1. Oil: An Arbitrage Opportunity? Suppose that: • The spot price of oil is US$19 • The quoted 1-year futures price of oil is US$25 • The 1-year US$ interest rate is 5% per annum • The storage costs of oil are 2% per annum • Is there an arbitrage opportunity?

  18. 2. Oil: Another Arbitrage Opportunity? • Suppose that: • The spot price of oil is US$19 • The quoted 1-year futures price of oil is US$16 • The 1-year US$ interest rate is 5% per annum • The storage costs of oil are 2% per annum • Is there an arbitrage opportunity?

  19. Exchanges Trading Futures • Chicago Board of Trade • Chicago Mercantile Exchange • BM&F (Sao Paulo, Brazil) • LIFFE (London) • TIFFE (Tokyo) • and many more (see list at end of book)

  20. Options • A call option is an option to buy a certain asset by a certain date for a certain price (the strike price) • A put is an option to sell a certain asset by a certain date for a certain price (the strike price)

  21. Profit ($) 30 20 10 Terminal stock price ($) 70 80 90 100 0 110 120 130 -5 Long Call on IBM Profit from buying an IBM European call option: option price = $5, strike price = $100, option life = 2 months

  22. Profit ($) 110 120 130 5 0 70 80 90 100 Terminal stock price ($) -10 -20 -30 Short Call on IBM Profit from writing an IBM European call option: option price = $5, strike price = $100, option life = 2 months

  23. Profit ($) 30 20 10 Terminal stock price ($) 0 40 50 60 70 80 90 100 -7 Long Put on Exxon Profit from buying an Exxon European put option: option price = $7, strike price = $70, option life = 3 mths

  24. Profit ($) Terminal stock price ($) 7 40 50 60 0 70 80 90 100 -10 -20 -30 Short Put on Exxon Profit from writing an Exxon European put option: option price = $7, strike price = $70, option life = 3 mths

  25. Payoff Payoff X X ST ST Payoff Payoff X X ST ST Payoffs from OptionsWhat is the Option Position in Each Case? X = Strike price, ST = Price of asset at maturity

  26. Types of Traders • Hedgers • Speculators • Arbitrageurs Some of the large trading losses in derivatives occurred because individuals who had a mandate to hedge risks switched to being speculators

  27. Hedging Examples • A US company will pay £1 million for imports from Britain in 6 months and decides to hedge using a long position in a forward contract • An investor owns 500 IBM shares currently worth $102 per share. A two- month put with a strike price of $100 costs $4. The investor decides to hedge by buying 5 contracts

  28. Speculation Example • An investor with $7,800 to invest feels that Exxon’s stock price will increase over the next 3 months. The current stock price is $78 and the price of a 3-month call option with a strike of 80 is $3 • What are the alternative strategies?

  29. Arbitrage Example • A stock price is quoted as £100 in London and $172 in New York • The current exchange rate is 1.7500 • What is the arbitrage opportunity?

  30. Exchanges Trading Options • Chicago Board Options Exchange • American Stock Exchange • Philadelphia Stock Exchange • Pacific Stock Exchange • European Options Exchange • Australian Options Market • and many more (see list at end of book)

  31. Futures Markets and the Use of Futuresfor Hedging

  32. Futures Contracts • Available on a wide range of underlyings • Exchange traded • Specifications need to be defined: • What can be delivered, • Where it can be delivered, & • When it can be delivered • Settled daily

  33. Margins • A margin is cash or marketable securities deposited by an investor with his or her broker • The balance in the margin account is adjusted to reflect daily settlement • Margins minimize the possibility of a loss through a default on a contract

  34. Example of a Futures Trade • An investor takes a long position in 2 December gold futures contracts on June 3 • contract size is 100 oz. • futures price is US$400 • margin requirement is US$2,000/contract (US$4,000 in total) • maintenance margin is US$1,500/contract (US$3,000 in total)

  35. A Possible Outcome Daily Cumulative Margin Futures Gain Gain Account Margin Price (Loss) (Loss) Balance Call Day (US$) (US$) (US$) (US$) (US$) 400.00 4,000 3-Jun 397.00 (600) (600) 3,400 0 . . . . . . . . . . . . . . . . . . 11-Jun 393.30 (420) (1,340) 2,660 1,340 4,000 + = . . . . . . . . . . . . . . . . . 3,000 < 17-Jun 387.00 (1,140) (2,600) 2,740 1,260 4,000 + = . . . . . . . . . . . . . . . . . . 24-Jun 392.30 260 (1,540) 5,060 0

  36. Other Key Points About Futures • They are settled daily • Closing out a futures position involves entering into an offsetting trade • Most contracts are closed out before maturity

  37. Delivery • If a contract is not closed out before maturity, it usually settled by delivering the assets underlying the contract. When there are alternatives about what is delivered, where it is delivered, and when it is delivered, the party with the short position chooses. • A few contracts (for example, those on stock indices and Eurodollars) are settled in cash

  38. Some Terminology • Open interest: the total number of contracts outstanding • equal to number of long positions or number of short positions • Settlement price: the price just before the final bell each day • used for the daily settlement process • Volume of trading: the number of trades in 1 day

  39. Convergence of Futures to Spot Futures Price Spot Price Futures Price Spot Price Time Time (a) (b)

  40. Questions • When a new trade is completed what are the possible effects on the open interest? • Can the volume of trading in a day be greater than the open interest?

  41. Regulation of Futures • Regulation is designed to protect the public interest • Regulators try to prevent questionable trading practices by either individuals on the floor of the exchange or outside groups

  42. Accounting & Tax • If a contract is used for • Hedging: it is logical to recognize profits (losses) at the same time as on the item being hedged • Speculation: it is logical to recognize profits (losses) on a mark to market basis • Roughly speaking, this is what the treatment of futures in the U.S.and many other countries attempts to achieve

  43. Long & Short Hedges • A long futures hedge is appropriate when you know you will purchase an asset in the future & want to lock in the price • A short futures hedge is appropriate when you know you will sell an asset in the future & want to lock in the price

  44. Basis Risk • Basis is the difference between spot & futures • Basis risk arises because of the uncertainty about the basis when the hedge is closed out

  45. Long Hedge • Suppose that F1 :Initial Futures Price F2: Final Futures Price S2: Final Asset Price • You hedge the future purchase of an asset by entering into a long futures contract • Cost of Asset=S2 -F2+F1= F1+ Basis

  46. Short Hedge • Suppose that F1 :Initial Futures Price F2: Final Futures Price S2: Final Asset Price • You hedge the future sale of an asset by entering into a short futures contract • Price Realized=S2 -F2+F1= F1+ Basis

  47. Choice of Contract • Choose a delivery month that is as close as possible to, but later than, the end of the life of the hedge • When there is no futures contract on the asset being hedged, choose the contract whose futures price is most highly correlated with the asset price. There are then 2 components to basis

  48. Optimal Hedge Ratio • Proportion of the exposure that should optimally be hedged is where S : spot price, F : futures price, sS : standard deviation of DS , sF : standard deviation of DF & r: coefficient of correlation between DS & DF

  49. Rolling The Hedge Forward • We can use a series of futures contracts to increase the life of a hedge • Each time we switch from 1 futures contract to another we incur a type of basis risk

  50. Forward Contracts vs Futures Contracts FORWARDS FUTURES Private contract between 2 parties Exchange traded Non-standard contract Standard contract Usually 1 specified delivery date Range of delivery dates Settled at maturity Settled daily Delivery or final cash Contract usually closed out settlement usually occurs prior to maturity

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