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Introduction Chapter 1

Introduction Chapter 1. DERIVATIVES : FORWARDS FUTURES OPTIONS SWAPS. DERIVATIVES ARE CONTRACTS: Two parties Agreement, or Contract Underlying security Contract termination date. The Difference between Derivatives:. The contract determines the rights and/or obligations of the

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Introduction Chapter 1

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  1. IntroductionChapter 1

  2. DERIVATIVES: FORWARDS FUTURES OPTIONS SWAPS

  3. DERIVATIVES ARE CONTRACTS: Two parties Agreement, or Contract Underlying security Contract termination date

  4. The Difference between Derivatives: The contract determines the rights and/or obligations of the two parties in relation to the sale/purchase of the underlying asset.

  5. The Nature of Derivatives A derivative is a contract whose value depends on the values of other more basic underlying variables In particular, it depends on the market price of the so called: underlying asset.

  6. Underlying assets: Stocks Interest bearing securities: Bonds Foreign currencies: Euro, GBP, AUD,… Metals: Gold, Silver… Energy commodities: Crude oil, Natural gas, Gasoline, heating oil… Agricultural commodities: Wheat, corn, rice, grain feed, soy beans, pork bellies… Stock indexes

  7. Ways Derivatives are Used • To hedge risks • To speculate (take 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

  8. Types of risk: Price risk Credit risk Operational risk Completion risk Human risk Regulatory risk Tax risk

  9. IN THIS CLASS WE WILL ONLY ANALYZE THE RISK ASSOCIATED WITH THE SPOT MARKET PRICE OF THE UNDERLYING ASSET

  10. PRICE RISK: At time t, the asset’s price at time T is not known. Probability distribution ST St t T time

  11. FORWARDS A FORWARD IS A CONTRACT IN WHICH: ONE PARTY COMMITS TO BUY AND THE OTHER PARTY COMMITS TO SELL A SPECIFIED AMOUNT OF AN AGREED UPON COMMODITY OF A SPESIFIC QUALITY FOR A PREDETERMINED PRICE ON AN AGREED UPON FUTURE DATE AT A GIVEN LOCATION

  12. Delivery and payment Buy or sell a forward t T Time BUY = OPEN A LONG POSITION SELL = OPEN A SHORT POSITION

  13. 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

  14. Foreign Exchange Quotes for USD/GBP on DEC 19, 2007

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

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

  17. A FUTURES is A STANDARDIZED FORWARD TRADED ON AN ORGANIZED EXCHANGE. STANDARDIZATION THE COMMODITY THE QUANTITY THE QUALITY PRICE QUOTES DELIVERY DATES DELIVERY PROCEDURES

  18. 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

  19. AN OPTION IS A CONTRACT IN WHICH ONE PARTY HAS THE RIGHT, BUT NOT THE OBLIGATION, TO BUY OR SELL A SPECIFIED AMOUNT OF AN AGREED UPON COMMODITY FOR A PREDETERMINED PRICE BEFORE OR ON A SPECIFIC DATE IN THE FUTURE. THE OTHER PARTY HAS THE OBLIGATION TO DO WHAT THE FIRST PARTY WISHES TO DO. THE FIRST PARTY, HOWEVER, MAY CHOOSE NOT TO EXERCISE ITS RIGHT AND LET THE OPTION EXPIRE WORTHLESS. A CALL = A RIGHT TO BUY THE UNDERLYING ASSET A PUT = A RIGHT TO SELL THE UNDERLYING ASSET

  20. Profit ($) 30 20 10 Terminal stock price ($) 30 40 50 60 0 70 80 90 -5 Long Call on Microsoft Profit from buying a European call option on Microsoft: option price = $5, strike price = $60

  21. Profit ($) 70 80 90 5 0 30 40 50 60 Terminal stock price ($) -10 -20 -30 Short Call on Microsoft Profit from writing a European call option on Microsoft: option price = $5, strike price = $60

  22. Profit ($) 30 20 10 Terminal stock price ($) 0 60 70 80 90 100 110 120 -7 Long Put on IBM Profit from buying a European put option on IBM: option price = $7, strike price = $90

  23. Profit ($) Terminal stock price ($) 7 60 70 80 0 90 100 110 120 -10 -20 -30 Short Put on IBM Profit from writing a European put option on IBM: option price = $7, strike price = $90

  24. A SWAP IS A CONTRACT IN WHICH THE TWO PARTIES COMMIT TO EXCHANGE A SERIES OF CASH FLOWS. THE CASH FLOWS ARE BASED ON AN AGREED UPON PRINCIPAL AMOUNT. NORMALLY, ONLY THE NET FLOW EXCHANGES HANDS. Principal amount = EUR100,000,000; semiannual payments. Tenure: three years. 7% Party B Party A 6-months LIBOR

  25. EXAMPLE: A RISK MANAGEMENT SWAP BONDS MARKET FL1 = 6-MONTH BANK RATE. FL2 = 6-MONTH LIBOR. FL1 LOAN 10% SWAP DEALER A BANK FL2 LOAN 12% FIRM A BORROWS AT A FIXED RATE FOR 5 YEARS

  26. THE BANK’S CASH FLOW: 12% - FLOATING1 + FLOATING2 – 10% = 2% + SPREAD Where the SPREAD = FLOATING2 - FLOATING1 RESULTS THE BANK EXCHANGES THE RISK ASSOCIATED WITH THE DIFFERENCE BETWEEN FLOATING1 and 12% WITH THE RISK ASSOCIATED WITH THE SPREAD = FLOATING2 - FLOATING1. The bank may decide to swap the SPREAD for fixed, risk-free cash flows.

  27. EXAMPLE: A RISK MANAGEMENT SWAP BOND MARKET FL1 10% SWAP DEALER A BANK FL2 FL2 FL1 SWAP DEALER B 12% FIRM A

  28. THE BANK’S CASH FLOW: 12% - FL1 + FL2 – 10% + (FL1 - FL2 ) = 2% RESULTS THE BANK EXCHANGES THE RISK ASSOCIATED WITH THE SPREAD = FL2 - FL1 WITH A FIXED RATE OF 2%. THIS RATE IS A FIXED RATE!

  29. WHY TRADE DERIVATIVES? THE FUNDAMENTAL REASON FOR TRADING DERIVATIVES IS TO HEDGE: THE PRICE RISK Exhibited by the Underlying commodity’s spot price volatility

  30. PRICE RISK IS THE VOLATILITY ASSOCIATED WITH THE COMMODITY’S PRICE IN THE CASH MARKET REMEMBER THAT THE CASH MARKET IS WHERE FIRMS DO THEIR BUSINESS. I.E., BUY AND SELL THE COMMODITY. ZERO PRICE VOLATILITY NO DERIVATIVES!!!!

  31. PRICE RISK: At time t, the asset’s price at time T is not known. Probability distribution ST St t T time

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

  33. THE ECONOMIC PURPOSES OF DERIVATIVE MARKETS HEDGING PRICE DISCOVERY SAVING HEDGING IS THE ACTIVITY OF MANAGING PRICE RISK EXPOSURE PRICE DISCOVERY IS THE REVEALING OF INFORMSTION ABOUT THE FUTURE CASH MARKET PRICE OF A PRODUCT. SAVING IS THE COST SAVING ASSOCIATED WITH SWAPING CASH FLOWS

  34. A Review of Some Financial Economics Principles Arbitrage: A market situation whereby an investor can make a profit with: no equity and no risk. Efficiency: A market is said to be efficient if prices are such that there exist no arbitrage opportunities. Alternatively, a market is said to be inefficient if prices present arbitrage opportunities for investors in this market.

  35. Valuation: The current market value (price) of any project or investment is the net present value of all the future expected cash flows from the project. One-Price Law: Any two projects whose cash flows are equal in every possible state of the world have the same market value. Domination: Let two projects have equal cash flows in all possible states of the world but one. The project with the higher cash flow in that particular state of the world has a higher current market value and thus, is said to dominate the other project.

  36. The Holding Period Rate of Return (HPRR): Buy shares of a stock on date t and sell them later on date T. While holding the shares, the stock has paid a cash dividend In the amount of $D/share. The Holding Period Rate of Return HPRR is:

  37. Example: St = $50/share ST = $51.5/share DT-t = $1/share T = t + 73days.

  38. A proof by contradiction: is a method of proving that an assumption, or a set of assumptions, is incorrect by showing that the implication of the assumptions contradicts these very same assumptions.

  39. Risk-Free Asset: is a security of investment whose return carries no risk. Thus, the return on this security is known and guaranteed in advance. Risk-Free Borrowing And Landing: By purchasing the risk-free asset, investors lend their capital and by selling the risk-free asset, investors borrow capita at the risk-free rate.

  40. The One-Price Law: There exists only one risk-free rate in an efficient economy. Proof: By contradiction. Suppose two risk-free rates exist in a market and R > r. Since both are free of risk, ALL investors will try to borrow at r and invest the money borrowed in R, thus assuring themselves the difference. BUT, the excess demand for borrowing at r and excess supply of lending (investing) at R will change them. Supply = demand only when R = r.

  41. Compounded Interest (p. 76) Any principal amount, P, invested at an annual interest rate, R, compounded annually, for n years would grow to: An = P(1 + R)n. If compounded Quarterly: An = P(1 +R/4)4n.

  42. In general: Invest P dollars in an account which pays An annual interest rate R with m Compounding periods every year. The rate in every period is R/m. The number of compounding periods is nm. Thus, P grows to: An = P(1 +R/m)mn.

  43. An = P(1 +R/m)mn. Monthly compounding becomes: An = P(1 +R/12)12n and daily compounding yields: An = P(1 +R/365)365n.

  44. EXAMPLES: n =10 years; R =12%; P = $100 1.Simple compounding, m = 1, yields: A10 = $100(1+ .12)10 = $310.5848 2.Monthly compounding, m = 12, yields: A10 = $100(1 + .12/12)120 = $330.0387 3.Daily compounding, m = 365, yields: A10 = $100(1 + .12/365)3,650 = $331.9462.

  45. DISCOUNTING The Present Value of a future income, FVT, on date T hence, is given by DISCOUNTING:

  46. DISCOUNTING Let cj, j = 1,2,3,….,; be a sequence of payments paid out m times a year over the next n years. Let R be the annual rate During these years. DISCOUNTING this cash flow yields the Present Value:

  47. CONTINUOUS COMPOUNDING In the early 1970s, banks came up with The following economic reasoning: Since The bank has depositors money all the time, this money should be working for the depositor all the time! This idea, of course, leads to the concept of continuous compounding. We want to apply this idea to the formula:

  48. CONTINUOUS COMPOUNDING This reasoning implies that in order to impose the concept of continuous time on the above compounding expression, we need to solve: This expression may be rewritten as:

  49. Recall that the number “e” is: Xe 1 2 100 2.70481382 10,000 2.71814592 1,000,000 2.71828046 In the limit 2.718281828…..

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