Derivatives and Risk Management (Financial Engineering) An Introduction

1. Derivatives and Risk Management (Financial Engineering)An Introduction Craig G. Dunbar http://www.ivey.uwo.ca/faculty/CDunbar/Derivatives_2003.htm

2. The Course • A course about tools • understand the structure of basic derivative building blocks: forwards, futures and options • introduce models for pricing • First part of course • lecture and problem based • applications are largely trading focused • exercise: S&P 500 futures trading simulation

3. The Course • Second part of the course • case-based applications • using derivatives to reduce financing costs • using derivatives to manage risks • derivatives as “real options” • special applications of derivatives pricing (e.g. M&A)

4. Level of Math • Comfort with math is required but there is no complex mathematics (e.g. no calculus) • Must feel comfortable with symbolic algebra • e.g. nrm = interest rate from time n to m • Must be comfortable with “e” and “ln” • ea x eb = e a+b ea / eb = e a-b • ln (a x b) = ln(a) + ln(b) ln (a / b) = ln(a) - ln(b) • ln(ea) = a

5. Evaluation • Assignments + two exams • assignments : trading simulation report + mini - projects • exams: problem based • Alternatives • A project • Participation • only evaluated during case discussions • counts only if it helps your grade

6. What are Financial Derivatives? • Securities whose value is derived from a more fundamental asset • Securities that exist in zero net supply • Represent a side bet on the fundamental asset

7. The Derivatives World Exchange Traded OTC Structured Embedded Forwards Options Swaps Bonds plus Warrants & Options Futures Options Interest Rate Currency Equity Commodity Securitization CMOs

8. The Uses of Financial Derivatives • Speculation • Play on forecast • Arbitrage • Play on mispricing • Risk Management • Reduce exposure

9. What Fueled the Growth in Derivatives? • Change in volatility in markets • Exchange rates became floating • Active control of interest rates • commodity prices

10. Exchange Rate Volatility

11. Interest Rate Volatility

12. Commodity Price Volatility

13. What Fueled the Growth in Derivatives? • Globalization • Revenues in different currencies • Operating Costs in different currencies • Liabilities in different currencies • Technological advances • Level of computerization • Modeling abilities • Regulatory changes • Changes in transactions costs

14. Why is this Area Important? • The market is massive • Growth rate in the last 10 years has been between 30 and 35 percent per year Source: Wall Street Journal

15. The Global OTC Derivatives MarketIncludes Interest rate swaps, currency swaps and interest rate optionsSource: International Swaps and Derivatives Association (www.isda.org) Notional principal (U$ Trillion) Annual trading (U$ Trillion)

16. The Global OTC Derivatives Market(Trillion U$; Source: www.bis.org)

17. The Global OTC Derivatives Market(Trillion U$; Source: www.bis.org)

18. Annual Futures & Options Contract VolumeMillions of contracts;excludes options on individual equities Source: Futures Industry Association

19. Canadian vs. International ExchangesNumber of contracts traded in millionsSources: CDCC annual report, various web-sites (www.cdcc.ca; www.cboe.com; www.cbot.com; www.liffe.com)

20. Losses and Hysteria • Metallgesellschaft $1b Oil derivatives ‘93 • Gibson Greetings $20m Interest Swaps ‘94 • Procter and Gamble $157m Int. Swaps ‘94 • Orange County $1.5b Structured Notes ‘94 • Barings $1.3b Options and Futures ‘94 • Sumitomo $2.6bCopper Contracts ‘96

21. Continuous CompoundingThe Determination of Futures and Forwards Prices

22. Simple and Compound Returns • Suppose initial wealth W0 is invested for n years at an interest rate of R per year. • If interest is compounded annually, the wealth at end of n years (Wn) will be • Wn = W0 * (1 + R)n • If interest is compounded m times per year, the wealth at end of n years (Wn) will be • Wn = W0 * 1 + R n*m m

23. An Example • W0 = $1000; n = 5 years; R =10% per year. • Compounding once per year • Wn = 1000 * (1 + 0.1)5 = • Compounding semi-annually • Wn = 1000 * ( 1 + 0.1/2) 10 = • Compounding monthly • Wn = 1000 * ( 1 + 0.1/12) 60 =

24. Continuous Compounding R m*n lim 1 + = e R * n • From the previous example, compounding continuously • Wn = 1000 * e 5 * 0.1 = • Generally the relation between initial and terminal wealth is • Wn = W0 * e R * n • Rearranging, we get • R = ln (Wn / W0 ) ÷ n  m m

25. Properties of Continuous Returns • Continuously compounded returns are additive • Let W0 = $1000, R =10% over the first year and 12% over the second year, compounded continuously • W2 = • What was the (continuously compounded) return over the two years? • R =

26. An Example • The annualized rate of return on a 3 month t-bill is quoted as 5.2% • What is the equivalent continuously compounded return? Rc =

27. Pricing Forward Contracts • Notation • T = time until delivery date in forward contract (years) • S = price of asset underlying forward contract today • f = value of a long position in the forward contract today • F = today’s forward price • r = risk-free rate of interest per annum today with continuous compounding for an investment maturing at the delivery date

28. Pricing Forwards: No Income on Underlying Asset • An example • 90-day Forward contract on non-dividend paying stock • Stock price is $20, 90-day bond yields 4% • What should be the forward price (F)? • Investment strategy • Borrow $20 to buy one share of stock • Enter forward contract to sell one share in 90 days for a forward price F(Note: price today to enter contract, f, is 0)

29. No Arbitrage • Suppose that the forward price is $21 • Cash flow at execution of strategy = 0 • Cash flow at delivery in 3 months • Sell stock through forward for $21 • Pay back borrowing and interest • Profit = • To prevent arbitrage, the forward price F must be just enough to pay off the loan • F =

30. Valuing Forward Contracts • Value of contract at the time it is entered into is zero • At other times, the value of the contract, f, is given by f = (F1 – F0) * e -r * T where F0= originally negotiated forward price F1 = current forward price • Strategy • borrow (F1 – F0) * e -r * T today, buy contract with forward price F0 and sell contract with forward price F1 • Cash flow at maturity is zero, so up front cost must be zero to prevent arbitrage