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FINA0301 Derivatives Faculty of Business and Economics University of Hong Kong Dr. Huiyan Qiu

Overview and Preparation Introduction to Derivatives. FINA0301 Derivatives Faculty of Business and Economics University of Hong Kong Dr. Huiyan Qiu. Outline. Course Overview and Class Information Introduction to Derivatives: in general What is a derivative? Derivatives markets

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FINA0301 Derivatives Faculty of Business and Economics University of Hong Kong Dr. Huiyan Qiu

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  1. Overview and Preparation Introduction to Derivatives FINA0301 DerivativesFaculty of Business and Economics University of Hong Kong Dr. Huiyan Qiu

  2. Outline • Course Overview and Class Information • Introduction to Derivatives: in general • What is a derivative? • Derivatives markets • Technical preparation • Time value of money • Basic transaction including short-selling • No-arbitrage principle

  3. Overview of the course • The course is about: • the concept, the use, the pricing of derivatives. • Objective of the course: • this course aims to provide you with a general introduction to the modern financial engineering: the construction of a financial product from other products.

  4. Topics covered in this course • Chapter 1 Introduction to Derivatives. • Part I: Insurance, hedging, and simple strategies. Chapter 2, 3 and 4 • Part II: Forwards, futures, and swaps. Chapter 5, 6.1, 6.2, 7, and 8 • Part III: option pricing. Chapter 9, 10, 11 • Part IV: financial engineering and corporate applications. Chapter 12, 13

  5. Assessment Final grade is curve-based. No more than 25% of students will be awarded A+, A, or A-. The median grade is B-.

  6. Class Information Meeting Schedule: Wednesday 11:30-12:25 (TT 404) Friday 10:30-12:25 (TT 404) Number of students:63 Subclass F and G (19, 51) are offered by other instructors on Tuesday and Thursday afternoon. Note: data collection is based on the registration information as of January 9, 2012. 6 6

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  8. What are Derivatives? • A derivative security is a financial instrument whose value derives from that of some other underlying asset or assets whose price are taken as given. • Remark: The value of a derivative is in a relative sense. No need to inquire into the deeper economic forces that determine the prices of the underlying assets.

  9. Types of Derivatives • Forward contracts and futures contracts are agreements to buy or sell an asset at a certain future time T for a certain price K. • Swaps are similar to forwards, except that the parties commit to multiple exchanges at different points in time. • A call option gives the holder the right to buy the underlying asset by a certain date T for a certain price K . • A put option gives the holder the right to sell the underlying asset by a certain date T for a certain price K .

  10. A Concrete Example • You enter an agreement with a friend that says: • If the price of a bushel of corn in one year is greater than $3, you will pay him $1 • If the price is less than $3, he will pay you $1 • This agreement is a derivative • Questions: • What happens one year later? (outcome, carry-out) • Why do you or your friend want to enter this agreement at the first place?

  11. Uses of Derivatives • Risk management • Hedging: where the cash flows from the derivative are used to offset or mitigate the cash flows from a prior market commitment. • Speculation • Where derivative is used without an underlying prior exposure; the aim is to profit from anticipated market movements. • Reduce transaction costs • Regulatory arbitrage

  12. End users Corporations Investment managers Investors Intermediaries Market-makers Traders Observers End user End user Intermediary Three Different Perspectives • EconomicObservers • Regulators • Researchers

  13. Derivatives Markets • The over-the-counter or “OTC” market: where two parties find each other then work directly with each other to formulate, execute, and enforce a derivative transaction. • Forward contracts, most swaps • The exchange market: where buyer and seller can do a deal without worrying about finding each other. • Futures contracts, most options • Risk-sharing is one of the most important functions of financial markets.

  14. Measures of Market Size and Activity • Four ways to measure a market • Open interest: total number of contracts that are “open” (waiting to be settled). An important statistic in derivatives markets. • Trading volume: number of financial claims that change hands daily or annually. • Market value: sum of the market value of the claims that could be traded. • Notional value: the scale of a position, using with reference to some underlying asset.

  15. Exchange Traded Contracts • Contracts proliferated in the last three decades Examples of futures contracts traded on the three derivatives market • What were the drivers behind this proliferation?

  16. Increased Volatility… • Oil prices: 1947–2006 • Dollar/Pound rate: 1947–2006 Figure 1.1 Monthly percentage change in the producer price index for oil, 1947–2006. Figure 1.2 Monthly percentagechange in the dollar/pound($/£) exchange rate, 1947–2006.

  17. …Led to New and Big Markets • Exchange-traded derivatives • Over-the-counter traded derivatives: even more! Figure 1.3 Millions of futures contracts traded annually at the Chicago Board of Trade (CBT), Chicago Mercantile Exchange (CME), and the New York Mercantile Exchange (NYMEX), 1970–2006. The CME and CBT merged in 2007.

  18. Derivatives Products in HK • Exchange-traded derivatives products in HKEX include: • Equity Index Products(futures and options on Hang Seng Index, H-shares Index, Mini-Hang Seng Index, Mini H-shares Index, and Dividend futures) • Equity Products (stock futures and stock options) • Interest Rate and Fixed Income Products(HIBOR futures and Three-year exchange fund note futures) • Gold Futures • OTC market products: numerous

  19. Hong Kong Mercantile Exchange • HKMEX: an electronic commodities exchange • “… HKMEx seeks to become the preferred platform where international and mainland market participants come together to trade commodity contracts for investment, hedging and arbitrage opportunities.” • Formally began trading on May 18, 2011 • Products • 32 troy ounce gold futures: May 18, 2011 • 1,000 troy ounce silver futures: July 22, 2011 • Website: http://www.hkmerc.com

  20. Futures Exchanges in China • Dalian Commodity Exchange (1993.02) • Zhengzhou Commodity Exchange (1998.08) • Shanghai Futures Exchange (1999.12) • China Financial Futures Exchange (2006.09) • CFFEX is the first financial derivatives exchange in China. http://www.cffex.com.cn/ • 16 April, 2010, the CSI index futures started to trade

  21. Technical Preparation • Time value of money, future value, present value, APR, EAR • Continuous compounding (Appendix B) • Basic transaction: short-selling (§1.4) • No Arbitrage Principle

  22. $100 $110 Time Value of Money • Time value of money refers to a dollar today is different from a dollar in the future • Time value of money is measured by the interest rate for the period concerned. • To compare money flows, we must convert them to the same time point. • Which one is more valuable?

  23. Future Value and Present Value where FV = future value PV = present value r = the quoted annual interest rate m = the number of times interest is compounded per year n = the number of compounding periods to maturity

  24. A Simple Example • $100 is deposited for a year at quoted annual percentage rate (APR) of 12% with monthly compounding. • Given 12% APR, the monthly interest rate is 1%. At the end of each month, interest is calculated and added to the principle to earn more interest. • End of month 1: $100(1+1%) • End of month 2: $100(1+1%)(1+1%) = 100(1+1%)2 • : • End of month 12: $100(1+1%)12 = $100(1+12.68%) • 12.68% is the effective annual rate (EAR).

  25. APR and EAR • APR: annual percentage rate • EAR: effective annual rate APR = 10%

  26. Continuously Compounding • Continuously compounding: n → ∞ (infinity) by definition of e. • Consider a stock paying continuous dividend with annual rate of δ. Claim:The present value of 1 share at time T is then S0e-δT. • How can dividend be continuously paid? • Example: stock index, mutual fund

  27. Continuous Dividend Payment • Annual dividend yield is . Let’s first assume daily compounding, then daily dividend yield is . • At day t, per share, there is dividend in cash, which is equivalent to unit of shares. • In stead of keeping cash dividend (varying), we reinvest to accumulate more shares. • Starting with one share at day 0, at the end of the year, total number of shares is . • If continuous compounding  shares.

  28. Continuous Dividend Payment • That it, one share today will result in shares one year later. • To result in one share T years later, number of shares needed today is thus . • Therefore, the present value of 1 share at time T is S0e-δT.

  29. Basic Transactions • Buying and selling a financial asset (cost) • Brokers: commissions • Market-makers: bid-ask (offer) spread • Example: Buy and sell 100 shares of XYZ • XYZ: bid = $49.75, offer = $50, commission = $15 • Buy: (100 x $50) + $15 = $5,015 • Sell: (100 x $49.75) – $15 = $4,960 • Transaction cost: $5,015 – $4,960 = $55

  30. Short-Selling • When price of an asset is expected to fall • First: borrow and sell an asset (get $$) • Then: buy back and return the asset (pay $) • If price fell in the mean time: Profit $ = $$ –$ • What happens if price doesn’t fall as expected? • If the asset pays dividend in between, who gets the dividend payment?

  31. Short-Selling • Example: short-sell IBM stock for 90 days • The lender must be compensated for dividends received (lease rate of the asset)

  32. Short-Selling (cont’d) • Why short-sell? • Speculation • Financing • Hedging • Credit risk in short-selling • Collateral and “haircut” • Interest received from lender on collateral • Scarcity decreases the interest rate • Repo rate in bond markets • Short rebate in the stock market

  33. Example • Assume that you open a 100 share position in Fanny, Inc. common stock at the bid-ask price of $32.00 - $32.50. When you close your position the bid-ask prices are $32.50 - $33.00. If you pay a commission rate of 0.5% and the effective market interest rate over your holding period is 2%. • What is your profit or loss if • Case 1: you purchase the stock then sell; • Case 2: you short-sell the stock then close the position.

  34. Example (cont’d) • You pay ask price when you purchase a stock and you get bid price when selling a stock. • If the market interest rate is ignored, • Case 1: loss of $32.50 • Case 2: loss of $132.50 • When the market interest rate of 2% is taken into account, • Case 1: loss of $97.825 • Case 2: loss of $68.82

  35. Discussion • Question 1: Why the loss in short-selling is more than the loss in outright purchase? (In the case that the market interest rate is zero.) • Question 2: Interest rate seems to have positive effect on the profit/loss on short-selling but negative effect on the profit/loss on outright purchase. Why? • Question 3: at what interest rate, profit/loss from short-selling or from outright purchase is the same?

  36. Pricing Approaches • Much of this course will focus on the pricing of a derivative security. In general there are two approaches to price an asset (or a contract or a portfolio): • Pricing an asset using an equilibrium model: • Determine cash flows and their risk • Use some theory of investor’s attitude towards risk and return (e.g. CAPM) to figure out the expected rate of return • Conduct discounted cash flow analysis to find the present value of future cash flows

  37. Pricing Approaches • Pricing an asset by analogy (using no-arbitrage): • Find another asset, whose price you know, that has the same payoffs of the asset to be priced. • Arbitrage is any trading strategy requiring no cash input that has some probability of making profits, without any risk of a loss • Law of One Price:two equivalent things cannot sell for different prices. • Law of No Arbitrage: a portfolio involving zero risk, zero net investment and positive expected returns cannot exist.

  38. Law of No Arbitrage • Can one expect to continually earn arbitrage profits in well functioning capital markets? • From an economic perspective, the existence of arbitrage opportunities implies that the economy is in an economic disequilibrium. • Assumptions: • No market frictions (transaction costs? bid/ask spread? restriction on short sales? taxes?) • No counterparty risk (credit risk? collateral requirements? margin requirements?) • Competitive market (liquidity concern?)

  39. Two Examples • Example 1: the effect of dividend payment on stock price change • Example 2: how to make arbitrage profit

  40. Cum-Dividend/Ex-Dividend Prices • A stock that pays a known dividend of dtdollars per share at date t • Stc = the cum-dividend stock price at date t • Ste= the ex-dividend stock price at date t • Assumptions • no arbitrage opportunities, • no differential taxation between capital gains and dividend income • The following relation can be shown to hold Stc = Ste + dt

  41. No Arbitrage Argument • Suppose that Stc < Ste + dt • buy the stock cum-dividend • receive the dividend • sell the stock ex-dividend • reap the arbitrage profits (Ste + dt) – Stc > 0 • Suppose that Stc > Ste + dt • sell the stock at the cum price • buy it back immediately after the dividend is paid • reap the arbitrage profits (Stc– Ste) – dt > 0

  42. No-Arbitrage Pricing Method • Example: • Current stock price S0 = $25.00, there is no dividends payment in the following 6 months • The continuously compounded risk-free annual interest rate = 7.00% • A contract (forward contract): agreement to buy the stock at time 6 for F0, 6 = $26.00 (forward price) • Is there arbitrage profit to make? (Is the forward contract fairly priced?)

  43. Example (cont’d) • How to generate a portfolio (synthetic contract) which duplicates the cash flowsand value of the contract under consideration • Cash flows of the contract: • Time 0: Zero • Time 6: Outflow of $26 and inflow of S6 at time 6 (value of the contract: S6– 26.) • Synthetic contract: borrow $25.00 to buy the stock • Time-0 cash flow: Zero

  44. Example (cont’d) • At time 6, • Synthetic contract: pay back the borrowed money and still have the stock. Payment: 25[ e(.07)(6/12) ] =25.89 • Forward contract: pay $26.00 to have the stock • Conclusion: the contract is over-priced! Sell it! (Short it!) At the same time, buy (long) the synthetic contract!

  45. Example (cont’d) • At Time 0 (Cash) • Borrow $25.00 at a 7.00% annual rate for 6 months • Buy the stock at $25.00 • Write the forward at $26.00 • Between 0 and 6 (Carry) • At time 6 • Pay back borrowed money:25[ e(.07)(6/12) ] =25.89 • Get $26.00 from the forward (and give up the stock) • Net payoff: $0.11

  46. Learn from the Example • Arbitrage-free forward price: F0, T = S0 erT • Forward price is the deferred value of the spot price • The deferred rate is the risk-free rate • Exercise: • S0= $25.00; F0, 6 = $25.50 • The continuously compounded risk-free annual interest rate = 7.00% • What arbitrage would you undertake? How to make profit?

  47. Something is worth whatever it costs to replicate it Derivatives securities are by definition those for which a perfect replica can be constructed from other better-known securities. • The role of models: find the replica. • Buying the replica is the same as buying the derivative. • Selling the replica is the same as hedging the derivative. • Absence of arbitrage implies the two have the same price.

  48. After-class Exercises Work on the following problems to check your knowledge on the time value of money and no-arbitrage principle. 1. An interest rate is quoted as 5% per annum with semiannual compounding. What is the equivalent rate with (a) annual compounding, (b) monthly compounding, and (c) continuous compounding? 2. An investor receives $1,100 in one year in return for an investment of $1,000 now. Calculate the percentage return per annum with: (a) Annual Compounding, (b) Semiannual Compounding, (c) Monthly Compounding, (d) Continuous Compounding

  49. 3. Your grandfather put some money in an account for you on the day you were born. You are now 18 years old and are allowed to withdraw the money for the first time. The account currently has $3,996 in it and pays an 8% interest rate. • How much money would be in the account if you left the money there until your 25th birthday? 65th birthday? • How much money did your grandfather originally put in the account? 4. You purchased 100 shares of stock which pays share dividend with continuous compounding rate of 1%. Five years later, the stock price is HK$50 per share. What is the worth of your investment?

  50. 5. If you need €15,000 in three years, how much will you need to deposit today if you can earn 8 percent per year compounded continuously? 6. Suppose Bank One offers a risk-free interest rate of 5.5% on both savings and loans, and Bank Enn offers a risk-free interest rate of 6% on both savings and loans. • What arbitrage opportunity is available? • Which bank would experience a surge in the demand for loans? Which bank would receive a surge in deposit? • What would you expect to happen to the interest rates the two banks are offering? 7. Suppose the stock price is $35 and the continuously compounded interest rate is 5%. Assuming dividends are zero, what is the 6-month arbitrage-free forward price?

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