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Derivatives I Problem Solving Session

Derivatives I Problem Solving Session. DERIVATIVES │ CFA LEVEL I. Harvard Extension School MGMT E-2900b CFA Exam Level I April 20, 2010. Derivatives I Problem Solving Session. Jeffery Lippens Lecturer Tray Spilker Teaching Assistant. DERIVATIVES │ CFA LEVEL I. Derivatives.

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Derivatives I Problem Solving Session

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  1. Derivatives I Problem Solving Session DERIVATIVES│CFA LEVEL I • Harvard Extension School • MGMT E-2900b • CFA Exam Level I • April 20, 2010

  2. Derivatives I Problem Solving Session • Jeffery Lippens • Lecturer • Tray Spilker • Teaching Assistant DERIVATIVES│CFA LEVEL I

  3. Derivatives • Topic Area Weights for the CFA Exam DERIVATIVES│CFA LEVEL I

  4. Derivates I Problem Solving Session • Introduction to Derivative Markets & Instruments • Options Markets, Puts & Calls, & Put-Call Parity • Risk Management Applications of Option Strategies DERIVATIVES│CFA LEVEL I Study Session 17 Readings 67,70 & 72

  5. Introduction to Derivatives • A derivative security is: • a financial asset that bears no risk. • a financial asset that offers a return based on the return of another asset or security. • a financial asset with no maturity. DERIVATIVES│CFA LEVEL I

  6. Introduction to Derivatives • A derivative security is: • a financial asset that bears no risk. • a financial asset that offers a return based on the return of another asset or security. • a financial asset with no maturity. DERIVATIVES│CFA LEVEL I

  7. Introduction to Derivatives • Exchange-traded derivatives: • are standardized and backed by a clearinghouse. • are largely unregulated and backed by a dealer counterparty. • include forwards and swaps. DERIVATIVES│CFA LEVEL I

  8. Introduction to Derivatives • Exchange-traded derivatives: • are standardized and backed by a clearinghouse. • are largely unregulated and backed by a dealer counterparty. • include forwards and swaps. DERIVATIVES│CFA LEVEL I

  9. Introduction to Derivatives • A customized, or bespoke, agreement to sell 37,500 pounds of coffee in one month is an example of: • a futures contract. • a swaption. • a forward commitment. DERIVATIVES│CFA LEVEL I

  10. Introduction to Derivatives • A customized, or bespoke, agreement to sell 37,500 pounds of coffee in one month is an example of: • a futures contract. • a swaption. • a forward commitment. DERIVATIVES│CFA LEVEL I

  11. Introduction to Derivatives • A futures contract is most likely: • adjusted daily to account for profits and losses. • a contingent claim. • traded over-the-counter (OTC). DERIVATIVES│CFA LEVEL I

  12. Introduction to Derivatives • A futures contract is most likely: • adjusted daily to account for profits and losses. • a contingent claim. • traded over-the-counter (OTC). DERIVATIVES│CFA LEVEL I

  13. Introduction to Derivatives • A swap is least likely: • the exchange of one asset for another. • a series of options contracts. • traded over-the-counter (OTC). DERIVATIVES│CFA LEVEL I

  14. Introduction to Derivatives • A swap is least likely: • the exchange of one asset for another. • a series of options contracts. • traded over-the-counter (OTC). DERIVATIVES│CFA LEVEL I

  15. Introduction to Derivatives • The right but not the obligation to sell an asset at a particular price in the future is an example of: • a short futures position. • a call option. • a put option. DERIVATIVES│CFA LEVEL I

  16. Introduction to Derivatives • The right but not the obligation to sell an asset at a particular price in the future is an example of: • a short futures position. • a call option. • a put option. DERIVATIVES│CFA LEVEL I

  17. Introduction to Derivatives • Which of the following could be considered benefits of derivatives: they (1) provide price information, (2) allow investors to manage risk, (3) provide access to leverage, and (4) reduce transactions costs? • 2 & 4 • 1, 2, & 4 • All of the above DERIVATIVES│CFA LEVEL I

  18. Introduction to Derivatives • Which of the following could be considered benefits of derivatives: they (1) provide price information, (2) allow investors to manage risk, (3) provide access to leverage, and (4) reduce transactions costs? • 2 & 4 • 1, 2, & 4 • All of the above DERIVATIVES│CFA LEVEL I

  19. Introduction to Derivatives • The “law of one price” argues that: • two assets with identical payoffs will have the same price. • arbitrage opportunities do not exist. • risk management is futile. DERIVATIVES│CFA LEVEL I

  20. Introduction to Derivatives • The “law of one price” argues that: • two assets with identical payoffs will have the same price. • arbitrage opportunities do not exist. • risk management is futile. DERIVATIVES│CFA LEVEL I

  21. Introduction to Derivatives • Explained: • Arbitrage is the process of creating “risk-less” profit when assets with identical payoffs become mispriced; buy the lower priced asset and sell (short) the higher priced asset. The Law of One Price enforces this relationship. DERIVATIVES│CFA LEVEL I

  22. Option Markets and Contracts • Which of the following is in the money? • a put option with S > X • a call option with S – X > 0 • a put option with S – X > 0 DERIVATIVES│CFA LEVEL I

  23. Option Markets and Contracts • Which of the following is in the money? • a put option with S > X • a call option with S – X > 0 • a put option with S – X > 0 DERIVATIVES│CFA LEVEL I

  24. Option Markets and Contracts • Which of the following is not in the money? • a put option with X – S < 0 • a put option with S < X • a call option with S – X > 0 DERIVATIVES│CFA LEVEL I

  25. Option Markets and Contracts • Which of the following is not in the money? • a put option with X – S < 0 • a put option with S < X • a call option with S – X > 0 DERIVATIVES│CFA LEVEL I

  26. Option Markets and Contracts • Contrary to European options, American options: • cannot be exercised prior to maturity. • will always vary in price against a European option due to exchange rate risk. • may have a higher value versus a similar European option. DERIVATIVES│CFA LEVEL I

  27. Option Markets and Contracts • Contrary to European options, American options: • cannot be exercised prior to maturity. • will always vary in price against a European option due to exchange rate risk. • may have a higher value versus a similar European option. DERIVATIVES│CFA LEVEL I

  28. Option Markets and Contracts • Explained: • An American option gives the option holder the right to exercise the option prior to expiration DERIVATIVES│CFA LEVEL I

  29. Option Markets and Contracts • Which of the following about puts and calls is most accurate? • Option prices are positively correlated to the time to maturity. • The price of the underlying security will exhibit more volatility than the option. • An increase in market interest rates will increase the value of a call and decrease the value of a put. DERIVATIVES│CFA LEVEL I

  30. Option Markets and Contracts • Which of the following about puts and calls is most accurate? • Option prices are positively correlated to the time to maturity. • The price of the underlying security will exhibit more volatility than the option. • An increase in market interest rates will increase the value of a call and decrease the value of a put. DERIVATIVES│CFA LEVEL I

  31. Option Markets and Contracts • Five inputs to options prices: • S = price of underlying stock • X = exercise price of the option • T = time to expiration • Rf = risk-free rate • V = volatility of underlying stock price • Positive Correlation: • Calls  S, T, Rf, & V • Puts X, T, & V • Negative Correlation: • Calls  X • Puts S & Rf DERIVATIVES│CFA LEVEL I

  32. Option Markets and Contracts • Explained (cont) • C = S + P – X / (1+Rf)T • P = C – S + X / (1 + Rf)T • As Rf ↑ X / (1 + Rf )T ↓ • Call ↑ • Put ↓ DERIVATIVES│CFA LEVEL I

  33. Option Markets and Contracts • Which of the following is least accurate? • The holder of a put has the right to sell to the writer of the option. • The writer of a call has the obligation to buy to the holder of the option. • The holder of a call has the right to buy from the writer of the option. DERIVATIVES│CFA LEVEL I

  34. Option Markets and Contracts • Which of the following is least accurate? • The holder of a put has the right to sell to the writer of the option. • The writer of a call has the obligation to buy to the holder of the option. • The holder of a call has the right to buy from the writer of the option. DERIVATIVES│CFA LEVEL I

  35. Option Markets and Contracts • Explained: • Writer: has the obligation to buy from a put holder and sell to a call holder. • Holder: has the right, but not the obligation, to buy when holding a call, or sell when holding a put. DERIVATIVES│CFA LEVEL I

  36. Option Markets and Contracts • Question 14 – 16: • Consider a call option with a strike of $42.50, priced at $10, when the underlying stock trades at $50 • What is the time value of the call? • $7.50 • $5.00 • $2.50 DERIVATIVES│CFA LEVEL I

  37. Option Markets and Contracts • Consider a call option with a strike of $42.50, priced at $10, when the underlying stock trades at $50 • What is the time value of the call? • $7.50 • $5.00 • $2.50 DERIVATIVES│CFA LEVEL I Intrinsic Value = S – X = $50 - $42.50 = $7.50 Time Value = $10 - $7.50 = $2.50

  38. Option Markets and Contracts • Question 14 – 16: • Consider a call option with a strike of $42.50, priced at $10, when the underlying stock trades at $50 • What is the lower bound of the call price? • $7.50 • $5.00 • $2.50 DERIVATIVES│CFA LEVEL I

  39. Option Markets and Contracts • Question 14 – 16: • Consider a call option with a strike of $42.50, priced at $10, when the underlying stock trades at $50 • What is the lower bound of the call price? • $7.50 • $5.00 • $2.50 DERIVATIVES│CFA LEVEL I Lower Bound of a Call: Ct = max [0, St – X] = max [0, $50 – $42.50]= $7.50

  40. Option Markets and Contracts • Question 14 – 16: • Consider a call option with a strike of $42.50, priced at $10, when the underlying stock trades at $50 • What is the upper bound of the call price? • $10.00 • $50.00 • $42.50 DERIVATIVES│CFA LEVEL I

  41. Option Markets and Contracts • Question 14 – 16: • Consider a call option with a strike of $42.50, priced at $10, when the underlying stock trades at $50 • What is the upper bound of the call price? • $10.00 • $50.00 • $42.50 DERIVATIVES│CFA LEVEL I • Upper Bound of a Call: Ct ≤ St • Why pay more for the right to buy an asset than the asset is worth?

  42. Option Markets and Contracts • What is the lower bound of a European put option with a strike of $50, when the underlying stock trades at $40, the risk-free rate is 2%, and there is 3 months to maturity? • $10.00 • $9.75 • $9.02 DERIVATIVES│CFA LEVEL I

  43. Option Markets and Contracts • What is the lower bound of a European put option with a strike of $50, when the underlying stock trades at $40, the risk-free rate is 2%, and there is 3 months to maturity? • $10.00 • $9.75 • $9.02 DERIVATIVES│CFA LEVEL I Max [0, X / (1+Rf)T – S] Max [0, 50/(1.02)(.25) – 40 Max [0, 9.75] = $9.75

  44. Option Markets and Contracts • What is the lower bound of an American call option on non-dividend paying stocks? • Max [0, X – S] • Max [0, X/(1+Rf)T – S] • Max [0, S – X/(1+Rf)T] DERIVATIVES│CFA LEVEL I

  45. Option Markets and Contracts • What is the lower bound of an American call option on non-dividend paying stocks? • Max [0, X – S] • Max [0, X/(1+Rf)T – S] • Max [0, S – X/(1+Rf)T] DERIVATIVES│CFA LEVEL I

  46. Option Markets and Contracts • Explained: • C = Max [0, X – S] • c = Max [0, s – x/(1+rf)T] • Because the American option has greater properties than the European option, S – X/(1+Rf)T] must also be the lower bound for an American call option • Thus, C = Max [0, S – X/(1+Rf)T] DERIVATIVES│CFA LEVEL I

  47. Option Markets and Contracts • How would an investor adjust the put-call parity formula for assets that generate cash flows? • Reduce the strike price by the future value of the cash flows. • Reduce the underlying asset value by the present value of the cash flows. • Add the future value of cash flows to the underlying asset value. DERIVATIVES│CFA LEVEL I

  48. Option Markets and Contracts • How would an investor adjust the put-call parity formula for assets that generate cash flows? • Reduce the strike price by the future value of the cash flows. • Reduce the underlying asset value by the present value of the cash flows. • Add the future value of cash flows to the underlying asset value. DERIVATIVES│CFA LEVEL I

  49. Option Markets and Contracts • A forward rate agreement, has the same payoff as: • A long position in an interest rate call option • A short position in an interest rate put option • A long position in an interest rate call and a short position in an interest rate put option DERIVATIVES│CFA LEVEL I

  50. Option Markets and Contracts • A forward rate agreement, has the same payoff as: • A long position in an interest rate call option • A short position in an interest rate put option • A long position in an interest rate call and a short position in an interest rate put option DERIVATIVES│CFA LEVEL I

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