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2-138 1 Bond Fundamentals 2 Introduction (options, future, and other derivatives) 3 Mechanics of futures markets 4 Hedging strategies using futures 5 Interest Rates 6 Determination of forward and futures prices 7 Interest rate futures 8 Swaps 9 Properties of stock options 10 Trading strategies involving options 11 Foreign Exchange Risk 12 Mechanisms for Dealing with Sovereign Risk Exposure Financial Markets and Products-(30%)
3-138 Bond Fundamentals What is a bond? Issuer/borrower Issuer/borrower Bondholder/lender Bondholder/lender Indenture bond money

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4-138 Characteristics of Bond Issuer Maturity Face Value/Par Value Coupon Rate Bond Fundamentals
5-138 What’s the FV of an initial \$100 after 3 years if y = 10%? FV = ? 100 0 1 2 3 10% Future Values

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6-138 1 2 3 0 PV = FV 1 /(1+y) FV 1 PV = FV 2 /(1+y) 2 FV 2 PV = FV 3 /(1+y) 3 FV 3 Present Values
7-138 Effective Annual Rate (EAR) Where: periodic rate = stated annual rate / m m = the number of compounding periods per year Example: Computing EAR for a rang of compounding frequencies Using a stated rate of 6%, compute EAR for semiannual, quarterly, monthly, daily compounding . Notes: what is EAR if continuous compounding? m EAR=(1 + periodic rate) -1

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8-138 Examples EXAMPLE 1: FRM EXAM 2002—QUESTION 48 An investor buys a Treasury bill maturing in 1 month for \$987. On the maturity date the investor collects \$1,000. Calculate effective annual rate (EAR). A. 17.0% B. 15.8% C. 13.0% D. 11.6% EXAMPLE 2: FRM EXAM 2002—QUESTION 51 Consider a savings account that pays an annual interest rate of 8%. Calculate the amount of time it would take to double your money. Round to the nearest year. A. 7 years B. 8 years C. 9 years D. 10 years
9-138 Price-Yield Relationship T t t t=1 C P = (1 + y) t where: C = the cash flow (coupon or principal) in period t t = the number of periods (e.g., half-years) to each payment T = the number of periods to final maturity y = the discounting rate per period

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10-138 Price-Yield Function cF Perpetual bonds: P= y
11-138 Taylor Expansion 0 0 1 1 ' '' 2 1 0 0 0 ( ), ( ), ( ) Taylor expansion: 1 ( ) ( )( ) . .. 2 P f y P f y P f y P P f y y f y y = = = = + ∆ + ∆ + : duration convexity

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12-138 Macaulay Duration Definition : the average time to wait for each payment, weighted by the present value of the associated cash flow. 0 1 2 100 100 y=10% 2 2 2 1 100/(1 10%) 100/(1 10%) 1 2 [100/(1 10%)] [100/(1 10%) ] [100/(1 10%)] [100 /(1 10%) ] =0.5238+0.9524=1.4762 ( ) T t t D t w = + + = × = × + × + + + + + +
13-138 Modified Duration * 1 D D y = + * 2 1 [ ]( ) [ ]( ) . .. 2 P D P y C P y ∆ = - × ∆ + × ∆ + Modified duration Taylor expansion for the change in the price of a bond

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