Lecture 3 no sol

# Lecture 3 no sol - IMSE3010 Financial Engineering Lecture 3...

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IMSE3010 Financial Engineering Lecture 3 Fixed-Income Securities Common Stocks Miao Song Dept of Industrial & Manufacturing Systems Engineering

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1/24/2011 2 Review of Lecture 2 ± Present Value ² Annuity and Perpetuity ² Mortgage Calculation ± Fixed-Income Securities ² Fixed-Income Markets ² Term Structure of Interest Rate ² Bond Pricing
Discount Bonds vs. Coupon Bonds ± Discount Bond ² Get \$1 payment at maturity t ² B t = 1 / (1 + r t ) t ± Coupon Bond ² Definition ± Maturity T ± Coupon rate c ± Face value / principle P ² Cash Flow ± Get coupon C = c×P at any time t = 1,…,T ± Get principle P at maturity T ² B = B 1 ×C + B 2 ×C + … + B T ×C + B T ×P 1/24/2011 3

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1/24/2011 4 Agenda ± Fixed-Income Securities ² Yield-To-Maturity ² Forward Interest Rates ² Risks Associated with Bonds ± Common Stocks
Yield-to-Maturity ± What is the average annual return (IRR) if an investor buy the bond today and hold it until maturity? ± Yield-to-maturity of a bond, denoted by y, is given by ± Given maturity, principle and coupon rate, one to one mapping between YTM and bond price ± In the market, it is conventional to quote bond prices in YTM 1/24/2011 5

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Example ± Current 1- and 2-year spot interest rates are 5% and 6%, respectively. ± What is the price of a 2-year Treasury coupon bond with par value of \$100 and a coupon rate of 6%? ± What is the YTM? ± What is the difference between YTM definition and bond pricing formula? ± What is the YTM of discount bonds? 1/24/2011 6

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Relationship between YTM and Bond Price ± When is YTM = coupon rate? ± When is YTM = 0? ± When is YTM = ? ± If YTM increasing / decreasing in bond price? 1/24/2011 8
YTM as a Function of Bond Price ± A 2-year Treasury coupon bond with par value of \$100 and a coupon rate of 6% 1/24/2011 9

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1/24/2011 10 Agenda ± Fixed-Income Securities ² Yield-To-Maturity ² Forward Interest Rates ² Risks Associated with Bonds ± Common Stocks
Forward Interest Rate ± Spot interest rate: rates for transaction between today, 0, and a future date, t ± Forward interest rate: rates for a transaction between two future dates, e.g., t 1 and t 2 ± For a forward transaction to borrow money in the future ² Terms of the transaction are agreed on today, t = 0 ² Loan is received on a future date t 1 ² Repayment of the loan occurs on date t 2 ± Future spot rate = current corresponding forward rate?

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Lecture 3 no sol - IMSE3010 Financial Engineering Lecture 3...

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