13 14 Bond Prices and Term Structure Brief

13 14 Bond Prices and Term Structure Brief - Bond Valuation...

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Comm367 1 COMM 367 Bond Valuation and Term Structure of Interest Rates
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Comm367 2 Pricing of Coupon Bonds u Bond Value = PV Coupons + PV Face Value If the interest rate is constant, where: C = Coupon paid each period r = Discount rate per period t = Number of periods t T t t B r F r C P ) 1 ( ) 1 ( 1 + + + = =
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Comm367 3 Valuing Coupon Bonds: Example 1 A bond has five years to maturity, an $80 annual coupon, and a $1000 face value. If the going rate on bonds like this one is 10%, How much is this bond worth? Time 0 1 2 3 4 5 Coupons $80 $80 $80 $80 $80 Face Value $1000 Answer: $924.18
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Comm367 4 Valuing Coupon Bonds: Example 2 Consider a 2-year U.S. Treasury Note with annual coupon rate of 8% (coupons paid semiannually) and face value $1000. The YTM is 10%. What is the fair price of the T-note today? Note: The effective annual yield is (1+5%)2 -1 = 10.25% 54 . 964 $ ) 05 . 1 ( 1000 ) 05 . 1 ( 40 4 4 1 0 = + = = t t P
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Comm367 5 Holding Period Returns of Bonds u Dollar returns from holding a bond for a certain period Coupon income Capital gain/loss u One-period holding period return yield   gain   capital     yield   current loss) (or    gain   Capital Income   Coupon HPR  0 0 + = + = P P
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Comm367 6 Valuing Coupon Bonds: Example 2 (Cont’d) u Suppose you decide to sell the bond right after you receive the 1st coupon and the yield (YTM) remains the same. What is your HPR? 3 1 40 (5% , 3) 1000 / (1.05) $972.77 40 972.77 964.54 964.54 964.54 4.15% 0.85% 5% P PVAF HPR = × + = - = + = + =
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Comm367 7 Valuing Coupon Bonds: Example 2 (Cont’d) u Suppose you decide to sell it right after you receive the 1st coupon when the yield (YTM) drops to 6%. What is your HPR? 3 1 40 (3% , 3) 1000 / (1.03) $1028.29 40 1028.29 964.54 964.54 964.54 4.15% 6.61% 10.76% P PVAF HPR = × + = - = + = + =
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8 Some Results u Coupon rates and bond prices If C/F > YTM, then P0 > F sell at a premium If C/F = YTM, then P0 = F sell at par If C/F < YTM, then P0 < F u What causes bond prices to change? Change in interest rates
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This note was uploaded on 08/03/2011 for the course ECON 503 taught by Professor Motherfucker during the Spring '11 term at Aarhus Universitet.

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13 14 Bond Prices and Term Structure Brief - Bond Valuation...

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