Chap4Notes - Bond Price - Yield Relationship $1400 Bond...

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1 Bond Price - Yield Relationship 800 1000 1100 1200 1300 $1400 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Discount Rate Bond Value 6 3/8 The Price-Yield relationship for an option- free bond is a convex ; non-liner relationship Bond prices and market interest rates (yields) move in opposite directions. . Bond Price - Yield Relationship (2) Consider a 5% coupon 30 year bond selling at par. What will be the impact of a 1% change in yield in either direction ( y = ±1%) on the price of this bond? h @ y = 6% b P B = $86.16 b % = –13.84% h @ y = 4% b P B = $117.38 b % = +17.38% c This implies that the price-yield relationship is a nonlinear, non-symmetrical relationship, and the price-yield graph will be convex to the origin. Bond Price - Yield Relationship (3) Consider a 5% coupon; 3-year bond selling at par. Now a change in yield of 1% in either direction ( y = ±1%) has a smaller impact: h @ y = 6%, b P B = $97.33 b % = –2.71% h @ y = 4%, b P B = $102.80 b % = +2.80% c The shorter is the Term to Maturity; the lower is the bond price volatility.
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Bond Price - Yield Relationship (4) Consider a 1% coupon ; 30-year bond, selling for $38.18 to yield 5%. h @ y = 6%, b P B = $30.81 b % = –19.31% h @ y = 4%, b P B = $47.86 b % = +25.34% c The lower the coupon rate, the higher is the bond price volatility. Factors affecting Bond Price Volatility Bond price volatility (i.e. the degree of its price sensitivity to a changes in interest rates) depends three factors: Coupon rate: the lower the coupon rate, the higher is the bond price volatility. Term To Maturity: the longer is the Term to Maturity; the higher is the bond price volatility. The Yield to Maturity: the higher is the Yield to Maturity; the lower is the bond price volatility. Duration – A Measure of Bond Price Volatility s Duration is a measure of the sensitivity of the price of a bond to changes in interest rate. s It encompasses all theses three factors -- Maturity, Coupon Rate, and Initial required Yield -- that affect bond price volatility. s Duration can be considered as a weighted average of the “TIMES ” of the cash flow of a bond from the present until the various payments are received, where weights are proportional to the present value of each cash flow. s
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This note was uploaded on 04/26/2010 for the course FIN 333 taught by Professor Nasseh during the Spring '10 term at Saint Louis.

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Chap4Notes - Bond Price - Yield Relationship $1400 Bond...

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