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Chap4Notes

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

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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? head2right @ y = 6% barb4right P B = \$86.16 barb4right % = –13.84% head2right @ y = 4% barb4right P B = \$117.38 barb4right % = +17.38% checkbld 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: head2right @ y = 6%, barb4right P B = \$97.33 barb4right % = –2.71% head2right @ y = 4%, barb4right P B = \$102.80 barb4right % = +2.80% checkbld The shorter is the Term to Maturity; the lower is the bond price volatility.

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2 Bond Price - Yield Relationship (4) Consider a 1% coupon ; 30-year bond, selling for \$38.18 to yield 5%. head2right @ y = 6%, barb4right P B = \$30.81 barb4right % = –19.31% head2right @ y = 4%, barb4right P B = \$47.86 barb4right % = +25.34% checkbld 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 square4 Duration is a measure of the sensitivity of the price of a bond to changes in interest rate. square4 It encompasses all theses three factors -- Maturity, Coupon Rate, and Initial required Yield -- that affect bond price volatility.
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