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Bloomberg - Fixed Income Securities And Derivatives Handbook

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Extra info for Bloomberg - Fixed Income Securities And Derivatives Handbook Analysis And Valuation (Choudry, Cfa Level 2)

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The strips corresponding to the coupon payments have face values that equal percentages of the nominal value of the bond itself, with successively longer maturity dates; the strip corresponding to the final redemption payment has the face value and maturity date of the bond. A bond issued at time i and maturing at time T makes w payments (C1 … Cw) on w payment dates (t1, … tw-1, T ). K. 74 Bond Pricing and Spot and Forward Rates 51 function of time: C (t ), i < t ≤ T . Investors purchasing a bond at time t that matures at time T pay P(t, T ) and receive the coupon payments as long as they hold the bond.

How sensitive a bond’s price is to changes in its yield. This measure is obtained by applying a mathematical property known as a Taylor expansion to the basic equation. The relationship between price volatility and duration can be made clearer if the bond price equation, viewed as a function of r, is expanded as a Taylor series (see Butler, pp. 112–114 for an accessible explanation of Taylor expansions). 13). 13) where r = the yield to maturity of an annual-coupon-paying bond As stated above, Macaulay duration equals modified duration multiplied by (1+r).

A second-order measure of interest rate risk uses second-order derivatives. It measures the curvature of the price-yield graph and the degree to which this diverges from the straight-line estimation. Convex- 42 Introduction to Bonds ity can thus be regarded as an indication of the error made when using Macaulay and modified duration. A bond’s convexity is positively correlated to the dispersion of its cash flows: all else being equal, a bond whose cash flows are more spread out in time—that is, more dispersed—than another’s will have a higher convexity.

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