Brailsford3eSM_Ch06 - Chapter 6 Bonds Learning objectives...

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Copyright © 2006 Nelson Australia Pty Limited Chapter 6 Bonds Learning objectives After the completion of this chapter, you should be able to: value coupon paying bonds understand the impact of coupons on bond price and returns understand the relationship between duration, convexity and bond price changes use duration to immunise a single liability describe and estimate the yield curve given a sample of coupon-paying bonds Key points 1 Bonds are priced by treating coupon payments as zero-coupon paying bonds. 2 Changes in bond prices can be estimated using duration and convexity. 3 Duration also used in immunising a bond position. Chapter outline 6.1 Introduction 1 Coupon bonds are generally issued with term greater than 12 months. 2 Example include government bonds, semi-government bonds and corporate securities (eg. debentures). 6.2 Pricing of a coupon-paying bond 1 Coupon bonds are priced by discounting coupons and face value. 2 Discounting equation is more easily expressed as an annuity. 3 Where coupon rate is greater than (less than) the discount rate, implies price is greater than (less than) the face value. 4 Need to adjust for coupon timing and ex-interest bonds. 6.3 Duration and convexity 1 Macaulay’s duration provides measure of sensitivity of a coupon paying bond price to changes in one plus the yield. One of the advantages of Macaulay’s duration is that it is simplistic and easy to use. 2 Fisher-Weil duration not necessarily the price according to market conventions. 3 Portfolio duration is additive, calculated by value-weighting the individual bond duration measures. 4 Duration is pivotal time to maturity, and is used to immunise the value of a bond from parallel shifts in the yield curve.
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2 Investments: Concepts and Applications Solutions Manual Copyright © 2006 Nelson Australia Pty Limited 5 Convexity takes into account the fact that the relationship between bond price and yield is not linear. 6.4 Estimation of zero-coupon yield curve 1 Spot rate curve is the yield curve for coupon-paying bonds. 2 Commonly estimated using quadratic approximation. 6.5 Indexed bonds 1 Bonds linked to some economic variable (ie. indicator). 2 An example is an inflation-linked bond, whereby the nominal (real) amount of the coupon increases to offset (remains unchanged due to) changes in inflation. Solutions to text problems Problems and applications 1 Coupon bonds can be viewed as a portfolio of zero coupon bonds. The following diagram shows how the coupon paying bond can be broken down into zero coupon bonds. Here it is assumed the coupon paying bond pays coupons of $100 on each coupon date and has a face value of $10,000. C(1) C(2) C(3) C(4) + principal Standard coupon bond 100 100 100 100 + 10,000 === === === ========== This bond can be duplicated using a portfolio consisting of four zero coupon bonds as follows. Zero coupon bond 1
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This note was uploaded on 02/06/2011 for the course FINM 3402 at Queensland.

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Brailsford3eSM_Ch06 - Chapter 6 Bonds Learning objectives...

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