Blaha, Z. S. - Jindřichovská, I.: Duration and Convexity of Fixed-Income Securities; Politická ekonomie, 1 1996 (pp. 109-117), ISSN 1210-0455;
|Author(s):|| † Dr. Zdenek Sid Blaha M.A., D.B.A., |
|Type:||Articles in refereed journals|
|ISSN / ISBN:||1210-0455|
|Published in:||Politická ekonomie|
|Abstract:||The Concept of Duration & Convexity: An Overview
The duration of a bond is a measure of how long, on average, the holder of this fixed-income instrument has to wait before receiving cash payments. A zero-coupon bond that matures ins
syears has a duration ofs
syears. However, a coupon-bond maturing ins
syears has a duration of less thans
syears. This is because some of the cash payments are received by the holder prior to year n.
The duration of a bond is simply a measure of the responsiveness of its market price (intrinsic, or present value) to a change in interest rates. The greater the relative percentage change in a bond price in response to a given percentage change in interest rate, the longer the duration. In computing duration, we consider not only the maturity or term over which cash flows are received but also the time pattern of interim cash flows. Put differently, duration specifies the elasticity of the bond price to movements in yield (required rate of return).
We can achieve greater precision in measuring the bond's responsiveness to yield shifts (Δy), however, by also accounting for the bond's convexity. This is especially important when considering moderate —or large— changes in interest rates. Mathematically, duration is (only) a first approximation of the price/yield relationship. That is, duration attempts to estimate a convex relationship with a straight line (the tangent line). Hence, we have to take into account the fact that accuracy of the approximation also depends on the convexity -bowedness- of the price/yield relationship. Using convexity in conjunction with duration allows us to arrive at a more accurate estimate of the percentage change in bond price attributable to a given basis point change in yield.