Risk

Section: Fixed Income Risk — Duration and Convexity Estimated study time: 45 minutes Content: Interest rate risk is the primary risk facing most fixed income investors — when rates rise, bond prices fall, and vice versa. Duration is the primary measure of a bond's price sensitivity to interest rate changes. Macaulay duration is the weighted average time to receive the bond's cash flows, where each cash flow is weighted by its present value as a proportion of the bond's total price. For a zero-coupon bond, Macaulay duration equals its maturity. For a coupon bond, Macaulay duration is less than maturity because coupon payments are received earlier. Modified duration = Macaulay duration / (1 + YTM/m), where m is the number of coupon periods per year. The approximate percentage price change for a given change in yield is: % Price Change ≈ –Modified Duration × ΔYield. For example, a bond with a modified duration of 7 will experience approximately –7% price change for a +1% (100 basis point) increase in yield. Duration is additive for portfolios: portfolio duration = weighted average of individual bond durations, weighted by market value. Duration increases with: longer maturity (more distant cash flows), lower coupon rates (a larger proportion of value comes from the far-distant par payment), and lower yields (lower discount rates increase the relative weight of longer cash flows). Duration is particularly important for immunization strategies — matching portfolio duration to a liability's duration to make the portfolio's value insensitive to parallel yield curve shifts. Convexity accounts for the curvature in the price-yield relationship that duration alone misses. Because the actual price-yield relationship is convex (curved), the linear approximation from duration overstates losses…