Yield-Based Bond Convexity and Portfolio Properties

Why duration alone misjudges large yield moves, how convexity measures the curvature of the price-yield relationship, how to combine duration and convexity into a sharper price-change estimate (in percent and in currency), and how to measure and interpret the duration and convexity of a bond portfolio.

1. 1. Convexity: measuring the curveDuration draws a straight line through a curved price-yield relationship; convexity measures how much the curve bends away from that line.Free14 min
2. 2. What drives convexity, and why investors value itLong maturity, low coupon, low yield and widely spread cash flows all raise convexity, and more convexity means better price behaviour when yields move a lot.12 min
3. 3. Estimating price changes with duration and convexityAdd the convexity adjustment, half of convexity times the squared yield change, to the duration estimate, and the price-change estimate moves much closer to the truth.Video · 6 min13 min
4. 4. Integrated cases: a negative-yield zero priced by handWith a negative yield and a settlement date inside the year, a spreadsheet price function is no help: you price the zero by hand, shift the yield by 1 bp to estimate duration and convexity, and then test the duration-plus-convexity estimate against a full repricing.15 min
5. 5. Money convexity: the adjustment in currencyMoney convexity is annual convexity times the position's full value, and it turns the convexity adjustment into currency units next to money duration.11 min
6. 6. Portfolio duration and convexityIn practice, a portfolio's duration and convexity are the market-value-weighted averages of its bonds' measures: easy to use, but valid only for parallel yield-curve shifts.Video · 7 min13 min