Convexity in Fixed Income Portfolio Management

Fixed income portfolio management plays a crucial role in achieving investment objectives while managing risk. Convexity, a concept within fixed income markets, has gained significant attention due to its impact on portfolio optimization.

Most fixed income investors are very familiar with the use of various duration (Macaulay, Modified, Option Adjusted, Effective…) measures to estimate the interest sensitivity of their portfolios. The most widely used measure is modified duration, which assumes that the relationship between the price of a bond and yield is linear. This assumption is valid as long as yield moves are infinitely small. Nevertheless, over the past 20 months, bond yields have moved significantly as central banks raised interest rates globally, and started to unwind some of the quantitative easing policies with the aim to fight soaring inflation. From the US to Germany to Japan, yields that were almost unthinkable at the start of 2023 are now within reach. By the end of September, the 10-year German Government yields are close to 3%, a level not reached since 2011. Their US equivalent are back in line with the average from before the Global Financial Crisis rising above 4.50%, even touching as high as 5% in October 2023.

This situation has reverted and fixed income markets delivered strong returns in November. The Bloomberg US Aggregate bond index, which tracks total returns across the US fixed income spectrum, rose circa 4.4%, marking the best monthly performance since May 1985. Yields on 10-year US Treasuries have fallen more than 100 basis points since its 16-year high reached on 19th October. This sudden change in fixed income sentiment is being driven by investors’ views that interest rates have now peaked as inflation prints across major developed economies are falling fast, undershooting consensus estimates.

Read this document to learn about the concept of convexity, its formula, and the implications it holds for various fixed income instruments, including long-term treasury bonds, convertible bonds, and investment-grade corporate bonds.