Narrate Difference between duration and convexity

 Duration and convexity are both measures used in fixed-income investments to assess the sensitivity of bond prices to changes in interest rates. However, they represent different aspects and provide distinct insights. Here are the important differences between duration and convexity:

1.     Definition: Duration measures the average time it takes to receive the bond’s cash flows, including both coupon payments and principal repayment. Convexity, on the other hand, measures the curvature of the price-yield relationship of a bond.

2.     Sensitivity to Interest Rates: Duration provides an estimate of the percentage change in a bond’s price for a given change in interest rates. It captures the linear relationship between bond prices and interest rates. Convexity, however, accounts for the non-linear relationship between bond prices and interest rates, offering a more accurate measure of the price sensitivity.

3.     Price Predictability: Duration provides a reasonably reliable estimate of the bond’s price change when interest rate change. It assumes that the relationship between bond price and interest rates is linear. Convexity, with its consideration of the non-linear relationship, offers a more refined measures and improves the accuracy of the price predictions, especially for larger interest changes.

4.     Shape of the Price-Yield Curve: Duration assumes a straight-line relationship between bond prices and yields, implying a liner approximation. Convexity recognizes that the price-yield curve is not straight line but rather curved, indicating that the relationship is more complex and non-linear.

5.     Portfolio Management: Duration is commonly used for managing interest rate risk in fixed-income portfolios. It helps in assessing the overall sensitivity of the portfolio to interest rate changes. Convexity supplements duration by providing additional information on the potential magnitude of price changes and helps in fine-tuning risk management strategies.

6.     Bond Types: Duration and convexity can be applied to various types of fixed-income securities, including government bonds, corporate level bonds, mortgage-backed securities, etc. They are useful for evaluating the price behavior of individuals bonds as well as portfolios comprising multiple bonds.

7.     Calculation: Duration can be calculated directly using mathematical formulas or estimated using specialized software. Convexity, however, involves a more complex calculation that requires the second derivative of bond’s price-yield function. It is often calculated using software or financial calculations.

8.     Units of Measures: Duration is expressed in terms of years, representing the time-weighted average of the bond’s cash flows. Convexity is a dimensions measures, representing the relative change in duration.

9.     Interpretation: Duration is widely used measures for bond management and risk assessment. It indicates how sensitive a bond’s price is to charges in interest rates. Convexity complements duration by providing additional insights into the shape and curvature of the price-yield relationship, enabling a more nuanced understanding of bond price movements.

 

Overall, Duration and convexity are both valuable tools in fixed-income investing, with duration providing a simplified measure of sensitivity and convexity offering a more comprehensive and accurate analysis of price-yield relationships.