Duration and Convexity

Imagine you have a seesaw at a playground. When you apply a small push at one end, the other end moves in response — the amount it moves depends on where you push and how much force you use. In the world of bonds, duration and convexity measure how much a bond’s price will move in response to changes in interest rates, helping investors understand the sensitivity and risk of their fixed income investments.

What is Duration?

Duration is a measure of a bond’s price sensitivity to interest rate changes. Specifically, it estimates the percentage change in a bond’s price for a 1% change in interest rates. The higher the duration, the more sensitive the bond price is to changes in interest rates.

There are different types of duration:

1. Macaulay Duration: The weighted average time (in years) until the bond’s cash flows are received.
   

2. Modified Duration: Adjusts Macaulay Duration to directly estimate price sensitivity, showing the percentage price change for a 1% change in yield.
   

Formula for Modified Duration:
Modified Duration = Macaulay Duration / (1 + y/n)

Where:

• y = yield to maturity
  
• n = number of coupon periods per year
  

Example:

A bond with a modified duration of 5 means that for every 1% increase in interest rates, the bond’s price will fall approximately 5%.

What is Convexity?

Convexity measures the curvature in the relationship between bond prices and interest rates. It accounts for the fact that the price-yield relationship is not linear but curved. Convexity provides a more accurate estimate of price changes for large movements in interest rates, improving upon duration’s linear approximation.

• Positive convexity means bond prices rise more for a decrease in yields than they fall for an equivalent increase.
  
• Bonds with higher convexity are less affected by interest rate volatility and are generally preferred by investors.
  

Why Are Duration and Convexity Important?

1. Risk Measurement: Duration helps investors quantify the interest rate risk associated with a bond or bond portfolio.
   

2. Portfolio Management: Understanding duration and convexity allows portfolio managers to immunize portfolios against interest rate movements or to position for expected rate changes.
   

3. Pricing Accuracy: Convexity improves the accuracy of price change estimates for bonds, especially when interest rates fluctuate significantly.
   

In India, bond investors closely monitor duration and convexity when investing in government securities and corporate bonds. These metrics are important for managing portfolios, especially given the Reserve Bank of India’s monetary policy actions, which affect interest rates.

Duration and convexity are vital tools for fixed income investors to manage interest rate risk and understand how bond prices respond to market changes. In the next chapter, we will explore State Government Bonds — a key segment within the fixed income market offering unique opportunities and risks.