How does the duration of a fixed income security affect its price sensitivity to interest rate changes?

The duration of a fixed income security is a key factor that determines its price sensitivity to changes in interest rates. Duration is a measure of the weighted average time it takes for an investor to receive the present value of all expected future cash flows from a fixed income security, including coupon payments and the final principal payment. It is expressed in years and serves as a useful tool for assessing interest rate risk in fixed income investments.

Here's how duration affects the price sensitivity of a fixed income security to interest rate changes:

1. Inverse Relationship: There is an inverse relationship between a fixed income security's duration and its price sensitivity to interest rate changes. As a general rule, the longer the duration, the greater the price sensitivity, and vice versa. Securities with longer durations are more sensitive to changes in interest rates compared to those with shorter durations.

2. Price and Yield Relationship: When interest rates rise, the prices of existing fixed income securities fall. Conversely, when interest rates decline, bond prices rise. The relationship between bond prices and yields is not linear; rather, it is convex. This means that the percentage change in bond prices is greater for a given change in yield when yields are higher.

3. Higher Coupon, Lower Duration Sensitivity: Bonds with higher coupon rates tend to have lower durations and, consequently, lower price sensitivity to interest rate changes. This is because the higher coupon payments provide more cash flow in the earlier years, reducing the weighted average time to receive cash flows.

4. Longer Maturity, Higher Duration Sensitivity: Bonds with longer maturities generally have higher durations and, thus, greater price sensitivity to interest rate changes. Longermaturity bonds have more extended periods to receive cash flows, making them more exposed to changes in interest rates.

5. ZeroCoupon Bonds and Duration: Zerocoupon bonds have the highest duration among all bonds with similar maturities. This is because zerocoupon bonds do not make periodic coupon payments, and the entire return is received at maturity, leading to a longer weighted average time to receive cash flows.

6. Modified Duration: Modified duration is a variation of duration that measures the percentage change in the bond price for a 1% change in yield. It is a more practical measure for small changes in yield, as it accounts for the convex relationship between bond prices and yields.

Investors and fixed income analysts use duration as a risk management tool to understand how sensitive a fixed income security's price is to interest rate movements. By considering the duration of different securities within a portfolio, investors can optimize their fixed income holdings based on their risk tolerance and investment objectives.