What is the relationship between duration and interest rate risk in fixed income investments?

Duration is a key concept in fixed income investing that measures the sensitivity of a bond's price to changes in interest rates. It helps investors understand the interest rate risk associated with a fixed income investment. Here's how duration and interest rate risk are related:

1. Duration and Price Sensitivity: Duration provides an estimate of how much a bond's price will change in response to a change in interest rates. Bonds with longer durations are more sensitive to changes in interest rates, meaning their prices will experience larger percentage changes compared to bonds with shorter durations. The relationship between duration and price sensitivity is inverse: as duration increases, price sensitivity to interest rate changes also increases.

2. Duration and Macaulay Duration: Macaulay Duration is the weighted average time it takes for an investor to receive the bond's cash flows (interest payments and principal repayment). It is used to calculate duration. Macaulay Duration is expressed in years and represents the bond's weighted average maturity.

3. Modified Duration: Modified Duration is a modified version of Macaulay Duration that provides a more direct measure of price sensitivity to interest rate changes. Modified Duration is calculated as Macaulay Duration divided by one plus the bond's yield to maturity. It represents the approximate percentage change in a bond's price for a 1% change in yield.

4. Interest Rate Risk: Duration helps investors assess the interest rate risk of a fixed income investment. When interest rates rise, bond prices generally decrease, and vice versa. By comparing the durations of different bonds, investors can gauge which bonds are more or less sensitive to interest rate changes. Bonds with longer durations have higher interest rate risk as their prices are more sensitive to changes in interest rates.

5. Hedging Interest Rate Risk: Duration can also be used to hedge interest rate risk. Investors can create a portfolio with a desired duration by combining bonds with different durations. By managing the overall duration of the portfolio, investors can offset the interest rate risk of individual bonds or positions.

It's important to note that duration is a useful measure, but it has limitations. It assumes a parallel shift in the yield curve, meaning that all interest rates change by the same amount. In reality, the yield curve may change in a nonparallel manner, which can impact the relationship between duration and price sensitivity. Other factors, such as credit risk and market conditions, should also be considered when assessing the overall risk of a fixed income investment.