Dollar duration is a measure of interest rate risk that quantifies the sensitivity of the price of a fixed-income security or a portfolio of fixed-income securities to a 1% change in interest rates. It is a useful metric for bond investors and portfolio managers who want to assess the potential impact of interest rate movements on the value of their bond holdings.

The dollar duration of a bond or a bond portfolio is calculated as follows:

\[ \text{Dollar Duration} = -\frac{1}{100} \times \text{Modified Duration} \times \text{Market Value} \]

Here are the key components of the formula:

– **Modified Duration:** Modified duration is a measure of the sensitivity of a bond’s price to changes in interest rates. It is expressed as a percentage and is a modified version of Macaulay duration, adjusted for changes in interest rates.

– **Market Value:** This represents the current market value of the bond or bond portfolio.

– **1/100:** This term is included to convert the modified duration from a percentage change in bond price to a dollar change for a 1% change in interest rates.

The negative sign in the formula reflects the inverse relationship between bond prices and interest rates; as interest rates rise, bond prices generally fall, and vice versa.

Key points about dollar duration:

1. **Interest Rate Sensitivity:**

– Dollar duration provides an estimate of how much the price of a bond or a bond portfolio is expected to change in response to a 1% change in interest rates. It quantifies the interest rate risk associated with fixed-income investments.

2. **Duration Matching:**

– Dollar duration is often used in duration matching strategies, where investors attempt to match the duration of their bond portfolios with their investment time horizon or liabilities. This helps minimize interest rate risk.

3. **Convexity Consideration:**

– While dollar duration provides a linear approximation of interest rate risk, it does not account for the curvature in the bond price-yield relationship. Convexity, another risk measure, addresses the curvature and provides a more accurate estimate of bond price changes for larger interest rate movements.

4. **Portfolio Management:**

– Portfolio managers use dollar duration to assess and manage interest rate risk in bond portfolios. By understanding the dollar duration of individual securities and the overall portfolio, managers can make informed decisions to adjust the portfolio’s risk exposure.

5. **Duration vs. Dollar Duration:**

– Duration is a relative measure of interest rate risk, expressed as a weighted average time to receive the bond’s cash flows. Dollar duration, on the other hand, provides an absolute measure in currency terms, reflecting the potential change in portfolio value.

6. **Limitations:**

– Dollar duration assumes a parallel shift in the yield curve, meaning that interest rates across all maturities change by the same amount. In reality, yield curve shifts can be non-parallel, and other factors, such as changes in credit spreads, can also impact bond prices.

Investors and portfolio managers use dollar duration as part of their risk management and asset allocation strategies. It helps them assess the interest rate risk associated with their bond holdings and make informed decisions based on their risk tolerance and investment objectives.