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Aggregate money duration

What Is Aggregate Money Duration?

Aggregate money duration is a measure of the overall interest rate sensitivity of a portfolio of fixed-income securities, expressed in currency units. It quantifies the approximate change in the monetary value of a bond portfolio for a given change in interest rates. As a concept within fixed income analysis, aggregate money duration provides portfolio managers and investors with a critical tool to understand and manage interest rate risk. Unlike duration measures expressed in years, aggregate money duration directly translates interest rate changes into potential gains or losses in the portfolio's value.

History and Origin

The foundational concept of duration, from which aggregate money duration is derived, was introduced by Canadian economist Frederick Robertson Macaulay in his seminal 1938 work, The Movements of Interest Rates, Bond Yields and Stock Prices in the United States since 1856. Macaulay sought to provide a more accurate measure of a bond's effective maturity beyond its stated term, considering the timing of all its cash flows. While Macaulay's initial focus was on what is now known as Macaulay duration, his work laid the groundwork for subsequent developments in duration analysis, including modified duration and, by extension, aggregate money duration. The adoption of duration as a primary tool for measuring interest rate risk gained significant traction in the 1970s, as interest rates became more volatile and investors sought better metrics to assess bond price sensitivity6, 7.

Key Takeaways

  • Aggregate money duration quantifies a bond portfolio's sensitivity to interest rate changes in monetary terms.
  • It provides a direct estimate of the potential dollar (or other currency) change in a portfolio's value for a given change in interest rates.
  • Portfolio managers use aggregate money duration to manage interest rate risk and implement hedging strategies.
  • A higher aggregate money duration indicates greater sensitivity of the portfolio's value to interest rate fluctuations.

Formula and Calculation

The aggregate money duration for a portfolio is calculated by summing the money durations of each individual security within the portfolio. The money duration of a single bond is derived by multiplying its modified duration by its current market bond price.

The formula for the money duration of a single bond is:

Money Durationbond=Modified Durationbond×Bond Pricebond\text{Money Duration}_{\text{bond}} = \text{Modified Duration}_{\text{bond}} \times \text{Bond Price}_{\text{bond}}

For a portfolio, the aggregate money duration is then:

Aggregate Money Durationportfolio=∑i=1n(Modified Durationi×Bond Pricei)\text{Aggregate Money Duration}_{\text{portfolio}} = \sum_{i=1}^{n} (\text{Modified Duration}_{i} \times \text{Bond Price}_{i})

Where:

  • (\text{Modified Duration}_{i}) = the modified duration of bond i
  • (\text{Bond Price}_{i}) = the market price of bond i
  • (n) = the total number of bonds in the portfolio

The estimated change in a portfolio's value (in currency) due to an interest rate change can be approximated using the aggregate money duration:

ΔPortfolio Value≈−Aggregate Money Durationportfolio×ΔYield\Delta \text{Portfolio Value} \approx - \text{Aggregate Money Duration}_{\text{portfolio}} \times \Delta \text{Yield}

Where:

  • (\Delta \text{Portfolio Value}) = the change in the portfolio's market value
  • (\Delta \text{Yield}) = the change in the portfolio's yield (expressed as a decimal, e.g., 0.01 for a 1% change)

Interpreting the Aggregate Money Duration

Interpreting aggregate money duration is straightforward: it indicates the approximate monetary loss or gain a portfolio could experience for a 1% (or 100 basis point) change in interest rates. For example, if a portfolio has an aggregate money duration of $500,000, it suggests that a 1% increase in interest rates would lead to an approximate $5,000 decline in the portfolio's value ($500,000 * 0.01 = $5,000). Conversely, a 1% decrease would lead to an approximate $5,000 increase. This direct monetary translation makes aggregate money duration particularly useful for risk management and setting specific tolerance levels within portfolio construction strategies. It helps investors quantify the potential impact of interest rate movements on their total capital.

Hypothetical Example

Consider a portfolio containing two coupon bonds:

Bond A:

  • Current Market Price: $1,000
  • Modified Duration: 5 years

Bond B:

  • Current Market Price: $2,500
  • Modified Duration: 8 years

First, calculate the money duration for each bond:

  • Money Duration (Bond A) = $1,000 (Price) * 5 (12345