Although duration measures can be calculated for individual bonds, in reality, most investors hold a portfolio of bonds, and when this is the case, it's often more useful for investors to measure sensitivities at the portfolio level.

In practice, what's typically done is to calculate portfolio sensitivities as a weighted average of the individual bond positions.

For example, let's take McCauley duration.

We can calculate the weighted McCauley duration of a portfolio by multiplying each bond's McCauley duration by its weight in the portfolio.

This weight is typically based on the current market values.

The result is a portfolio wide macauley duration that gives us a good sense of the overall interest rate sensitivity of the portfolio.

This can then be compared to the sensitivity of a benchmark.

For instance, the same approach can be applied to modified duration.

However, for DV01, the process is slightly different.

Since DV01 already accounts for the size of each bond position, we simply sum up the individual DV01 values across the portfolio.

The portfolio DV01 then tells us how much the portfolio's value is expected to change for each basis point move in yields.

While these approaches are relatively simple and straightforward, they do come with a limitation, both the weighted average portfolio modified duration and the portfolio DV01, only approximate value changes in the case of a parallel shift of the yield curve.

In other words, they assume that yields at all maturities move by the same amount.

If, however, a portfolio consists of very different bonds such as one year bonds and 30 year bonds, it might not be realistic to assume that yields for both these maturities will always move in the same way.

In such cases, it's helpful to get a more granular view of the portfolio's interest rate risk, to better understand where along the yield curve the portfolio's risks are concentrated, and to assess curve risk more accurately, we can use a tool called an interest rate Delta Ladder.

The interest rate Delta Ladder provides a more detailed breakdown of a bond portfolio's interest rate risk.

Then portfolio duration measures by segmenting the portfolio based on time to maturity.

Each step on the ladder represents a specific time to maturity, often referred to as key rates.

Here's how we calculate it step by step.

First, we define the key rates we'll be analyzing.

These might include one year, two year, three year, five year, et cetera, depending on the structure of the portfolio.

Next, we calculate the current portfolio value using the actual yield curve.

This means that one year bonds are priced using the one year yield, two year bonds with the two year yield, and so on.

The result is the initial portfolio value under current market conditions.

Now we shift the first key rate, for example, the one year rate up by one basis point.

With this new slightly adjusted yield curve, we recalculate the portfolio value.

The difference between the original portfolio value and this new hypothetical portfolio value represents the DV01 for the one year key rate.

For example, if the portfolio's value decreases by $20,000, then the one year DV01 of the portfolio would be negative $20,000.

This tells us how sensitive the portfolio is to interest rate changes at the one year maturity point.

After that, we bring the first key rate back to its original level and shift the next key rate.

For example, the two year rate by one basis point.

Once again, we recalculate the portfolio value and determine the DV01 for the second key rate.

This process continues for each key rate.

Although these calculations are more complex than portfolio duration calculations, the benefit is clear.

The investor can now see how their portfolio is exposed to interest rate changes at a variety of different points of the yield curve.