Many financial institutions mistakenly think of effective duration as a measure of time, as opposed to a measure of price sensitivity. When measuring duration in terms of time, institutions are actually calculating a "Macaulay" or cash flow duration. Effective duration represents the percent change in the price of an asset for a given change in rates.
Another common misconception is that effective duration is always measured using 100 BP increments. In fact, effective duration can be measured for all levels of rate movements, and is most accurate in predicting price changes for very small changes in rates. One example would be a 10 BP movement in rates.
To help clarify how effective duration works, consider this scenario: Assume an asset has a 6% effective duration using 100 BP rate movements. This asset's price should rise and fall by approximately 6% for a 1% parallel change in interest rates. For parallel changes in the yield curve, effective duration does an adequate job of estimating price changes, but what happens when rates don't move in parallel fashion?
In most cases, when rates move at each point along the yield curve, it doesn't happen in equal increments. We refer to this as changes in the shape of the curve. This means rates at the 10-year part of the curve will most often move in different increments than rates at the two-year part of the curve. In some cases, the rates may even move in different directions.
So, how does effective duration fit into this problem? The answer is, very poorly. An asset with an effective duration of 6% may have some sensitivity to the 10-year part of the yield curve and some sensitivity to the three-year part on the curve. Therefore, its price may not move 6% when rates fall, depending on how much each point on the curve decreases.
Let's take a look at a 30-year mortgage loan as an example. A new 30-year mortgage loan with a rate of 4.50% has an effective duration of 6.50%. However, the loan has the following sensitivities to each point on the curve, as demonstrated in the table accompanying this article.
This table shows the key rate duration estimates for our mortgage loan example. Also referred to as "partial durations" in some circles, it basically breaks down the effective duration into individual periods along the curve. The top line represents the effective duration at each point on the curve, while the bottom line represents the percent of each point on the curve in relation to the total effective duration.
As indicated, the 30-year loan is 33% sensitive to the nine-year portion of the curve, more than at any other point. That means if the nine-year point increases or decreases, it will impact the price of the asset more than any equal rate change at any other single point on the curve. This type of analysis is particularly important if you care about using an effective duration number in anything other than a standard ALM run that only looks at parallel changes in rates.
One specific application for this type of analysis would be hedging an asset from changes in interest rates. Looking only at the total effective duration of 6.50% would lead to the conclusion that a 7-year borrowing or a swap transaction with a 6.5% effective duration would be needed to effectively hedge the asset. However, since the borrowing and swap are bullet cash flows, almost 100% of their sensitivity is at their effective duration point on the curve, which in this case is seven years. So, if rates increased 100 bps on the seven-year point on the curve only, the asset would lose 0.88%, while the swap or borrowing would gain 6.5%.
To counteract this issue, the correct hedge will align positions along each portion of the yield curve in equal sensitivities to the asset, so that when the yield curve changes shape, the financial institution receives the correct offsetting change in value.
Travis Goodman, is senior financial advisor for
