Using Duration to Scale Interest-Rate Effects on Asset Valuations
Summary
The document proposes using duration as a rough way to visualize how interest-rate changes affect bond prices and, by analogy, other asset valuations. For a bond, it gives the approximation that a rate rise of x percentage points leads to a price decline of about duration multiplied by x percent. This captures the idea that the same absolute yield change can have a larger estimated price impact for a longer-duration asset.
It suggests estimating an asset class’s average duration to approximate its sensitivity to rates, including when comparing changes in risk-free yields under fixed earnings and equity-risk-premium assumptions. The method is explicitly rough: duration and maturity differ, and non-bond asset values depend on other drivers. Those drivers, their relationships to valuations, and estimated asset-class duration can change over time. The document provides an illustrative bond calculation, but no empirical validation for applying the approximation to equities or other asset classes.
Key ideas
- Duration provides a rough estimate of bond price sensitivity to changes in interest rates.
- For bonds, the document approximates the percentage price decline as duration multiplied by the rate increase in percentage points.
- An estimated average duration can be used to sketch rate sensitivity for other asset classes.
- The analogy is limited because other valuation drivers matter and asset-class sensitivities can change over time.
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Full text
# How to scale t-bond yield movements on a chart to visualize its relative impact to the pricing of other assets? # How to scale t-bond yield movements on a chart to visualize its relative impact to the pricing of other assets? How does one scale bond yields on a chart to visualize its relative impact to asset valuations? I.e., so that the risk-free rate moving from 1->2% shows as a much larger movement than 11->12%. For instance, assuming stocks have a constant equity risk premium and EPS, the risk-free rate moving from 1%->2% impacts CAPM more than 11%->12%. How do I scale yield movements to show the relative impact to valuations with those assumptions? ## Answer by Alper (score 0, accepted) https://quant.stackexchange.com/a/71438 In bonds, it is suggested that an $x$ ppt increase in the relevant interest rate will result in approximately $y$ percent decline in the valuation of a bond with a duration of $n$ years such that $y = nx$. In example, if a bond has a duration of 5 years and the interest rate most applicable to the bond, such as the interest rate for similar bonds, increases by 2 ppt (for example 1% to 3%), the bond's price is expected to decline by 10% (=5*2%). You may use this formula to estimate the potential rough impact of interest rate changes on a certain asset class other than a fixed income instrument by guestimating the rough average duration of the assets in the respective class. Note that duration and maturity are not necessarily the same. There are many good sources on the internet but I reckon you can start with the "Duration Definition" article from investopedia.com. Of course, this is all pretty rough and dirty and may work somewhat better for certain asset classes than the others because there is usually more than one factor that drives the valuation of an asset class. In addition, both the relations between these factors and the respective asset class as well as the factors themselves, such as the average duration of the asset class, may change over time.
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.