The following article is reprinted from the May/June, 1999 issue of
On the Edge, the Interactive Data Fixed Income Analytics bimonthly newsletter.

Back-to-Basics:  Interpreting Key Rate Durations

Teri Geske
Senior Vice President, Product Development

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In previous Back-to-Basics articles we have discussed how and why interest rate risk is measured using effective duration and convexity.  To be more precise, we should say that duration and convexity measure the sensitivity of fixed income securities and portfolios to a change in the overall level of interest rates as measured by a parallel shift in the Treasury spot curve.   Over the past five years, the level of interest rates (determined by the yield of the 30 year Treasury) has ranged from below 5.00% to almost 8.00%; during the same period, the slope of the Treasury curve (YTM_30yr – YTM_1yr) ranged from about 25 basis points to over 270 basis points.  Clearly, not all shifts in the yield curve are parallel.  Therefore, managing interest rate risk requires an understanding of a portfolio’s sensitivity to both a change in the level of rates and to changes in the slope of the yield curve. The concept of Key Rate Durations has gained popularity as one approach to measuring exposure to non-parallel shifts in the term structure, so in this Back-to-Basics column we thought it would be useful to review what Key Rate Durations are and how they can be used to understand a portfolio’s yield curve risk.

Key Rate Durations measure a bond's or portfolio's price sensitivity to independent shifts along the yield curve at important or “key” points, typically the on-the-run points.   Before we get into how the Key Rate values are computed, let’s discuss why we might want to isolate a bond or portfolio’s sensitivity to shifts at specific points on the curve.  Assume we wish to construct a portfolio so that its overall interest rate risk (its effective duration) matches the duration of a benchmark.  We know that we can structure the portfolio in a number of ways to achieve the target duration (e.g. barbelled, bulleted, laddered, etc.), but even a perfectly matched effective duration reveals nothing about the portfolio’s sensitivity to non-parallel yield curve shifts relative to the benchmark.  Key Rate Durations allow us to make this comparison by “deconstructing” a bond’s or portfolio’s effective duration into its component parts.  Intuitively, we know that a bond maturing in ten years and callable in two years is sensitive to both a change in the 10 year and 2 year points on the yield curve.  We know that the bond’s effective duration will be somewhere between the effective duration of a two year bullet and a ten year bullet, but the security cannot be viewed as either a “10 year” or a “two year” bond.  Using Key Rate Durations we can quantify the relative sensitivity of the bond’s price to changes at both of these points on the curve.  A CMO Interest Only (IO) tranche has a negative effective duration because a decline in interest rates causes the IO’s price to fall (and faster prepayments reduce the interest payments to the IO holder).  The IO’s Key Rate Durations are mostly positive but the value at the 10 year point is negative (even if the security is not expected to receive any cash flow at that point in time), because the 10 year Treasury rate drives the refinancing component of the prepayment forecast. By definition, the sum of a bond’s Key Rate Durations is equal to its Effective Duration; thus, Key Rate Durations may be thought of as an extension of effective duration in risk management and in portfolio vs. benchmark comparisons.

Key Rate Durations are computed by shifting each key Treasury spot rate down and up by some amount, (e.g. 100 bps, assuming effective duration is calculated using this shift) and recomputing a bond’s price, holding all other spot rates and the bond’s OAS constant.  The average percentage change in price is the bond’s Key Rate Duration for that point on the curve.  The shift is “anchored” at the key rates immediately before and after the rate that is being shocked – for example, assume the key points on the curve are defined as the 6 month, 1 year, 2 year, 5 year, 10 year and 30 year rates.  To compute the 10 year Key Rate Duration, we assume that the shift at the 10 year rate is fully absorbed by the time we reach either the 5 year or 30 year points on the curve:    

For a bullet maturity bond, the largest Key Rate Duration will correspond to a shift in the Treasury rate which is closest to the bond's maturity date, as a shift in this rate would have the greatest impact on the bond's price.  The Key Rate Durations corresponding to shifts in Treasury rates earlier than the bond's maturity date will be smaller, as they reflect the changes in the present value of the coupon payments received as a percentage of the bond's price.  For callable bonds, key rate durations reveal the sensitivity to the bond’s call date as well as its maturity date.

For amortizing instruments such as mortgage pass-throughs, CMOs, ABS and ARMs, Key Rate Durations indicate the relative importance of a shift at different parts of the curve given the pattern of expected principal repayments.  If a security's cash flows are "front-loaded" relative to its average life, the earlier Key Rate Durations will be relatively large.  If the cash flows are "back-end loaded" relative to its average life, the later Key Rate Durations will be larger.  As mentioned earlier, key rate durations also reveal sensitivity to points on the curve that affect prepayments.  A well-protected PAC would have a smaller 10 year key rate duration than a support tranche (backed by similar collateral, etc.), because a change in refinancings as triggered by a shift at the 10 year point on the curve would impact the support tranche more than the PAC.

In BondEdge’s Compare system, nine Key Rate Durations are calculated for each security in a portfolio, representing the percentage price change of the security for a 100bp shift in each of nine spot rates corresponding to the on-the-run Treasury yields.  Key Rate Durations for the Indices modeled in Compare are also provided, allowing you to compare a portfolio to a benchmark in a way that may reveal structural mismatches not readily identified by other summary portfolio measures. At both the individual security and portfolio levels, key rate durations can provide valuable insights about term structure sensitivity.

We hope this discussion of key rate durations has been useful.  A more in-depth comparison of duration measures and yield curve risk is available in the Interactive Data Fixed Income Analytics publication, “Beyond Duration:  Dissecting Yield Curve Risk” by Wesley Phoa, Ph.D.  To request a copy of this paper, please visit us at www.interactivedata-fia.com or contact your Interactive Data Fixed Income Analytics representative.   If you would like us to cover a certain topic in a future “Back-to-Basics” article, please contact marketing at fia.marketing@interactivedata.com.