Back-to-Basics: Key Rate Durations*
(*updated from a previous article on this topic)

Teri Geske
Senior Vice President, Product Development

Since two portfolios with the same duration can have very different sensitivities to shifts at the short, intermediate or long end of the yield curve, managing interest rate risk requires an understanding of yield curve risk, i.e. the sensitivity of an asset, liability or balance sheet to a change in the slope or shape of the yield curve. This Back-to-Basics article discusses the concept of Key Rate Durations and how they can be used to measure exposure to non-parallel shifts in the yield curve.

Computing Key Rate Durations
Key Rate Durations measure an asset’s or portfolio’s price sensitivity to independent shifts along the yield curve at important or “key” points, such as those corresponding to the on-the-run Treasury maturities. They are computed by decreasing and increasing each key Treasury spot rate by some number of basis points (e.g., +/-50bps or +/-100bps) and re-computing the asset’s (or liability’s) price (present value), holding all other spot rates constant. The average percentage change in the asset’s value resulting from these shifts is its Key Rate Duration for that point on the curve. The key rate shift is “anchored” at the key rate points immediately preceding and following the point that is being measured – for example, assume the key points on the curve are defined as the 6 month, 1 year, 2 year, 3 year, 5 year and 10 and 30 year rates. To compute the 5 year Key Rate Duration, we assume that the shift at the 5 year point is fully absorbed by the time we reach either the 3 year or 10 year points on the curve:

Interpreting and Using Key Rate Durations
For bullet maturity assets and liabilities, the largest Key Rate Duration will correspond to a shift in the Treasury rate which is closest to the maturity date, as a shift in this rate would have the greatest impact on the price (i.e., on the present value of the cash flows). The Key Rate Durations corresponding to shifts in Treasury rates earlier than the maturity date will be smaller, as they reflect the changes in the present value of the interest payments received as a percentage of the overall present value. As discussed below, the Key Rate Durations for callable assets reveal the sensitivity of price to the call date as well as to the maturity date.

KRDs reveal the impact of embedded call or put options on the overall duration of an asset or portfolio by showing how sensitive a call option or prepayment forecast may be to a shift in a key interest rate. Consider the case of a bond maturing in ten years that is continuously callable at par after two years. Intuitively, we know that the price of this asset is sensitive to a change in both the ten year and two year points on the yield curve, because a change in the two year rate would affect the likelihood of the call being exercised, while a change in the ten year would affect the present value of the principal payment expected at the final maturity date if the bond is not called prior to maturity. 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 security, but the bond cannot be viewed as either a “10 year” or a “2 year” instrument. 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.

For amortizing instruments and loans such as mortgage loans or pass-throughs, CMOs and asset-backed securities, Key Rate Durations indicate the relative importance of a shift at different parts of the curve given the pattern of principal repayments. The price of a mortgage-backed security is sensitive to a shift in the Treasury rates that are used to discount the collateral cash flows (either passed through directly or distributed to the tranches in a CMO deal), and at the same time may be highly sensitive to a shift in the rate, usually the 10 year Treasury yield, that determines the rate of new mortgages and therefore affects the borrower’s incentive to refinance and prepay the underlying mortgages. 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. Since prepayments are affected by movements in the 10 year Treasury rate, a well-protected PAC tranche of a CMO deal will 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. As an extreme example, a CMO Interest Only (IO) tranche has a negative effective duration because a decline in interest rates causes the IO’s price to fall (as faster prepayments reduce the interest payments to the IO holder). Most of the IO’s Key Rate Durations are positive but at the 10 year point the KRD is negative, even if the security is not expected to receive any cash flow at that time, because the 10 year Treasury rate drives the refinancing component of the prepayment forecast.

Now that we have reviewed Key Rate Duration values for different security types, we discuss why we might want to isolate a portfolio’s sensitivity to shifts at specific points on the curve. Assume we wish to construct a portfolio so that its interest rate sensitivity matches that of a benchmark, or a liability the portfolio is intended to fund. Even if the option-adjusted durations of the portfolio and liability are perfectly matched, this says nothing about their relative sensitivity to non-parallel yield curve shifts. We know that we can structure a portfolio in a number of ways to achieve a duration target (e.g. barbelled, bulleted, laddered, etc.), and these various structures have different sensitivities to non-parallel yield curve moves. Key Rate Durations allow us to compare yield curve exposures between a portfolio and a benchmark by “deconstructing” the overall effective duration of each asset in the portfolio into its component parts. By definition, the sum of an asset’s Key Rate Durations equals its effective duration, and the KRDs for a portfolio are equal to the weighted average of the KRDs of the individual assets in the portfolio; therefore, Key Rate Durations may be thought of as an extension of effective duration in risk management and in portfolio vs. benchmark comparisons.

In the Tracking Error analysis in BondEdge, the differences between a portfolio’s and benchmark’s key rate durations are used to measure the relative sensitivity to changes along the underlying yield curve. By multiplying the differences in KRDs by the volatilities associated with each key point on the yield curve, and incorporating the correlations across the potential yield curve shifts, the Tracking Error captures a full range of possible interest rate moves without relying on any single yield curve point to define “interest rate risk”.

One drawback of KRDs is that interpreting the individual key rate values themselves may not be particularly intuitive. Since it is extremely unlikely that a single point on the Treasury curve will exhibit an isolated “jump” upwards or downwards while all other points on the curve remain fixed, it is sometimes difficult to describe what the individual KRDs mean. However, when viewed in relative terms, we can easily make some useful observations. For example, if Portfolio #1 has a KRD at the 1-year point of 0.527 and a 5-year KRD of 0.844, and Portfolio #2 has a 1-year KRD of 1.19 and a 5-year KRD of 0.35, then Portfolio #2 is roughly twice as sensitive to shifts at the short end of the yield curve than Portfolio #1, and is less than half as sensitive to shifts at the intermediate part of the curve. We can also say that Portfolio #2 is much more sensitive to changes in short-term rates than to movements in the intermediate part of the curve, whereas Portfolio #1 is more sensitive to shifts in intermediate rates than to movements at the short end of the curve.

A Key Rate Duration analysis makes it easy to compare a portfolio to a benchmark or a liability 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 and in a way that no single duration measure can.

For a more in-dept comparison of duration measures and yield curve risk, please refer to the white paper entitled, "Beyond Duration: Dissecting Yield Curve Risk", available on the BondEdge Private Client Site and by request at www.interactivedata-fia.com.