William G. De Leon, Ravi K. Mattu
Duration, or the sensitivity of an investment to interest rate levels, is the single most important risk metric for a fixed income portfolio. It is important to note that this sensitivity measure is related to, but not identical to, a security’s or a portfolio’s expected volatility. Yet even though textbook treatments of duration present it as a simple, unambiguous concept, in fact numerous factors influence interest rates and hence the measurement of “duration” can be nuanced.
Two factors contribute to this complexity. First, the measurement of an individual security’s interest rate sensitivity may depend upon complex valuation models that are approximations to the actual economic value delivered by the security. Second, for portfolios that are exposed to multiple interest rates across both the maturity spectrum and different currencies, quoting a single “duration” requires balancing the relative volatility and correlation among these interest rates.
Despite these nuances, we frequently encounter duration quotations (for example, published durations on fixed income benchmarks) presented as though no such subtleties exist. These duration quotations average duration exposures across maturities and across currencies, implicitly assuming that yields across maturities and currencies are equally volatile and perfectly correlated. Additionally, securities with credit risk are often treated as having no default risk when calculating duration.These assumptions are what economists call heroic, and while they may facilitate coming to a single quoted figure for interest rate risk, they are not the whole story. At PIMCO, we approach the task of understanding interest rate risk with a more complete view of the risk dynamics driving interest rate sensitivity, and we encourage our clients and other investors to do the same.Our approach aims to incorporate sophisticated security valuation analytics drawing on our proprietary research on interest rate dynamics, mortgage prepayments, defaults, and other factors determining security cash flows, as well as empirical research into the relative volatility and correlations among interest rates across maturities and currencies. To be sure, the markets are dynamic and we dynamically revisit our own methods to find better ways to measure and manage risk for our clients and their portfolios. While we are always striving to provide better metrics, we recognize that a number of these advances depart from industry conventions. Looking at the portfolio through a prism that breaks the risk into finer gradations adds to our understanding and ability to manage risk, but we still maintain more traditional measures in our systems for comparability with other sources and for those clients who match fixed income assets to liabilities calculated using more traditional methods.The factors cited above may be understood as corresponding to, in the first place, a subtlety related to the proper measurement of security-level interest rate sensitivity, and in the second, a subtlety related to the proper estimation of portfolio risk.
We do not mean to imply that there is absolutely no consensus on these points in the market. Indeed, academics and industry practitioners agree broadly that duration should reflect the factors we have named: callability, prepayments, defaults, and interest rate volatility, along with other factors. Academics and practitioners also certainly agree that global yield curves and yields of different maturities are imperfectly correlated and differentially volatile. However, the consensus falls far short of specific agreement upon or synchronization of the details or the models used, and the differences, in some cases, are large enough to create substantial differences in stated durations.Duration isn’t so simpleDuration is often used as a shorthand way to communicate the interest rate risk of a fixed income portfolio. Textbook duration is defined as the percentage change in the price of a portfolio for every 1% (100 basis points) change in all interest rates. If the entire yield curve were to move in parallel – along with global yield curves moving in tandem – and the timing and magnitude of cash flows were known, then duration would be an unambiguous measure of effective interest rate exposure. This measure does not account for initial conditions and allows for negative yields. While the market has occasionally observed negative yields, most market participants consider zero the lower bound and calculations which use negative rates may be misleading in determining rate sensitivities.
While no single number can capture the interest rate risks of a global bond portfolio, PIMCO believes forward-looking measures of duration (e.g., hard cyclical duration) that seek to capture the relative volatility and correlations of various sovereign curves, while also adjusting for the impact of embedded options and default risk, are more useful in managing this risk. Here is a quick guide to some of our duration measures.
Traditional or Textbook Duration The percentage change in the price of a portfolio for a parallel 1% (100 basis points) change in interest rates.
PIMCO Duration PIMCO’s internally computed duration. Key methodological differences between PIMCO’s duration and other sources include our use of a two-factor model that incorporates both rate and credit volatility for defaultable credits, and our proprietary mortgage and structured finance analytics. However, it is still calculated for a parallel 100-basis-point change in interest rates.
Cyclical Duration Adjusts the PIMCO duration measure to take account of cyclical interest rate volatility. Beta adjustments are applied to all maturities and currencies. The reference point is the five-year U.S. Treasury yield, and it is shifted by 100 basis points.
Hard Duration Adjusts the PIMCO duration measure by using a security’s option-adjusted spread (OAS) as an indication of its sensitivity to credit. The higher the OAS on the security, the less sensitive it will be to changes in interest rates.
Hard Cyclical Duration Applies both the hard and cyclical beta adjustments to the PIMCO duration measure.
No part of this material may be reproduced in any form, or referred to in any other publication, without express written permission. Pacific Investment Management Company LLC, 840 Newport Center Drive, Newport Beach, CA 92660, 800-387-4626. ©2013, PIMCO.
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