Interactive Data Fixed Income Analytics-fixed income portfolio and credit risk analytics

The following article is reprinted from the October/September, 2001 issue
of On the Edge, the Interactive Data Fixed Income Analytics bimonthly newsletter.

Choosing a Mortgage Duration

Kamel Bazizi, Ph.D.
Vice President, Research & Consulting

Investment managers may choose to overweight mortgage-backed securities over Treasuries based on expectations for relative performance between these sectors. One of the most important contributions to performance within this investment strategy will be the assumed duration of the mortgages. This duration assumption is equally important for those attempting to hedge the interest rate risk inherent in holding MBS positions. In this article we discuss the strengths and weaknesses of different ways MBS durations are measured. We consider option-adjusted (also known as “effective”) durations, empirical durations, and durations derived from coupon spreads.

Typically there is a high degree of dispersion between these three different MBS durations, as can be seen in the table and graphs below. The table compares the different measures of duration for 30-year FNMA and GNMA TBA collateral, as of 7/31/2001. For instance, for GNMA 7.0% pools, the option adjusted duration is 3.7 versus 2.7 for the empirical duration. In this case, the duration difference is one full year and hedging these pools based on one measure versus the other has a significant implication on the success of the hedging strategy. In this article, we examine the assumptions underlying the derivation of each of these durations, and their respective strengths and weaknesses. Traditionally, option-adjusted durations have been used successfully for relatively longer horizons, often most appropriate for investment managers and mortgage servicers, while empirical durations have been more adequate for those with shorter horizons, such as mortgage pipeline hedgers, while coupon spread durations have been popular among mortgage traders.

Many investors rely on option-adjusted durations generated by a model to measure the interest rate sensitivity of their MBS holdings. This measure is calculated by assuming a small shift in the Treasury or Libor yield curve in an option-adjusted spread (OAS) framework. An OAS framework is typically based on a Monte Carlo simulation, which captures a mortgage security’s performance over a range of scenarios. In the simulation, a large number of interest rate paths are selected from an interest rate distribution, which is centered on forward rates. Cash flows for the mortgage security are determined using a prepayment model, which gives prepayment rates at each node along each interest rate path. An option-adjusted spread is then derived via an iterative search technique. Once the OAS is found, the model duration is captured by raising the interest rate curve by a small amount, and then reflecting this shift in the paths. New cash flows are generated and a new price is found. The process is repeated for a small downward shift. The average absolute price change, stated as the percentage of the current price, is the option-adjusted duration. Note that option-adjusted durations can differ substantially across dealers’ models. Those differences stem from the generation of the interest rate curve, the volatility assumption, and most importantly, the prepayment model. The advantage of option-adjusted durations is that, unlike empirical durations that assume that the future market environment will be the same as it has been historically, they capture some market changes more readily and perform better over time. In fact, portfolio managers and mortgage servicers who typically measure performance or hedge risks over a number of months, rely on option-adjusted durations successfully.

We now discuss empirical durations, which reflect how the market is currently trading mortgage securities. An empirical duration with respect to changes in Treasury rates is derived by running a simple linear regression of the change in a mortgage price against the change in the 10-year Treasury yield. To compute empirical durations, one must decide on the number of days of data to use in the regression; in this analysis we use 20 trading days. The advantage of this approach is that it relies solely on observed changes in market prices and yields. However, empirical durations can be misleading if the market is in a different trading environment than it was over the base measurement period. First of all, if mortgage spreads widen or tighten substantially more than experienced over the base period, empirical durations can perform poorly. Secondly, empirical durations only capture movement of mortgage performance to the 10-year Treasury rate. Therefore, non-parallel shifts in the yield curve are not captured by empirical durations, as witnessed by the steepening of the yield curve during the last few months. Lastly, empirical durations have uncertainties due to the methodology itself used in the regression analysis. Empirical durations can provide a good hedge for shorter horizons, such as mortgage pipeline hedging, since these limitations are likely to have less of an impact over a short time period.

Many mortgage traders compute durations from coupon spreads. These durations are derived using the prices of adjacent coupons. For example, if the market were to rally 50 basis points, the coupon-spread approach assumes that FNMA 7.5s would trade where the FNMA 8.0s trade now. If the market sold off 50 basis points, that same coupon-spread approach assumes that FNMA 7.5s would trade like the current 7.0s. Thus we know the price behavior of FNMA 7.5s up and down 50 basis points, and we can now compute a duration using this approach. Note that deriving durations from coupon spreads is very assumption-dependent. It assumes that if rates fall 50 basis points, FNMA 7.5s will trade where the 8.0s trade now, and if rates rose 50 basis points, then 7.5s would trade where 7.0s do now. This analysis ignores any WAC or WAM differences priced into different coupons. Moreover, it ignores the general refinancing trend of the market. In fact, if rates were to decline by 50 basis points, prepayment fears would ignite and 7.5s would trade worse than 8.0s do now. On the other hand, if rates increased by 50 basis points, we would expect 7.5s to trade at a premium over where 7.0s are presently trading.

The coupon-spread methodology, which performs poorly over time due to these unreasonable assumptions, is only popular among mortgage traders seeking a quick estimate of durations. Mortgage investors typically rely on option-adjusted duration for analysis and hedging when the time horizon is relatively long, and empirical durations for hedging over short horizons. Due to the assumption that that the future trading environment will be the same as the base measurement period, empirical durations can have a good performance only over a short horizon. Some mortgage lenders also use empirical durations successfully for hedging their pipeline portfolios. Over the long term, a mortgage investor will do better using option-adjusted durations that are computed using a combination of prepayment and term structure models with the flexibility to capture future market changes.