By William F. McCoy, a director with Derivative Solutions Inc., a leading provider of analytical software for fixed income, with an emphasis on mortgage and asset-backed securities. For more information, please see their Web site at

Over the past year, yields on Treasuries have fluctuated more in response to supply considerations than other macro-economic influences. In response, some investors have considered the LIBOR curve1 as the benchmark for valuation. The situation, as always, is more complicated for mortgage-backed security investors.

Mortgage valuation involves two sets of interest rates. First, future mortgage rates need to be projected, which represent the new rate that a homeowner would refinance into. These future rates, along with information about the mortgage, are fed into a prepayment model that determines the prepaid principal. The coupon cash flow, plus the prepaid and scheduled principal, is then discounted back along the valuation curve.

While the implications of alternative valuation curves have been explored elsewhere, investors should also consider the implications of how they derive future mortgage rates. There are several issues to consider for future mortgage rates:

First, there are estimation issues regarding the derivation of the mortgage spread over the base rate, either Treasury or LIBOR.

Second, the choice of the base rate, either Treasury or LIBOR, influences the future level and evolution of the mortgage rate.

Third, the relationship between mortgage rates and discount rates has implications for the consistency of valuation.


The choice of the base rate has an impact on the estimation of the mortgage spread.

While the most obvious difference is in the level of the mortgage spreads, LIBOR rates are also higher than Treasury rates. More importantly, given the recent volatility in the Treasury market, the higher standard deviation of the Treasury-based mortgage spread indicates the estimate is more unstable, than if 10-year LIBOR was used. In a statistical sense, the higher the standard deviation, the less confidence the investor has that they have estimated the current mortgage spread correctly. A higher standard deviation also implies that estimates of future mortgage rates are more volatile than constructed. The volatility induced by estimating the mortgage rate may be different than the market volatility of the "true" mortgage rate.

Future Mortgage Rates

The choice of the base rate influences the level and path of future mortgage rates as well. The mortgage spread estimates are added to the forward path of 10-year Treasury or 10-year LIBOR rates. If the forward mortgage rate curve is level, then mortgages are exposed to a nearly constant refinancing opportunity. If the forward mortgage curve rises, then mortgages are exposed to a decreasing refinancing opportunity. Thus changes in the shape of the forward mortgage rate curve influence the timing and level of refinancing opportunities, which, given the path-dependent nature of mortgages, have critical implications for mortgage valuation. For instance, one can analyze the IO, PO and collateral of FNS 3032 using the forward mortgage curve based on either Treasury or LIBOR.

To highlight the difference, compare the future mortgage rate at years 2, 5, and 10:

Given the current curve shapes, the Treasury-based mortgage rate is continually lower than the LIBOR one, and has more variability. These differences imply lower average lives for Treasury-based analysis, and relatively benefits the PO at the expense of the IO.


The third implication is subtler. First, issuers of mortgages frequently look to the Treasury market to set their rates. Thus, LIBOR-based mortgage rates will not behave as Treasury-based mortgage rates, and may not reflect the actual evolution of future mortgage rates. This difference in behavior could cause discrepancies between mortgages and their hedges. Second, investors may value securities versus the LIBOR curve, while deriving the future mortgage rates from the Treasury curve (or vice versa). Under certain initial yield curve shapes and valuation scenarios, the future mortgage rate could be below the valuation rate. Investors need to consider how unlikely scenarios could skew the valuation. As investors explore alternate valuation methods for mortgages, they will uncover opportunities both within mortgages and across sectors. However, they need to examine all the implications of these methods to insure that the opportunities exist, and are not inadvertent by-products of valuation parameters.

1 Actually, the curve would be the constant maturity swap rate, which is the coupon-bond equivalent of LIBOR. The constant maturity swap rate is derived from the zero-coupon LIBOR rates.

2 FNS 303 is backed by FNMA 7.5%, 30-year collateral, with a WAM of 349 months. As of 6/10/00, the IO was priced at 35-11, the PO was priced at 61-21, and the collateral was priced at 97-07, and discounted to Treasury curve.

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