FRBSF Economic Letter
2000-01; January 01, 2000
 Economic
Letter Index
Measuring Interest Rate Risk for Mortgage-Related Assets
Measuring interest rate risk--that is, the risk that interest rate fluctuations
might impair a firm's profitability or viability--is important both to
financial institutions and to their regulators. Generally, methods for
measuring interest rate risk focus on the duration of financial
instruments, which is one way to characterize the sensitivity of their
values to interest rate changes. However, measuring duration can be quite
difficult, particularly for assets and liabilities with embedded interest-related
options.
This Economic Letter focuses on residential mortgage-related assets,
which typically embed interest-related options through borrowers' right
to prepay their debts before the end of the mortgage term. It explains how
these prepayment options affect duration and describes how some methods
used to measure interest rate risk for mortgage-related assets incorporate
this dependence of duration on prepayments.
Duration
Some early efforts to promulgate standardized methods for measuring interest
rate risk (e.g., Basel 1993) emphasized Macaulay duration, which
is a measure of the cash-flow-weighted time until maturity of an instrument.
Currently, however, most interest rate risk measurement methods (e.g.,
those discussed in Basel 1997, 1999) emphasize modified duration,
which is the price elasticity of an instrument with respect to a change
in yields. Generally, modified duration is defined with respect
to changes in the yield-to-maturity. To keep matters simple, typical computations
of modified duration use parallel shifts in the yield curve, where yields
at each maturity horizon change by the same amount. In this context, a
duration of 5 would indicate that the price of an asset would change by
5% for a 1 percentage point change in yield. For a (zero-coupon, non-amortizing,
default-free, noncallable) bond with all cash payments to the investor
occurring at the maturity date, there is an unambiguous relationship between
the bond's yield-to-maturity, current price, and remaining term to maturity.
For example, on such a bond a modified duration of 5 also would indicate
that there are 5 remaining years to maturity.
However, more generally the modified duration of an instrument is sensitive
to the timing and amounts of interim receipts of cash flows. The payment
of interest and principal before the maturity of an instrument shortens
its duration relative to zero-coupon, non-amortizing bonds of equal maturity.
As the coupon rate increases, the modified duration of a noncallable bond
decreases. Also, modified duration is lower for amortizing bonds, on which
some principal is scheduled to be returned before final maturity, than for
non-amortizing bonds, on which principal is returned only at final maturity.
The existence of an option for a borrower to return additional principal
before the scheduled return dates also affects a bond's value and its modified
duration. The predicted effects on mortgage bond value and duration depend
on how the valuation model specifies (default and prepayment) option-exercise
behavior and specifies market valuation of these uncertain option-related
cash flows.
The influence of prepayments on the modified
duration of MBS
The prepayment of principal is particularly important to measuring the
duration of mortgage-related assets. Bank portfolios tend to contain large
exposures to residential mortgage-related assets, including whole mortgages
held in portfolio, mortgage-servicing rights, and mortgage-backed securities
(MBS). This Letter focuses on one of these major asset classes,
(agency) 30-year fixed-rate MBS passthroughs, which distribute cash flows
to MBS bondholders in proportion to the receipt of interest and principal
from the underlying pool of mortgage borrowers. Interest payments are
determined by an MBS passthrough coupon rate, which tends to be about
50 basis points above the mortgage rate on the underlying mortgage loans,
with this difference diverted to cover the costs of servicing the mortgages
and insuring against default.
Although the stated maturity of an MBS is the remaining term until maturity
of the underlying mortgage loans (about 30 years at issuance of the MBS),
almost all of the cash from an MBS will be received before the stated maturity
date. In addition to the scheduled receipt of interest and principal (amortization)
each month in the mortgage term, MBS tend to experience early return of
principal as borrowers either voluntarily prepay or default and trigger
mortgage insurance payoffs.
The magnitude of prepayments depends on current interest rates and other
aspects of the economic environment. At a given MBS passthrough coupon,
prepayments tend to increase as current yields decline. The increasing
prepayments effect is particularly large near the refinancing "threshold,"
which is where the spread between current yields and the given coupon
begins to exceed the minimal level of refinancing transactions costs.
Below that threshold, prepayments on residential mortgages largely are
due to defaults and to early payoffs by households who sell their homes
in order to move to other residences.
Figure 1 illustrates the
relationship between refinancing incentive spreads and prepayments using
data on the historical prepayment rates of 30-year fixed-rate Freddie
Mac passthroughs. On average, only about 1/4% of the remaining mortgages
per month prepaid for those MBS with mortgage coupons well below the prevailing
primary mortgage rate, spreads below negative 1-1/2 percentage points.
Prepayment rates remained well below 1% per month for other (narrower
negative and slightly positive) spreads below 1/2 percentage point. Then,
prepayment rates increased noticeably as this spread widened above 1/2
percentage point. For MBS with coupons about 2 percentage points above
the current primary market rate, prepayments averaged about 5% per month.
The existence of such a high degree of prepayment sensitivity to the position
of current market yields relative to the coupon rates on the outstanding
mortgages makes the duration of MBS instruments shift with market conditions,
with the degree of shifting dependent on whether the MBS have relatively
high or relatively low coupons. The degree to which duration changes with
yields is known as the convexity of the instrument. When current
yields are low enough to make refinancing potentially attractive to a significant
fraction of mortgage borrowers in the foreseeable future, MBS exhibit negative
convexity; that is, as yields increase, MBS bond prices become more
sensitive to changes in yields. This is the opposite of the case for noncallable
bonds with nonzero coupons; such bonds demonstrate a mild degree of positive
convexity.
The size of the negative convexity of MBS can be illustrated using empirical
duration measures for Freddie Mac 30-year passthroughs. The empirical
duration measures calculate duration from the observed average degree
of co-movement between actual MBS market prices and Treasury yields in a
particular sample period. As illustrated in Figure
2, for deep discount MBS with passthrough coupons about 2 percentage
points below the current par coupon, the empirical duration is about 6-1/2%.
To put this number in perspective, note that this is equivalent to the modified
duration and Macaulay duration of a zero-coupon (non-amortizing, noncallable)
bond with a term to maturity of 6-1/2 years. The historical relationships
shown in the figure suggest that if current yields drop by about 2 percentage
points, narrowing the refinancing incentive gap from -2 percentage points
to zero, then duration will drop to about 3-1/2%. Furthermore, the duration
of an MBS passthrough can shorten very substantially with a 4 percentage
point change in current yields. An MBS with a 2 percentage point coupon
premium over the current par coupon has tended to have a duration of less
than 1%, about 5-1/2 percentage points less than the duration of an MBS
with a 2 percentage point coupon discount.
Mortgage interest rates have been sufficiently variable in recent years
to create significant heterogeneity in the duration of the stock of MBS
passthroughs outstanding and to change the duration of specific vintages
of MBS over time. At the beginning of the 1990s, primary conventional mortgage
rates were slightly over 10% (Figure
3). Mortgage rates trended down to slightly below 7% in late 1993, were
back up to above 9% by the end of 1994 and have bounced up and down in roughly
the 7% to 8-1/2% range during the latter half of the 1990s. When primary
mortgage rates were at their peaks in 1990 and 1995, most of the stock of
outstanding MBS were from earlier years and bore passthrough coupons which
were low relative to newly issued mortgages; the average spread was negative
and exceeded 100 basis points. Such negative spreads between historical
and prevailing rates depressed refinancing activity (also shown in Figure
3) and implied that most outstanding MBS had relatively high durations;
Figure 1 implies that the
empirical durations were around 5%. However, when primary mortgage rates
dropped to troughs near 7% in each of 1993, 1996, and 1998, spreads between
outstanding and newly issued mortgage rates typically were positive and
wide; this boosted prepayments and in many cases lowered the durations of
the outstanding MBS to below 2%.
Alternative approaches to interest rate
risk measurement
The above calculations illustrate that the duration-gap approach to interest
rate risk measurement has major shortcomings for mortgage-related assets
because the duration of such assets can change significantly with changes
in current market yields. Accordingly, financial institutions and regulators
have developed alternative approaches to interest rate risk measurement
which, in principle, are better able to evaluate the degree of interest
rate risk in instruments with durations that change rapidly as market
conditions interact with embedded options. For example, the Office of
Thrift Supervision has developed a Net Portfolio Value (NPV) model that
simulates the effects of interest rate changes on the values of MBS passthroughs
and other mortgage-related assets by incorporating prepayment assumptions.
Also, the Office of Federal Housing Enterprise Oversight (OFHEO) has developed
an elaborate simulation model for predicting prepayments, defaults, and
mortgage asset values to be used in "stress tests" of Fannie Mae and Freddie
Mac, the two housing finance government-sponsored Enterprises for which
OFHEO is developing risk-based capital regulations.
Relative to the NPV model, OFHEO's model for conducting stress tests
is innovative in using housing prices as an additional predictor of mortgage
prepayment rates. This principle gains some support from recent research
by Mattey and Wallace (1999) which confirms that housing price changes
have had a statistically significant effect on prepayment rates of MBS
passthroughs.
Joe Mattey
Research Officer
References
Basel Committee on Banking Supervision. 1993. "Measurement of Banks'
Exposure to Interest Rate Risk." Consultative proposal (April).
Basel Committee on Banking Supervision. 1997. "Principles for the Management
of Interest Rate Risk" (September).
Basel Committee on Banking Supervision. 1999. "Consultative Paper on a New
Capital Adequacy Framework" (June).
Mattey, Joe, and Nancy Wallace. 1999. "Housing
Price Cycles and Prepayment Rates of U.S. Mortgage Pools." Federal Reserve
Bank of San Francisco Working Paper 99-12 (August).
Opinions expressed in this newsletter do not necessarily reflect
the views of the management of the Federal Reserve Bank of San Francisco
or of the Board of Governors of the Federal Reserve System. Editorial
comments may be addressed to the editor or to the author. Mail comments
to:
Research Department
Federal Reserve Bank of San Francisco
P.O. Box 7702
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