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Fine-tuning Price Waterhouse's model.

The model used to predict future claims against FHA's main insurance fund needs some tinkering. The FHA actuarial studies done to date have missed some of the finer points of claims behavior because of these flaws in the model.

The health of FHA's Mutual Mortgage Insurance Fund (MMIF)-- that insures most FHA single-family mortgages--has been the subject of great debate and interest in recent years. Policymakers have relied heavily on Price Waterhouse's actuarial studies of the MMIF in making policy changes ostensibly designed to improve the fund's future financial condition. These actuarial studies have, in turn, been based on the results of actuarial/econometric models of the claim and nonclaim termination (e.g., prepayment) experience of the MMIF. Hence, these actuarial studies are only as good as their underlying models.

Because the risk insured is an economic risk, all the results are highly speculative. In addition, because the results are affected by large numbers of economic variables, including the condition of a myriad of local housing markets within the United States, this modeling task is a difficult, if not impossible one. Ideally, such models should contain a small number of variables that are good predictors of future termination experience.

This article examines one aspect of the Price Waterhouse model used to forecast claim terminations. This concerns the overly broad classification of contract interest rates. Specifically, although mortgage interest rates may have changed drastically within an individual fiscal year, the Price Waterhouse claim termination model only employs the average annual contract interest rate. As a result, major differences in claim rates caused by changes in mortgage interest rates are not accurately incorporated into the model. My concern is that this could, in the extreme, invalidate Price Waterhouse's major conclusions concerning the financial condition of the MMIF.

In its ongoing analysis of the financial condition of the MMIF, (i.e., in actuarial studies published in June 1990, March 1992 and December 1992) Price Waterhouse has partitioned the MMIF's originations by fiscal year of endorsement. It's my view that such a partition blurs the effect of mortgage interest rate changes during a given fiscal year and that this could have a major impact on the results of their analysis.

Price Waterhouse has employed the endorsement year as the point of origination. The endorsement date is a function of HUD's mortgage processing system. During 1986 and 1987, there was a long lag between the endorsement date and the date of the origination of the mortgage. (This was caused by the large increase in FHA single-family business precipitated by a major decline in mortgage interest rates and the resulting backlog of mortgages to process.) I have seen extreme cases where mortgages are endorsed as much as 10 years after their origination. In order to more closely represent the date the loan was originated, I think it is more reasonable here to use the begin-amortization date of the mortgage, instead of the endorsement date.

I believe that it is even more preferable, however, to partition the originations either by month of origination or by a fine partition of the contract interest rates. (By fine partition, I mean partitioning contract interest rates into intervals of length of 1/8 or 1/4 percent.)

As this article will show, in an environment of rising interest rates, such as that experienced during the late 1970s and early 1980s, a moderate increase in interest rates is equivalent to a substantial decrease in the effective loan-to-value ratio of outstanding mortgages. The MMIF experience data for mortgages originated during fiscal years 1978 and 1986 demonstrate that a small difference in mortgage contract interest rates can make a large difference in the claim termination experience of MMIF-insured mortgages. It's my view that this effect is due in large part to the assumability of MMIF-insured mortgages.

The initial loan-to-value ratio is roughly defined as the ratio of the initial mortgage amount to the appraised value of the underlying property. However, the mortgage itself may have some value that should be factored into this assessment. The right of the borrower to prepay the mortgage if interest rates decline is equivalent to the borrower's having a "put" option on the mortgage. But the value of the mortgage itself, especially an assumable mortgage, can increase in value if mortgage interest rates increase. I contend that this increase in the value of the existing loan should be added to the appraised value of the property, to arrive at a truer measure of the economic worth of the property and the mortgage together.

For this reason, I define the "effective loan-to-value ratio" roughly as the outstanding balance of the mortgage amount, divided by the sum of the appraised value of the property and the extra value of the existing mortgage due to the contract interest rate being less than the currently available mortgage interest rate.

An increase in mortgage interest rates can dramatically increase the value of an MMIF-insured, fixed-rate, level-payment mortgage. This, in turn, decreases the effective loan-to-value ratio and thereby reduces the probability of that loan becoming a claim termination. This, of course, is due to the facts that 1) the assumability feature of MMIF-insured mortgages saves the prospective purchaser the closing costs of a new mortgage, and 2) an assumed loan will offer that purchaser smaller monthly payments in times when current market rates are higher. Thus, the assumability feature of mortgages carrying lower than current market rates is quite valuable in a rapidly rising interest rate environment.

Consider, for example, an assumable, MMIF-insured, 30-year mortgage, with an 8 percent contract interest rate. If mortgage interest rates were to rise to 10 percent, the effective loan-to-value (LTV) ratio of the mortgage would decline by as much as 16 percent. The following table illustrates the typical effect on loan-to-value ratios of such an increase in mortgage interest rates for loans having 30 years to maturity:
Original LTV Effective
Ratio New LTV ratio

97 percent 81.1 percent
95 percent 79.4 percent
90 percent 75.3 percent

Thus, a 2 percent increase in mortgage interest rates--from 8 percent to 10 percent--can be equivalent to a decline of as much as 16 percent in the effective loan-to-value ratio. If the 2 percent increase were to occur within a single fiscal year, the cumulative claim termination rate of mortgages originated when mortgage interest rates were at their nadir should be much lower than that of those originated when mortgage interest rates were at their top.

Another way of looking at this phenomenon is as follows. Suppose two neighbors in Anytown, U.S.A.--the Smiths and the Joneses--have adjacent, identical houses and identical 30-year, fixed-rate mortgages. The mortgages carry an 8 percent, contract interest rate and a $100,000 face amount. The only difference is that the Smiths have an assumable MMIF-insured loan and the Joneses have a conventional mortgage with private mortgage insurance and a due-on-sale clause.

Immediately after moving in, both the Smiths and the Joneses are forced to sell their houses because of job relocations. Meanwhile, mortgage interest rates have suddenly jumped to 10 percent. The Smiths' prospective, creditworthy buyer could assume their FHA loan and be subject to monthly payments to principal and interest of $733.77 with little or no closing costs. Jones' prospective, creditworthy purchaser will most likely have to get a new mortgage with a 10 percent contract interest rate and be subject to monthly payments to principal and interest of $877.58 plus much larger closing costs at settlement.

The $144 difference in the two monthly payments is substantial. Conceivably, it could prove crucial in saving the Smiths' house from foreclosure, while the Joneses may have no alternative but to give their lender the deed to their house in lieu of foreclosure. If a major employer in Anytown were to relocate its corporate headquarters to Atlanta and take 1,500 jobs out of the local community, this might make the selling process even harder. In such circumstances, the assumability feature would be of great value.

On the other hand, if both the Smiths and the Joneses had started out with mortgages at 10 percent annual interest rates and mortgage interest rates then fell to 8 percent, prospective buyers of both houses would very likely get new mortgages to take advantage of the substantial decline in interest rates. Obviously, in a declining interest rate environment, the assumability feature has little or no value. Under such economic conditions, both conventional and FHA mortgages should behave similarly, all else being equal.

Claim termination rates and rate changes

This example helps to explain why a change in mortgage interest rates is a key predictor of insurance claims on MMIF-insured mortgages. Because MMIF-insured mortgages are assumable (subject only to a credit check of the new purchaser), even if the original borrower is forced to relocate, the mortgage could well remain in force during a period of rising mortgage interest rates. In a rising interest rate environment, the assumability feature gives some MMIF-insured mortgages a major advantage over conventional mortgages with their due-on-sale clause. But clearly, this is more likely to occur in real estate markets where property values are steady or declining only moderately.

On the other hand, in a flat or declining interest rate environment, MMIF-insured mortgages have no such advantage. This contributes to the relatively high cumulative claim termination rates of mortgages with contract interest rates that are significantly higher than current mortgage rates. Thus we can see that in periods of changing interest rates, the MMIF mortgages with higher contract interest rates tend to have higher cumulative claim termination rates.

The period we will explore next was characterized by substantial interest rate swings, but it was also a time when the private mortgage insurers had pulled back sharply from the new origination market. This meant that the MMIF picked up a larger share of what was arguably higher-quality originations than was the case at other times in its history. This would have had some positive effect on claims experience.

Nevertheless, what this analysis will show is that in fiscal years, such as 1986, when mortgage interest rates dropped by almost 2 percent (i.e., from about 11.5 percent to almost 9.5 percent), the claim rates on mortgages originated early in the fiscal year were substantially higher than on those originated later in the fiscal year. Presumably some of the borrowers with high interest rate mortgages were able to obtain comparable housing with much lower monthly carrying charges. By combining the claim experience of these diverse groups of mortgages into the same category, those attempting to model the claim experience of MMIF mortgages fail to capture the wide distribution of claim termination rates experienced by the mortgages originated within such fiscal years. This could well have a severe deleterious effect on the results of their modeling.

If we carefully review the economic conditions that have prevailed since the late 1970s, we can see more clearly how changes in mortgage interest rates within fiscal years 1978 and 1986, led to large differences in cumulative claim rates for MMIF mortgages originated within these two fiscal years.

The economic backdrop

Prior to the late 1970s, mortgage interest rates were generally stable, although they did show an upward trend. During the spring of 1977, mortgage interest rates were about 8 percent. However, as former Chairman Paul Volcker's Federal Reserve Board moved to control inflation by tightening monetary policy, mortgage interest rates rose rapidly. They reached a peak in the fall of 1981, with the VA/FHA interest ceiling at 17.5 percent. Mortgage interest rates then fell to around 11 percent at the end of 1985 and below 9 percent during the first half of 1987. As this article is being written, mortgage interest rates are less than 8 percent.

As interest rates rose in the late 1970s and early 1980s, mortgage lenders offered such new products as adjustable-rate mortgages (ARMs) and graduated payment mortgages (GPMs), with deeply discounted initial rates and negative amortization. These products were designed to defer the impact of double-digit mortgage interest rates on homebuyers. Some private mortgage insurance companies endorsed such risky loans in order to maximize market share.

At the time, these companies viewed themselves as providers of a service more than as insurance companies. Often, the loans insured had high loan-to-value ratios. For example, approximately 50 percent of the loans privately insured during 1984 had loan-to-value ratios greater than 90 percent, and approximately 60 percent of these were ARMs or other loans with scheduled payment increases. Finally, certain private mortgage insurers had heavy concentrations of risk in overbuilt markets in energy-producing states.

These imprudent underwriting practices compounded the losses that resulted from the severe decline in property values in the energy-producing states during the mid- and late 1980s. According to industry data, the private mortgage insurance industry experienced direct incurred losses (without taking into account premiums earned) of more than $5.7 billion between 1985 and 1989.

During the mid-1980s, Moody's and Standard and Poor's insisted that all of the private mortgage insurers increase their capital in order to maintain their credit ratings. It proved to be a difficult time for some of the companies to raise capital. Moreover, the return on equity (ROE) of the industry was poor at the time. Consequently, a number of the parent companies of private mortgage insurers decided not to add capital but instead to stop writing new business.

As a consequence of this retrenchment from writing new business by its private insurance competitors, the MMIF was in an ideal position to pick up market share and higher-quality loans as interest rates fell during and after 1982. The number of MMIF-insured, 30-year, fixed-rate mortgage originations increased from 124,000 during 1981 to 400,000 during 1983 and to 950,000 during 1986.

The MMIF data

Figure 1 shows the cumulative claim and nonclaim termination experience of 30-year, fixed-rate mortgages originated during fiscal year 1986 under the MMIF.

Between October 1985 and September 1986, mortgage interest rates on MMIF-insured mortgages dropped from about 11.5 percent to about 9.7 percent. Specifically, on MMIF 30-year, fixed-rate mortgages, the average interest TABULAR DATA OMITTED TABULAR DATA OMITTED rate dropped from 11.47 percent on mortgages that began amortizing in October 1985 to 9.66 percent on mortgages that had a September 1986 amortization start date.

The corresponding cumulative claim and nonclaim termination rates for these two groups of originations show marked differences. The mortgages with an October 1985 begin-amortization date (with an average mortgage interest rate of 11.47 percent) have shown a 14.17 percent cumulative claim termination rate through December 1992. That compares with a cumulative claim termination rate of only 6.86 percent for mortgages having a September 1986 begin-amortization date (and an average mortgage interest rate of 9.66 percent).

The corresponding cumulative nonclaim termination rates are 52.7 percent for October 1985 originations versus only 22.6 percent for September 1986 originations. This is a substantial difference likely due almost entirely to the decline in mortgage interest rates to well below the levels prevailing in October 1985. (With mortgage interest rates currently below 8 percent, many borrowers who originated loans in September 1986 with interest rates of 9.5 percent or more may well refinance their loans during 1993. This new round of refinancing might narrow the large difference in cumulative nonclaim termination rates noted for these two groups of originations.)

Similarly, we believe that the decline in cumulative claim termination rates exhibited by the September 1986 originations is also due in large part to the decrease in interest rates. For the reasons previously discussed, a portion of the decline is most likely attributable to improvements in the quality of the MMIF originations due to the market retreat by the private insurers.

The FY 1978 experience

Figure 2 shows the cumulative claim and nonclaim termination experience of 30-year, fixed-rate mortgages insured during fiscal year 1978 under the MMIF. The 30-year, fixed-rate mortgages, with starting amortization dates of October 1977, had an average contract interest rate of 8.42 percent and a cumulative claim termination rate of 4.58 percent through December 1992. Those having amortization start dates in September 1978 had a 9.36 percent average contract interest rate and a 7.49 percent cumulative claim termination rate through December 1992.

The corresponding cumulative nonclaim termination rates are 44.7 percent for the October 1977 originations (with an average mortgage interest rate of 8.42 percent) versus 40.2 percent for September 1978 originations (with an average mortgage interest rate of 9.36 percent). These non-claim termination rates reflect a relatively small difference. Furthermore, the non-claim termination rates are low by more recent standards. The cumulative non-claim termination rates through December 1992 for 1981-1985 originations are between 57 percent and 68 percent.

Apparently, since 1978, mortgage interest rates have not declined enough (at least through most of 1992) for there to be a strong incentive for such borrowers to refinance their mortgages. (With interest rates now below 8 percent, this could change in the near future as those who originated loans in fiscal year 1978 with contract mortgage rates at slightly more than 8 percent may decide to pay off the remaining principal on their loans or refinance their loans.)

Significantly, however, the small increase in mortgage interest rates--from an average of 8.42 percent to 9.36 percent between October 1977 and September 1978 resulted in an 83 percent increase in the cumulative claim termination rate--from 4.58 percent to 8.42 percent.


The various Price Waterhouse actuarial studies of the MMIF have been used to justify major changes in FHA program underwriting requirements and premium rates. Both of these changes have had a substantial impact on the operation of the MMIF. These Price Waterhouse studies have also been used to estimate the economic value of the MMIF and its ability to meet its congressionally mandated capital requirements in the future. It is my view that Price Waterhouse's use of the average annual FHA contract interest rate in its model used to forecast claim terminations fails to capture dramatic changes in mortgage interest rates that have occurred within some recent fiscal years.

This is a potentially serious problem that, at the least, requires further in-depth study. In the extreme, it could invalidate Price Waterhouse's major conclusions concerning the financial condition of the MMIF. The existence of this potential problem suggests that the modeling should be redone using a more refined measure of the contract interest rate.


Thomas Nelson Herzog, Ph.D., A.S.A., is director of the statistical and actuarial analysis staff at the Office of Housing, U.S. Department of Housing and Urban Development, Washington, D.C.
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Author:Herzog, Thomas Nelson
Publication:Mortgage Banking
Date:Sep 1, 1993
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