“I am trying to choose between a 3/1 adjustable-rate mortgage at 4.625 percent and a fixed-rate mortgage at 5.875 percent, both 30 years. I don’t expect to be out of my house within three years. What is the best way to make this decision?”

Whether the adjustable-rate mortgage (ARM) or fixed-rate mortgage (FRM) turns out better depends on what happens to interest rates in the future, which no one knows. Shoppers faced with this decision should ask themselves, “Is this a risk worth taking,” and “can I afford to take it?”

The best way I know to deal with these questions is by determining what will happen to the rate and payment on the ARM if market interest rates change in ways that you specify. This “scenario analysis” provides a measure of the risk if rates increase, and the benefit if they don’t. It also allows you to determine the extent to which you can reduce the risk on the ARM by making the larger payment that you would have made had you selected the FRM.

A side benefit is that you can’t do scenario analysis without knowing all the features of the ARM that affect future rates and payments. The information you are forced to compile for this purpose you should have anyway. Otherwise, you don’t know whether you have found the best deal on your ARM.

For example, you told me that your 3/1 ARM had a rate of 4.625 percent, but that rate holds for only three years, after which the rate adjusts every year. You did not tell me what I needed to know to calculate the rate and payment after the three years. I found out that your ARM rate was tied to the one-year Treasury index, which had a recent value of 1.28 percent, and had a margin of 2.75 percent. After three years, your rate would equal the index at that time plus 2.75 percent, subject to an adjustment cap of 2 percent (no rate change can exceed 2 percent) and a maximum rate of 10.625 percent.

You need all that to do scenario analysis, but you also want it for shopping. If you could find the same 3/1 ARM with a 2.5 percent margin, you should grab it.

The numbers cited below all assume loan amounts of \$100,000, and came from calculator 7b on my Web site.

A stable-rate scenario provides the best measure of the potential benefit of the ARM. The payment would be \$514.14 for the first 36 months, and \$481.76 thereafter, as compared to \$591.54 on the FRM. If you made the \$591.54 payment on the ARM, you would pay it off in 257 months.

I used four rising-rate scenarios of gradually increasing severity: 1. Small rate increase: after two years, the index increases by .5 percent /year for three years; 2. Moderate rate increase: after one year, the rate index increases by .75 percent/year for four years; 3. Larger rate increase: starting immediately, the index increases by 1 percent/year for five years; and 4. Worst case: the index rises to 100 percent in month 2.

With the small rate-increase scenario, the payment remains lower on the ARM than on the FRM over the entire 30 years. If the borrower makes the FRM payment, he will pay off in 304 months. The borrower thus benefits if rates are stable or decline, or have a delayed rise of 1.5 percent over 3 years.

With the larger rate-increase scenarios, the benefits of the ARM over the first three or four years are followed by losses. Skipping to the worst case, the payment would rise from \$514.14 to \$630.64 in month 37, to \$754.44 in month 49, and to \$883.74 in month 61 where it would remain until payoff. It is useful to know whether you could deal with these increases, even though the likelihood of their occurring is very low.

These payment increases could be reduced by making the larger FRM payment in the first three years. If you paid \$591.54 rather than \$514.14 for 36 months, you would reduce the worst-case payment in months 61-360 from \$883.74 to \$856.01. The complete results for all the scenarios are shown in the Web version of this article.

Scenario analysis doesn’t provide definitive answers to the questions posed at the beginning of this article. However, it does allow you to make an informed judgment based on all available information. In the face of an uncertain future, that’s the best anyone can do.

The writer is Professor of Finance Emeritus at the Wharton School of the University of Pennsylvania.  Comments and questions can be left at www.mtgprofessor.com.

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