Mortgage borrowers face the difficult prospect of evaluating the costs and risks associated with the choice of terms for adjustable-rate mortgages. This study uses a simulation approach to model the choices. We represent the risk of the adjustable-rate mortages with distributions of present value-cost differentials for a variety of mortgage life periods. We provide insight on the financial planning aspect by modeling the impact of mortgage-rate changes on the size of payments for adjustable-rate mortgages. Simulation can yield nonintuitive results that may lead to better decision making by borrowers.
© 2003 Academy of Financial Services. All rights reserved.
JEL classification: G21
Keywords: Adjustable-rate mortgage; Choice; Simulation
Borrowers in the market for a mortgage today face a bewildering array of choices. One can choose between fixed-rate mortgages (FRMs) and adjustable-rate mortgages (ARMs). ARMs generally have the advantage of lower initial interest rates and payments. Although these rates and payments increase in subsequent years, ARMs are often advantageous to borrowers who anticipate a relatively short holding period.
Among ARMs, one can select from a wide variety of terms. Typically, they offer an interest rate and payment that remain the same for a fixed period of time. After that time, the lender adjusts the interest rate by adding a margin to a published interest-rate index. Both the amount of the margin and the selection of the index are indicated in the loan contract. For some ARMs, the interest rate and payment adjusts annually after the first year. For others, annual adjustment begins after 3, 5, or even 10 years. The common notation describes an ARM by indicating, first, the years until the first rate adjustment and, second, how frequently the rate adjusts. Thus, a 3/1 ARM has a three-year fixed period and adjusts annually after that time. The size of the annual adjustment is always limited-both the maximum adjustment in any given year and the maximum adjustment over the life of the loan. These limits are known as "caps" and they, too, vary from loan to loan. Templeton, Main and Orris (1996) showed that Monte Carlo simulations can shed light on the choice between an annually adjusting ARM and a FRM. This paper shows how Monte Carlo simulations can help a hypothetical borrower choose among ARMs.
The first simulation examines the choice of the length of the fixed period before the first interest-rate adjustment occurs. Borrowers can expect to pay a higher initial interest rate for the less risky ARMs that delay the date of first adjustment than for ARMs that begin adjustment sooner. We provide a simulation model that yields information on this cost and risk tradeoff. The simulation output allows a borrower to view the mean present value cost of an ARM at any date of termination, as well as probability distributions of present value-cost differentials between ARMs with different initial fixed periods. It also provides a distribution of the breakeven period-the number of years after initiation of the loan for which the ARM with the shorter fixed period maintains its present value-cost advantage over the ARM with a longer fixed period. Finally, the simulation permits insight into the financial planning aspect of the choice by modeling the impact of mortgage-rate changes on the size of payments for ARMs with various initial fixed periods.
The second simulation examines the choice of annual and lifetime caps for a standard one-year ARM. Borrowers can expect to pay a higher initial mortgage rate for less risky ARMs with lower caps. The same kind of output discussed above can help borrowers determine the circumstances under which they ought to be willing to pay a higher rate in exchange for the lower caps.
1. Literature review
There has been a limited academic literature so far dealing with mortgage choices, and much of that has dealt with the choice between FRMs and ARMs. …