Evaluating the interest-rate risk of adjustable-rate mortgage loans

Journal of Real Estate Research, The,  1997  by Raymond Chiang,  Thomas F Gosnell,  Andrea J Heuson

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Kau et al. also consider fixed-rate loans and provide simulations that are powerful enough to allow comparisons of the two types of funding. For example, the borrower's prepayment option is typically worth more on a fixed-rate loan than an ARM because the fixed-rate loan rate does not drop with market rates. In contrast, insurance is typically worth more on an ARM than on a fixed-rate loan because rising payments on the adjustable-rate debt may lead to increased default risk.

In addition, the Kau et al. results quantify the interest-rate risk trade-offs faced by lenders who must select some combination of adjustment parameters when quoting ARMs. For example, a higher margin (which raises future loan rates and payments) is required to offset the effects of a higher initial year teaser, a tighter annual rate change limit or a lower life-of-loan cap. Furthermore, caps and limits have a much more dramatic effect on ARM value when the underlying index is volatile; periodic limits influence ARM cash flows much more strongly than life-of-loan caps do; and upward adjustment limits are more constraining than downward adjustment limits because borrowers will prepay ARMs when rate drops are constrained.2

Given the recent attention focused on valuing adjustable-rate loans at origination and partitioning that value into cash flow and default and prepayment option components, it is puzzling to note that little effort has been made to quantify the interest-rate risk that teasers, limits and caps inpute to ARM loans as the loans age.3 Only one study (Ott, 1986), specifically addresses the relative interest-rate sensitivity of various ARM loans, but Ott limits his attention to interest-rate risk on the first interest-rate adjustment date.

A wide variety of adjustment indices and parameters appeared in the market when adjustable-rate mortgages were first introduced. Ott demonstrated that interest-rate sensitivity was positively related to the length of the adjustment period (the time for which payments are fixed), and to the choice of the index. For example, loans indexed to Treasury rates with terms longer than the adjustment period, to Federal Home Loan Bank Board mortgage rates, or to cost-of-fund indices, were found to lag market interest rates, increasing exposure to interest-rate risk.

The passage of time and market developments have resulted in a need to reexamine the interest-rate risk of an ARM. First, the sets of adjustment parameters typically offered on ARM loans have been reduced. One-year adjustment frequencies predominate and most ARMs are indexed directly to a corresponding Treasury rate. Second, as ARMs age, the focus of ARM lenders and researchers has extended beyond the initial rate adjustment date. From this perspective, the impact of periodic or life-of-loan rate adjustment constraints over time is much more important than behavior on the first adjustment date.

The methodology described in detail in the next section of the paper adopts the traditional finance concept of duration first proposed by Macauley (1938) as a measure of interest-rate risk. Recognizing that the elasticity of an ARM's price to changes in interest rates is non-zero when loan payments are constrained (e.g., during the current rate adjustment period and when rate change limits or caps hold in future periods), the approach uses simulation analysis to determine the probability of constrained payments, the value of constrained payments, and their duration. These are then used to measure the overall interest-rate risk of a given ARM loan.