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

• E-mail
• Print
• Link

Results in the Cunningham and Capone (1990) study show that ARMs do experience greater default risk than fixed-rate loans. Marginal increases in credit risk are especially acute for ARMs that have short adjustment frequencies and large caps, and the probability of foreclosure increases when the yield curve has a steep upward slope. These findings imply that the possibility of sustained payment increases generates the increased default risk on ARMs.

The model presented in equations (3) through (5) could easily be extended to incorporate default by adding a constant survival rate as in the method used to calculate the constant prepayment duration in Anderson, Barber and Chang (1993). Specifics could be derived from the current risk-free rate and an assumed recovery percentage (given the existence of private mortgage insurance) in the manner described by Altman (1988), but there are three compelling reasons not to do so. First, ARM lenders can diversify away the default risk on single loans because defaults should not be correlated across borrowers in a national loan portfolio. Second, results in Capone and Cunningham (1992) show that default and prepayment factors virtually offset each other in the derivation of termination probabilities for ARMs. Third, and most important, the inclusion of default, interest-dependent prepayments and/or non-interest-dependent prepayments shortens the expected maturity of the ARM over all but the shortest expected life assumptions. This decreases the interest sensitivity of the loan.8 Therefore, the omission of terminations caused by these sources provides a conservative assessment of the interest-rate risk of an ARM loan.

The Duration of an ARM

The components of the duration calculation process have now been specified so it is possible to partition the expected cash flows on an ARM into fixed- and variable-rate components. Recall that ARMs are not pure adjustable-rate loans because of the presence of upward and downward rate change constraints and the practice of fixing the loan rate and payments for the length of the adjustment period. The parts of an ARM that are comparable to a fixed-rate mortgage are the current year payments and the later period payments that are constrained by the caps (S2 and S3). The rest of the ARM is the portion unrestricted by the caps (S1), and is equivalent to a pure variable-rate loan.

Thus, an ARM's value is composed of:

The distribution between fixed or fully adjustable components depends on the volatility of the index and the severity of the caps. If the caps are tighter, the constraints will be more binding. Thus S2 and S3 will be more probable and the proportion of the fixed-rate mortgage will be larger. In the extreme case, the caps approach zero and the ARM becomes a fixed-rate mortgage.

Another important aspect of the typical ARM is that the rate adjustment process has a one-period lag. The monthly payment for the current year is always fixed and those fixed payments create interest-rate exposure. Ott (1986) shows that the fixed-rate component of an ARM is a positive function of the interval between successive adjustment periods. As the adjustment interval approaches the term-to-maturity (Tj, the fixed-rate proportion approaches one. The model above differs from that proposed by Ott in one major respect, however. Here, the fixed-rate portion of the ARM loan will never approach zero, even if the adjustment period is instantaneous, because of the presence of periodic and life-of-loan rate change constraints. Once the fixed-rate loan component of the ARM is specified, the interest-rate risk of the fixed-rate portion, DUR^sub b^, can be calculated as: