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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

Raymond Chiang*

Thomas F Gosnell**

Andrea J Heuson***

Abstract. This paper evaluates the interest-rate risk inherent in an adjustable-rate mortgage (ARM) with sporadic rate adjustments and possibly binding periodic and life-ofloan rate change constraints. Simulation analysis forecasts ARM cash flows, determines the probability that constraints will hold, and partitions the loan into fixed and variable components. Simulation parameters are then altered to measure the impact of changes in contract terms and market conditions on the interest-rate risk of a typical ARM loan. Interest-rate sensitivity is found to be significantly less than that of fixed-rate loans and remarkably insensitive to changes in loan margins or initial loan rates after the first few years of an ARM's life. Therefore, it is not surprising that lenders have used these features to lure borrowers to ARMs. Periodic rate change limits and volatility in the underlying index are the only factors that influence the interest-rate risk of an existing ARM in a substantive way.

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Introduction

Adjustable-Rate Mortgages (ARMs) were first offered by federally chartered depository institutions in 1981. Since that time they have become a widely accepted alternative to the fixed-rate, long-term mortgage loan. The ARM loan transfers some of the interest-rate risk of fixed-rate mortgage lending from the lender to the borrower. Under a fixed-rate loan, the lender must hold a below-market rate asset if market rates rise after the loan closes. It does not earn an above-market rate if interest rates fall, however, because borrowers can refinance the existing loan at the new, lower market rate.

The adjustable-rate loan minimizes unprofitable exposure to both upward and downward interest-rate movements by creating a debt instrument whose interest rate is seldom substantially different from the market rate. The ARM loan rate is adjusted periodically by adding a prespecified margin to the current value of a market-determined index. ARM lending is not free of interest-rate risk, however, because loan payments are fixed for the length of the adjustment period. Furthermore, periodic rate changes in either direction are subject to a prespecified limit while a prespecified premium added to the initial rate places a cap on the loan rate throughout the loan's life. Future rate adjustments are complicated further by the fact that the initial rate on most ARMs is significantly less than its fully indexed value (current index level plus stipulated margin), and caps and limits work off of stated rates, not fully indexed rates.

Caps and limits that temporarily constrain rate adjustments and fix loan payments during an adjustment period mean that ARMs are not purely variable rate debt and that ARM lenders are exposed to interest-rate risk. Despite the volume of ARM loans in existence, scant attention has been paid to the quantification of this interest-rate risk.

This paper assesses the interest-rate risk of an ARM loan by simulating cash flows under constrained and unconstrained rate changes and calculating the probability that each regime will hold. The expected value and duration of the constrained cash flows can then be calculated and used to determine the interest-rate sensitivity of the entire ARM loan.

The next part of the paper reviews previous academic research on the risk/return tradeoffs inherent in ARM lending. Section three demonstrates the interest-rate risk assessment methodology. Section four analyzes the relationship between an ARM's interest-rate sensitivity, its adjustment parameters and the volatility of the underlying index. Results suggest that the interest-rate risk of an ARM is relatively insensitive to the initial loan rate or the margin but fairly sensitive to the periodic rate change limit and to volatility in the underlying index. This result provides an economic justification for the fact that ARM lenders have relied on modifications in margins and teasers instead of smaller rate change limits to attract borrowers to ARM loans. The final section summarizes the paper's conclusions.

Risk/Return Trade-Offs in ARM Lending

The typical ARM loan has five parameters that govern the manner in which its interestrate path evolves through time. These are:

(1) the market index which initiates rate changes on the ARM;

(2) the margin that is added to the current value of the adjustment index to determine the fully indexed loan rate;

(3) the teaser, or discount off the fully indexed rate, that attracts borrowers interested in reducing loan payments in the early years of their mortgage;

(4) the annual rate change limit which prevents an ARM loan rate from rising or falling dramatically from year to year; and

(5) the life-of-loan cap which places a ceiling on the ARM rate throughout the loan's life, regardless of movements in the underlying index.

The interaction of these parameters as the ARM ages can create complicated relationships that underlie the cash flows on ARM loans. Since the value of an ARM is contingent on its actual cash flow, many authors have adapted contingent-claims models based on the seminal work of Cox, Ingersoll and Ross (1985) to the valuation of ARMs. 1 Two of the most comprehensive analyses to date were performed by the same authors (Kau, Keenan, Muller, and Epperson, 1990, 1993) who solved a series of partial differential equations to partition an ARM into four components. These are: (1) the value of the loan's cash flows to the lender; (2) the value of the prepayment option to the borrower; (3) the value of the default option to the borrower; and (4) the value of insurance against that default.

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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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