CMOs, duration risk and a new mortgage

Journal of Real Estate Research, The, Jan-Apr 2000 by Thode, Stephen F

Abstract

This article is the winner of the Real Estate Finance manuscript prize (sponsored by the Fannie Mae Foundation) presented at the 1999 American Real Estate Society Annual Meeting.

This article presents an alternative mortgage that retains the fixed-rate feature of a fixed-rate mortgage (FRM), but accelerates the principal amortization when interest rates rise, exposing the buyer to less duration risk in a rising interest rate environment. This mortgage, labeled the adjustable amortization mortgage (AAM), is shown to have lessened interest rate risk for the buyer as well as lower default risk, suggesting that it should be priced higher (at a lower rate of interest) than the typical FRM. It is also shown that mortgage-backed securities collateralized by an AAM have much less price volatility than mortgage-backed securities backed by FRMs.

Introduction

A large percentage of intermediate-to-long-term (fifteen years and longer) residential and commercial mortgages in the United States is sold into the secondary mortgage market (SMM). These mortgages are then bundled together, usually by credit quality, interest rate and term, and securities are sold using the cash flow from the bundled mortgages as the basis for payment. Although a variety of securities may be sold, one of the most common is the collateralized mortgage obligation (CMO), which is divided into separate slices or tranches-each with a different priority on the cash flow from the underlying mortgages.

Buyers of CMO trenches face a variety of risk factors-among them interest rate risk, prepayment risk and duration risk. Although CMO writers may take a variety of steps to attempt to reduce these risk factors, such as creating planned amortization class (PAC) trenches, pooling adjustable-rate mortgages, and the like, these risk factors cannot be eliminated entirely. In fact, prepayment risk (the risk that prepayments by mortgagors will differ from what is expected) remains a telling problem for CMO writers since virtually all residential mortgages may be prepaid in whole or in part at any time without penalty.

Prepayment risk is exacerbated by the fact that prepayments tend to accelerate as interest rates decline (home sales and refinancings increase), and to decelerate as interest rates rise (home sales and refinancings decrease). Thus, the duration of a CMO tranche investment tends to move in the same direction as interest rates. This is an especially acute problem when interest rates rise. In this environment, CMO investors see a decline in the value of their investments in two ways: the increase in interest rates reduces the present value of future interest and principal cash flows; and, as prepayments decline, duration increases-further diminishing the value of expected cash flows.

In this article, a new type of fixed-rate mortgage-the adjustable amortization mortgage (AAM)-is proposed as a partial solution to the prepayment risk/ duration risk problem faced by CMO investors. Like a standard fixed-rate mortgage (FRM), the interest rate on an AAM is fixed for the term of the mortgage; unlike a standard FRM, the payments (and, hence, the amortization of principal) increase in response to a rise in the general level of interest rates. It is shown that CMOs (and their respective tranches), which are written against pools of adjustable amortization mortgages, have much lower levels of prepayment risk and duration risk in a rising interest rate environment. Thus, owners of AAMs and the securities written against them have less downward price volatility. Ceteris paribus, AAMs and securities written against them should command premium prices (lower yields) than corresponding standard fixed-rate mortgages and securities written against them.

Prior Research

The effects of interest rate changes, prepayments and duration on the pricing of mortgages has been the subject of widespread research. Kau, Keenan, Muller and Epperson (1993) develop a contingent claims model for mortgage pricing based on the interest rate model of Cox, Ingersoll and Ross (1985). Kau et al. show that the prepayment option may be of great value to the borrower under a FRM and, hence, an important component in the pricing of FRMs. Haensly, Waller and Springer (1993) focus on duration and price behavior in FRMs.

Archer and Ling (1993) develop a model of mortgage prepayment, which includes suboptimal (non-interest-rate driven) prepayments as well as the endogenous interest-rate call, while Hakim (1997) analyzes the distinction between induced and autonomous mortgage prepayments. He finds evidence of a significant relationship between borrower characteristics, property age and regional mobility, and mortgage termination rates.

Thode (1991) develops a fixed payment, adjustable-rate mortgage (ARM) and demonstrates that it has less default risk and less interest rate risk than a standard ARM. Thode and Kish (1992, 1994) construct a FRM that uses a prepaid zero coupon treasury bond for principal repayment. They show that this mortgage has less prepayment (and duration) risk than a standard FRM.