PDF Ebook Anatomy of an ARM: The Interest Rate Risk of Adjustable Rate Mortgages
Recent surveys of major thrifts and mortgage bankers (see, for example, Inside Mortgage Finance) indicate that, while there are many different indices underlying adjustable rate mortgages in the U.S., four indices dominate the market:
- 1. The one year constant maturity Treasury yield,
2. One year LIBOR,
3. The Eleventh District Cost-of-Funds Index (EDCOFI),
4. The Federal Housing Finance Board (FHFB) national average contract interest rate.
The results of the Ott [18] ARM duration study, and numerous recent studies of the time series properties of EDCOFI, suggest that only the first of these indices adjusts instantaneously to changes in contemporaneous Treasury rates. The others adjust with a lag. Ott [18] uses a classical duration approach to show that this lag can have a significant impact on the interest rate sensitivity of ARMs. However, without explicitly modeling term structure dynamics, he cannot address the impact of mortgage prepayment, or additional common contract features such as interest rate caps. On the other hand, most recent ARM valuation models, using a contingent claims approach with a richer specification of interest rate dynamics, can analyze the impact of interest rate caps and prepayment, but they ignore the lag in the adjustment of the ARM coupon to the contemporaneous term structure (see, for example, Kau et al. [10], Schwartz and Torous [23], and McConnell and Singh [13]). No previous study simultaneously analyzes the interacting effects of both the time series properties of the index and prepayment/interest rate caps on the interest rate risk of ARMs.
This article analyzes the time series dynamics of the most commonly used ARM indices, and includes these dynamics in an ARM valuation model that builds upon techniques developed by Kau et al. [10], Kishimoto [11], and Stanton and Wallace [24]. Our model can simultaneously take into account the dynamics of the index, a realistic specification for interest rate dynamics, and nearly all standard ARM contract features, including both lifetime and periodic interest rate caps. Another major advantage of our approach is that it allows us either to determine endogenously the optimal prepayment policy for mortgage holders, or to use an empirically derived prepayment function.
We use our valuation model to compute the interest rate sensitivity for ARMs based on different indices, and with differing contract features. We find that the interest rate sensitiv-ity of an ARM is highly dependent on the dynamics of the index, prepayment behavior, term structure dynamics, and rate caps, with some surprising differences in the relative interest rate sensitivity of different contracts. In particular, we find that for uncapped ARMs, the slower the speed of adjustment of the index, the more interest rate sensitive is an ARM based on that index (since it more closely resembles a fixed rate loan). However, for otherwise identical ARMs with a lifetime maximum coupon rate cap, this ordering can paradoxically be reversed. We also find that changing the coupon reset frequency has a significant impact, and that using the wrong model for the index (ignoring the slow speed of adjustment) yields misleading results for the interest rate sensitivity of an ARM. The more often the coupon rate is reset, the worse the problem.
The article is in three sections. The empirical specification for ARM indices is discussed in section 2. Section 3 discusses the valuation methodology, and analyzes the effects of index dynamics, caps and margins on the interest rate sensitivity of ARM contracts. Section 4 concludes the article.
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PDF Ebook Anatomy of an ARM: The Interest Rate Risk of Adjustable Rate Mortgages
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