Different dynamics of the major ARM indices (one year constant maturity Treasury yield, one year LIBOR, EDCOFI, FHFB national average contract rate, etc.)lead to significant variation in the interest rate sensitivities of loans based on different indices. Changing assumptions about contract features, such as loan caps and coupon reset frequency, also has a significant, impact on results.
Classical duration tells us that the lag time (implicit in all the indices excepting the one year Treasury) can have a significant impact on the interest rate sensitivity of ARMs. Without explicitly modeling term structure dynamics, it becomes difficult to address the impact of mortgage prepayment, or additional common contract features such as interest rate caps, etc.
The time series properties of the index and prepayment/interest rate caps on the interest rate risk of ARMs all become important in projecting your answer...
For a given index, It, a model could be written as:
It = α + β r t + γ I t−1 + t
where r t is an instantaneous spot rate, and t is an error term. The coefficient β indicates the effect of the spot rate on the index each period, and γ indicates the speed at which the index adjusts. The extremes in the adjustment dynamics would be β = 0, where the index does not move at all with market rates, and γ = 0, where the index moves perfectly with the spot rate (the usual implicit assumption). |
