Defining a measure of prepayment uncertainty

While standard definitions for effective duration and convexity have gained universal
acceptance as measures of interest rate risk,5 no standard set of prepayment uncertainty
measures yet exists. Some proposed measures have been called ‘prepayment
durations’ or ‘prepayment sensitivities’ (Sparks and Sung, 1995; Patruno, 1994).
Here, we describe three measures that are readily understood and capture the
major dimensions of prepayment uncertainty. These measures are labeled overall
prepayment uncertainty, refinancing (‘refi’) partial prepayment uncertainty, and
relocation (‘relo’) partial payment uncertainty.
To derive an overall prepayment uncertainty measure, the ‘base case’ prepayment
speeds predicted by a model are decreased by 10%, then increased by 10%, and two
new prices are derived under the slower and faster versions of the model (holding
the term structure of interest rates, volatilities and security’s option-adjusted spread
constant):6
PSMMñ10%ñPSMMò10%
2îPBase caseSMM
î100
where Póprice and SMMósingle monthly mortality rate (prepayment speed
expressed as a series of monthly rates).
Computed this way, securities backed by discount collateral tend to show a
negative prepayment uncertainty. This makes intuitive sense, as a slowdown in
prepayment speeds means the investor must wait longer to be repaid at par. Conversely,
securities backed by premium collateral tend to show a positive prepayment
uncertainty, because faster prepayments decrease the amount of future income
expected from the high-coupon mortgage pool compared to the base case forecast.

Note that for CMOs, a tranche may be priced at a premium to par even though the
underlying collateral is at a discount, and vice versa. Therefore, one should not
assume that the prepayment uncertainty of a CMO is positive or negative simply by
noting whether the security is priced below or above par.