folio increases, especially when one allows for cor-
relation among participants.Modeling Loss Rates
More incremental analyses of pools became possi-
ble as computers became faster, and the value of
iterative statistical methods was better understood.
While often the actual default probability distribu-
tion of a specific pool may not be determined theo-
retically, it can be approximated and observed
through repeated random trials, just as the repeated
flipping of a coin will reveal the true probability of
heads to be 50%. Standard & Poor’s quantitative
group within structured finance has developed soft-
ware that uses a Monte Carlo methodology, featur-
ing such an iterative process to estimate the default
rate probability distribution for any pool entered.
The software has now been adapted to allow for
the analysis of municipal pools as well. From this
distribution is derived a set of stressed default rates
which vary according to the pool rating desired.
This methodology fully captures the effects of
obligor concentration, correlation, and obligor
credit quality in a simultaneous manner, thus per-
mitting more insight into incremental changes in
pool credit quality as pool composition evolves.
To derive the portfolio default probability distri-
bution, a default matrix is used to assign a specific
default probability to each participant obligation
based on the nature of the participant, its credit
quality, and the obligation’s maturity.Model Inputs
To run the simulation, the model requires each par-
ticipant’s asset type, par amount, rating, and matu-
rities. For most governmental entities, the asset type
will be the postal abbreviation for the state in
which the participant is located. For non-profit
organizations and certain other sectors, a sector-
specific code should be used (see table 1). The asset
type designation helps determine the correlation
between participants. Model inputs, or assets, are
at the maturity level, so a pool of 20 participants
with amortizing loans, each with 20 years remain-
ing on their obligations under the pool would have
20 x 20 or 400 assets. Alternatively, each loan may
be entered as a single asset, using the final maturity
or the weighted average maturity. Maturities are
required as the model uses the participant’s rating,
security, and length of maturity to arrive at partici-
pant default probabilities. The model then runs a
series of trials from which the default probability
distribution and resulting stressed default rates are
generated. While Standard & Poor’s will distribute
versions of the model so that pool programs may
use and become familiar with the software, we will
also require that participants provide the necessarydata so that we may run the default analysis in-
house before issuing a rating.Cash Flow Analysis
Once default stress levels have been established, the
issuing agency will be asked to prepare cash flows
incorporating the default assumptions. Because the
model produces aggregate portfolio default rates,
default rates should be applied against aggregate
repayments available to service debt each year that
defaults are recognized. To translate the percent of
asset or loan portfolio defaults into amounts need-
ed to absorb these defaults, recovery rates must also
be considered. Recovery rates will vary based on
the nature of pool participants and the security
being pledged (see table 1). For state revolving
funds (SRFs) and other government or quasi-gov-
ernment public purpose pools backed by water and
sewer utility pledges or GOs, the assumption that
obligors remain in default for four years and then
begin paying principal, interest, and other required
payments in full (at 100%) will continue. Pools
consisting of other types of obligations or that lack
government motive and oversight will have recov-
ery rates less than 100% after the four-year default
period. The methodology employed by the program
administrators in granting loans to participating
entities and monitoring the ongoing financial and
operating status of the borrowers may also influ-
ence duration assumptions.
While the Monte Carlo model reveals how much
of the pool should be expected to default, it reveals
nothing about the expected timing of defaults.
Standard & Poor’s will assume that all defaults
begin to occur over a four-year period, with 25%
occurring each year over the period. The end result
is that default scenarios will show some level of
default over a seven-year period (rather than a four-
year period), but 100% of the assumed defaults will
occur in only one year (rather than four years). Put
another way, if the assumed default rate for a given
portfolio at a given rating is 40%, then 25% x
40%, or 10% of aggregate debt service should be
defaulted in the first year of defaults, 50% x 40%,
or 20% in the second year, 75% x 40%, or 30% in
the third year, and 100% x 40% in the fourth year.
Finally, recovery levels should be factored in to
arrive at net defaulting amounts in each year. In
year five of the previous example, if we assume
90% recovery, then of the 10% of defaults that
began in year one, 10% x 90%, or 9% would
begin paying again, resulting in a net default rate of
40%-9%, or 31% (see table 2).
A pool’s vulnerability to participant defaults may
vary over the life of the rated bonds, so cash flow
runs should also demonstrate that the pool can
withstand the stressed default rate at any point inCross Sector Criteria44 Standard & Poor’s Public Finance Criteria 2007