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KRIS-CDO features high "ease of use" and
allows an end-user with no special information technology skills to get up
and running in minutes
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KRIS-CDO uses powerful servers hosted by
Kamakura in a highly secure computer facility shared with major financial
institutions and agencies of the U.S. government.
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The underlying KRIS default probabilities
have been repeatedly demonstrated as more accurate than agency ratings and
agency-supplied default probabilities as a basis for default prediction.
This accuracy advantage prevails at all time horizons tested out to five
years. Please contact Kamakura at
info@kamakuraco.com for a list of the world's most sophisticated
institutions who can confirm such performance advantages.
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Kamakura's default probabilities and CDO
analytics are free of conflict of interest. Kamakura does not trade in
collateralized debt obligations or profit from the ratings on
collateralized debt obligations. As a result, KRIS-CDO valuations in
general show a less optimistic view of CDO valuation than views advocated
by market participants with a vested interest in expanding the volume of CDO issuance.
For more details on Kamakura's KRIS default
probability services, please see the KRIS Version 4.1
brochure dated July
2007.
Portfolio Modeling Techniques in KRIS-CDO
Many market participants use a single period model
for modeling CDO tranches. While this technique is common and widely used,
it implies that as the correlation in the events of default increase, the
value of the equity tranche actually rises. When modeling is done on a
multiple period basis, however, it becomes clearer to the analyst that two
forces are at work when correlation (however modeled in KRIS-CDO) rises:
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All other things being equal, an increase in
correlation tends to shift the burden of default to more senior tranches
in the CDO
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All other things being equal, an increase in
correlation tends to move the losses nearer to the valuation date,
reducing coupon income, increasing payments by the tranche holder for the
losses, and reducing value.
The net effect of these two factors can be either
positive or negative, not always positive as a single period model may
indicate. The next few sections briefly discuss the portfolio modeling
techniques in KRM.
Copula/Merton Portfolio Modeling
The copula/Merton approach to portfolio modeling in
KRIS-CDO can be used with any of the default probability models in KRIS-CDO.
This means analysts can employ both reduced form and Merton default
probabilities in the modeling effort. The copula approach (as widely used in
the market place) assumes that the return on the value of company assets is
random and that this factor triggers the default/no default occurrence and
(in the multiple periods case) timing. If there are N reference names in the
portfolio underlying the CDO, there are N(N-1)/2 pairs of companies in the
portfolio. The copula approach assumes that the correlation between the
returns on the value of company assets is the same for all N(N-1)/2 pairs of
companies. In KRIS-CDO, this correlation value is user controlled. Users can
vary the correlation coefficient to see the impact of changing correlation
on both value and the loss distribution. The copula method implicitly
assumes that there is only one common random factor driving the event of
default. It also assumes that default probabilities are held constant for
the entire length of the modeling period. For richer assumptions about
macro-factors driving default, see the alternative techniques in KRIS-CDO
listed below.
Historical Sampling for Portfolio Modeling
Many users of KRIS-CDO feel that the copula approach
is unrealistic in two important respects: they feel that default
probabilities in fact are not constant and that multiple economic factors
drive default probabilities up and down over the business cycle. Historical
sampling is one approach that captures the implicit correlation in default
probabilities as they rise and fall over time. When users of KRIS-CDO select
historical sampling, the KRIS-CDO calculation engine in period 1 randomly
chooses a period in history and selects default probabilities from a
historical point in time for all reference names. Default/no default is then
simulated for period 1 for all reference names. KRIS-CDO then moves ahead to
period 2 and selects another historical period. Again, default probabilities
from that point in time are taken for all reference names. This process is
repeated over and over for however many periods and however many scenarios
the user has specified. This technique is commonly used by portfolio
managers who also have common stock in their portfolios because historical
returns are the basis for much of risk management in portfolios of common
stock. This historical sampling contains an important implicit assumption.
Because the historical periods are sampled randomly, instead of
sequentially, this technique assumes that the level of default probabilities
that results from the sampling is more important than the sequence in which
they occur.
Macro-Factor Driven Default Probability Portfolio
Modeling
Many other users of KRIS-CDO believe it is very
important to capture two key features of the "real world":
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The macro-factor drivers of default
probabilities which rise or fall over the business cycle
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The division in default probability movements
between systematic macro-factor driven movement and non-systematic
idiosyncratic movements in default probabilities.
When a user selects macro-factor driven portfolio
simulation, KRIS-CDO pulls critical modeling information from the KRIS
default probability data base. Using a core set of 27 international
macro-economic factors, Kamakura has created a linkage between these
macro-economic variables and the historical movements in default
probabilities for every company, every default model and every maturity of
default probability in the KRIS data base. The time period used for
estimation starts in 1990 and continues to the present. For each company,
statistically significant macro-factors have been identified and the
magnitude of the idiosyncratic risk has been captured. When using this
portfolio modeling technique, the default probability movements due to both
the systematic macro factors and the idiosyncratic risk of the individual
company's default probability are captured. This sharply contrasts with the
common assumption in the copula approach that the default probabilities are
known with certainty and the only unknown is whether the company defaults or
not, given the default probability. The macro-factor driven approach
recognizes the uncertainty in the default probabilities and models it
explicitly. For this reason, this technique generally produces losses and
value distributions for CDO tranches that are less optimistic than a copula
simulation, even if both runs are based on the same default model and the
same starting default probability values.
Zero Correlation Portfolio Modeling
The final portfolio modeling technique available to
users is the base case which assumes zero correlation in the events of
default. While this assumption is unrealistic, it is a critical point of
comparison for KRIS-CDO users. This approach, like the copula approach,
holds default probabilities constant over the modeling period. Its results
should be identical with a copula simulation with the same number of periods
in which the correlation is assumed to be zero. Because zero correlation
portfolio modeling is simulated using the uniform distribution instead of
the normal distribution, it runs much more quickly than the copula method
with zero correlation.
Other Features of KRIS-CDO
KRIS-CDO also has a number of other features that
allow for maximum accuracy in the valuation of synthetic CDOs and the
related simulation of losses:
Periodicity of the Analysis:
User-selected--Monthly, Quarterly, or Annually
Number of Periods: User-selected from 1 period
to N periods
Number of Scenarios: User-selected from 100 to
500,000 (with authorization)
Graphic User-Interface: Any industry standard
web-browser
User Servers Needed: None, other than a
standard personal computer with a web-browser
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