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Using EDF Momentum to Provide Insights into Credit Migration and Default Risk
Ozge Gokbayrak and Lee Chua, July 2010
This paper presents a study of momentum impact within the Moody’s Analytics
EDF™ (Expected Default Frequency) credit measure on patterns of default risk
and rating changes. We define momentum as the significant rise or fall of an issuer’s
one-year EDF level during a one-year Horizon. The main question motivating our study
is whether or not such momentum can provide useful information about future credit
events, thus improving the utility of EDF credit metric for risk managers and investors.
We find that deteriorating momentum in EDF credit measures signals a much higher
likelihood of default, whereas entities with improving momentum show lower levels
of default risk. In addition, we find that Moody’s rating changes are highly
correlated with momentum signals: Deteriorating momentum results in higher downgrade
rates, whereas improving momentum results in higher upgrades.
Navigating Through Crisis: Validating RiskFrontier® Using Portfolio Selection
Zhenya Hu, Amnon Levy, Jing Zhang, April 2010
Assessing credit risk and ensuring the effectiveness and reliability of credit models
are critically important to many risk managers and portfolio managers, especially
during financial crises. This validation study examines the measurement accuracy
of the portfolio credit risk models employed in Moody’s Analytics RiskFrontier.
To evaluate accuracy, we construct various credit default swap (CDS) portfolios
with different levels of risk. We then compare the modeled portfolio volatilities
obtained from RiskFrontier with the subsequently realized portfolio volatility over
the crisis period of January 2008 through May 2009. We focus on the comparison for
three risk measures: instrument unexpected loss, risk contribution, and portfolio
unexpected loss. We find high rank correlations between ex ante and ex post measures
of portfolio relevant risk. These findings validate the model’s ability to
capture changing levels of risk and the co-movements of credit exposures. We find
that the choices of accurate and forward-looking probability of default (PD) values,
as well as asset correlation measurement, are critical when determining the model’s
predictive power.
CDS-implied EDF™ Credit Measures and Fair-value Spreads
Douglas Dwyer, Zan Li, Shisheng Qu, Heather Russell and Jing Zhang, March 11, 2010
In this paper, we present a framework that links two commonly used risk metrics:
default probabilities and credit spreads. This framework provides credit default
swap-implied (CDS-implied) EDF (Expected Default Frequency) credit measures that
can be compared directly with equity-based EDF credit measures. The model also provides
equity-based Fair-value CDS spreads (FVS) that can be compared directly with observed
CDS spreads. CDS-implied EDF credit measures and fair-value spreads are powerful
tools that risk managers can use to extend coverage of credit risk measures, enhance
the assessment of default risk, and assess the relative value of various credits.
With CDS-implied EDF credit measures, we can provide default risk measures for the
population of entities without traded equity, such as private firms, subsidiaries
of public firms, and sovereigns, based on their CDS. For firms with both EDF credit
measures and CDS-implied EDF credit measures, risk managers can use both metrics
to enhance their assessments of credit risk at the entity level. That is, by comparing
information from both markets in a common metric and understanding the differences,
risk managers can gain valuable insights into the credit risk of these entities.
By using both measures, they can minimize the model risk of relying on one measure
alone and increase predictive power of credit risk measures. Additionally, fair-value
spreads can be used for mark-to-market valuation and as well as for portfolio management.
Implications of PD-LGD Correlation in a Portfolio Setting
Qiang Meng, Amnon Levy, Andrew Kaplin, Yashan Wang, Zhenya (Ella) Hu, February 2010
This paper discusses the implications of the Moody’s Analytics PD-LGD correlation
model on portfolio analysis. We provide numerical results to illustrate the impacts
of PD-LGD correlation on risk and return measures of credit portfolios. Under the
PD-LGD correlation model framework, recovery is correlated with the firm’s
underlying asset process via both systematic factors and idiosyncratic shocks. PD-LGD
correlation introduces additional variability into instrument value and portfolio
value distributions. At the instrument level, value distribution becomes more dispersed
under the PD-LGD correlation model, since a good credit state is not only associated
with a low default probability, but also with a high expected recovery amount. The
opposite is true for a bad credit state. At the portfolio level, the values of defaulted
instruments are correlated with systemic factors. An implication is that during
an economic downturn, not only with the number of defaults be higher, defaulted
instruments end to realize a lower recovery amount as well. As a consequence, portfolio
value distribution will have a heavier tail, resulting in a higher risk measures
(e.g., Unexpected Loss and capital) when accounting for PD-LGD correlation. Spreads
will also widen to compensate for the increased risk. As a real-world example, PD-LGD
correlation increases the capitalization rate of the International Association of
Credit Portfolio Managers (IACPM) portfolio from 5.24% to 7.23%, a relative increase
of 37.8%. For comparison purposes, this paper also provides results from a stressed
LGD model and illustrates that the downturn LGD recommended in Basel II may not
be conservative enough to compute the capital amount associate with 10bp target
probability.
Validating the Public EDF™ Model During the Credit Crisis in Asia and Europe
Ozge Gokbayrak and Lee Chua, November 19, 2009
In this paper, we validate the performance of the Moody’s Analytics EDF™
(Expected Default Frequency) model during the recent credit crisis. We analyze the
model’s performance during the past two and a half years, and compare this
performance with the model’s longer history (2001-2006). We focus on the model’s
ability to differentiate between good and bad firms, the timeliness of its default
prediction, and accuracy of levels for two primary samples: Asian and European non-financial
firms. The current credit crisis has elevated default rates in both samples. We
measure performance with predictive power, early warning, and level validation.
A separate, recent Moody’s Analytics study looks at North American non-financial
firms as well as global financial firms. Overall, the EDF model’s predictive
power is as good as or better than the previous period. The model provides an early
warning signal a few years before default occurs; EDF levels were conservative (higher
than subsequently realized default rate) before the crisis compared with later-realized
default rates, and levels were statistically consistent with later-realized default
rates. We find that EDF credit measures perform consistently well across different
time horizons and across regions. Our tests indicate that EDF credit measures provide
a very useful measure of credit risk that can be applied throughout the world.
Bank Failures Past and Present: Validating the RiskCalc V3.1 U.S. Banks Model
Douglas W. Dwyer and Daniel Eggleton, October 8, 2009
This document outlines the validation results for the RiskCalc v3.1 U.S. Banks model,
and highlights the deteriorating financial ratios present in the banking sector.
We contrast trends of key risk measures to those of the savings and loan crisis
of the late 1980s and early 1990s. We also explore the speed and nature of recent
bank failures and demonstrate the model?s strong performance in light of this rapidly
changing environment.
An Empirical Examination of the Power of Equity Returns vs. EDFsTM for Corporate
Default Prediction
Zhao Sun, PhD, CFA, January 2010
In this paper we study the effectiveness of using equity returns for corporate default
prediction. Specifically, we analyze whether using equity return information alone
can yield similar performance to EDFs in default prediction. We find that the answer
is no. Key results from our study are as follows.
EDFs exhibit superior default predictive power to 6-month cumulative equity returns
over a one year horizon, with the accuracy ratio of the former 27 percentage points
higher than that of the latter. Shorter equity return windows lead to even larger
differences in default prediction power.
For 97% of the firms analyzed in our study, equity returns underperform EDFs by
large margins as default risk indicators, sometimes even providing signals opposite
to realized default rates. It is only for the 3% of the worst performing firms--where
financial distress is most obvious-- that equity returns exhibit comparable prediction
power to EDFs.
EDFs consistently outperform equity returns as default risk signals over time. The
cohort accuracy ratios of EDFs are also much more stable than that of the equity
returns, ranging between 80% and 90%, while those equity returns were between 24%
and 83%.
There is a weak relationship between equity returns and default risk. Both EDFs
and realized default rates show a "smirk" - shaped relationship to equity returns.
In addition, there is a wide variation in EDFs among stocks with similar past equity
returns. In addition, there is a wide variation in EDFs among stocks with similar
past equity returns, suggesting that EDFs and equity returns contain directionally
different information.
When firms with high EDFs and high equity returns are compared with those with low
EDFs and low equity returns (i.e., EDFs and equity returns provide distinctly opposite
default warning signals), the realized default rate of the former group is 16 times
higher than that of the latter group, suggesting EDFs are a much more accurate predictor
of default.
When the one-year distance to default, or DD1 (a monotonic transformation of EDFs),
is pitted against equity returns in a regression setting, the coefficient estimate
of DD1 is of the expected sign and is statistically significant, while equity returns
provide no additional default prediction power in the presence of DD1.
Risk
Integration: New Top-down Approaches and Correlation Calibration
Nan Chen, Andrew Kaplin, Amnon Levy, and Yashan Wang, January 2010
While the sophistication and adoption of the data, models, and software systems
for individual risk types has become more widespread, the tools for consistently
measuring integrated risk lag. Typically, individual risk components are aggregated
in ways ranging from simple summation to employing copula methods that describe
the relationship between risk types. While useful, these "top-down" approaches are
limited in their ability to describe the interactive effects of various risk factors
that drive loss. In this study, new top-down approaches are developed with varying
degrees of sophistication and flexibility. Moreover, a bottom-up model is introduced
to allow for an appropriate calibration of a correlation structure in a top-down
framework that describes both interest rate dynamics as well as credit dynamics.
The analysis is presented within the context of integrating two separate risk systems
to arrive at an aggregated portfolio risk measure-the Fermat system, which models
market risk, and Moody’s Analytics RiskFrontier®, which analyzes credit
risk. The bottom-up model is designed as a two-dimensional interest rate and credit
lattice that explicitly accounts for options in the valuation and risk analysis
of corporate bonds and loans. In some cases-interest rate insensitive instruments
in particular-the differences between the two approaches are minimal, suggesting
a straightforward top-down approach is sufficient to describe integrated risk. However,
the calibration becomes much more important for instruments that face both interest
and credit risk. For example, the simple top-down approach can overstate Unexpected
Loss (UL) by more than 25% relative to the more precise correlation-calibrated approach
for a typical vanilla bond portfolio. This study provides a foundation for appropriate
calibration of top-down approaches.
Analyzing
the Impact of Credit Migration in a Portfolio Setting
Yaakov Tsaig, Amnon Levy, and Yashan Wang, October 2009
Credit migration is an essential component of credit portfolio modeling and risk
assessment. In this paper, we outline a framework for gauging the effects of migration
on portfolio risk measurements. We find that, for a typical loan portfolio, credit
migration can explain as much as 51% of volatility and 35% of economic capital.
We compare the migration effects implied by Moody’s ratings transitions with
those implied by transitions of the Moody’s Analytics Expected Default Frequency
(EDF™) credit measure. We find that migration of point-in-time credit quality,
measured by EDF transition rates, accounts for a greater fraction of total portfolio
risk when compared with through-the-cycle dynamics reflected by agency rating migrations.
We demonstrate that visual inspection of a transition matrix is insufficient to
assess the migration risk implied by it. In a stylized analytic setting, we show
that, when controlling for PD term structure effects, higher likelihood of moving
away from the current credit state does not necessarily imply greater risk. We review
methods for generating high-frequency transition matrices, needed for analyzing
instruments with cash flows or contingencies whose frequencies are asynchronous
to an available transition matrix. We demonstrate that the naive application of
such methods can result in material deviations to portfolio analytics. Further,
we use a perturbed transition matrix to show that small perturbations in the probabilities
of extreme downgrades result in large distortions to the volatility of the value
of certain instruments in the portfolio.
The Relationship Between Default Risk and Interest Rates: An Empirical Study
Andrew Kaplin, Amnon Levy, Shisheng Qu, Danni Wang, Yashan Wang, and Jing Zhang,
October 2, 2009
Understanding the relationship between credit and interest rate risk is critical
to many applications in finance, from valuation of credit and interest rate-sensitive
instruments to risk management. This study empirically examines the relationship
between interest rates and default risk using firm level corporate default data
in the United States between 1982 and 2008. We find significant negative contemporaneous
correlations between the changes in short interest rates and aggregate default rates,
with a particularly strong relationship around financial crises. We also explore
the explanatory power of interest rate variables in predicting default when conditioned
on EDF™ credit measures. In addition, we study the impact of changes in short
rates, expected changes in short rates, interest rate slopes, and unexpected changes
in short rates. Conditional on the EDF credit measure, interest rates and default
were not found to have any statistically significant correlation. Our findings have
a number of important implications for risk measurement and management.
Level and
Rank Order Validation of RiskCalc v3.1 United States
Douglas Dwyer, Daniel Eggleton, September 2, 2009
In this paper, we validate the Moody's KMV RiskCalc v3.1 United States private firm
default model. We show that the EDF™ (Expected Default Frequency) produced
by the model continues to rank order risk effectively by providing substantial discriminatory
power across multiple cuts of the data.
We also validate the EDF level produced by the model. For most development datasets
used to build private firm default models, direct level validation is not possible
due to multiple issues encountered when working with private firm data. The U.S.
is an exception, because we have been collecting loan accounting system data for
the past nine years from multiple banks. This data enables direct measurement of
the default rate on a cohort of active borrowers. Using the loan accounting system
data, we find that the EDF level is consistent with the realized default rates observed
over the last nine years.
The Relationship Between Average Asset Correlation and Default Probability
Joseph Lee, Joy Wang, and Jing Zhang, July 2009
Asset correlation and default probability are critical drivers in modeling portfolio
credit risk. It is generally assumed, as in the Basel II Accord, that average asset
correlation decreases with default probability. We examine the empirical validity
of this assumption in this paper. Overall, we find little empirical support for
this decreasing relationship in the data for corporate, commercial real estate (CRE),
and retail exposures. For corporate exposures, there is no strong decreasing relationship
between average asset correlation and default probability when firm size is properly
accounted for. For CRE and retail exposures, the empirical evidence suggests that
the relationship is more likely to be an increasing one.
Understanding Asset Correlation Dynamics for Stress Testing
Qibin Cai, Amnon Levy, and Nihil Patel, July 2009
The Moody’s KMV approach to modeling asset correlation in measuring portfolio
credit risk is to decompose a borrower’s risk into systematic and idiosyncratic
components. Pairs of borrowers within a portfolio are correlated through their exposures
to systematic factors. Specifically, there are two sets of inputs that determine
the pair-wise correlation. The first set of inputs is the proportion of risk that
is captured by the systematic factors, or R-squared values. The second set of inputs
is the correlations among the respective systematic factors, or systematic factor
correlations. Understanding how the components of asset correlation change through
time will allow us to investigate how asset correlation dynamics behave during periods
of economic stress. Although the time-varying correlation of equity returns has
been extensively researched, we have found few studies on the dynamics of asset
correlation over time. In this paper, we explore how both R-squared values and systematic
factor correlations change through time. We show that R-squared values are more
volatile than the systematic factor correlations. We also study the relationship
between changes in R-squared and changes in factor variance, as well as the relationship
between changes in factor correlation and changes in factor variance.
Validating
the Public EDF™ Model Performance during the Credit Crisis
Irina Korablev, Shisheng Qu, June 26, 2009
In this paper, we validate the performance of the Moody's KMV EDF™ (Expected
Default Frequency) model during the recent credit crisis. We analyze the model performance
during the past two years, and compare this performance to the model's longer
history (1996-2006). We focus on the model's ability to differentiate between
good and bad firms, the timeliness of its default prediction, and accuracy of levels
for two primary samples: North American non-financial firms and global financial
firms. The current credit crisis has elevated default rates in both samples. Defaults
during the current crisis are somewhat unique because added complexities involving
government bailouts created, in effect, ambiguous defaults. We measure performance
with predictive power, early warning, and level validation. We also compare the
performance of EDF credit measures with agency ratings and credit default swap (CDS)
spreads.
Overall, the EDF model's predictive power is as good as or better than in the
previous ten years, and is comparable with CDS spreads on their respective samples.
The model provides an early warning signal a few years before default occurs; EDF
levels were conservative (higher than subsequently realized default rate) before
the crisis compared with later-realized default rates, and levels were statistically
consistent with later-realized default rates.
An Overview of Modeling Credit
Portfolios
Amnon Levy, Dec 29, 2008
This document provides a high-level overview of the modeling methodologies implemented
in RiskFrontier™ to address the challenges faced by a credit risk manager
or a credit portfolio manager. RiskFrontier attempts to accurately model the value
of a credit investment at the analysis date and its value distribution at some investment
horizon, as well as the correlation between two instruments in a portfolio. The
approach is designed to explicitly analyze a wide range of credit investments and
contingencies, including term loans with prepayment options and grid pricing, dynamic
utilization in revolving lines of credit, bonds with put and call options, equities,
credit default swaps, and structured instruments.
Modeling Correlation of Structured Instruments in a Portfolio Setting
Tomer Yahalom, Amnon Levy, Andrew S. Kaplin, November 2008
Published
in Encyclopedia of Quantitative Finance, John Wiley & Sons Limited (www.interscience.wiley.com)
Traditional approaches to modeling economic capital, credit-VaR, or structured instruments
whose underlying collateral is comprised of structured instruments treat structured
instruments as a single-name credit instrument (i.e., a loan-equivalent). While
tractable, the loan-equivalent approach requires appropriate parameterization to
achieve a reasonable description of the cross correlation between the structured
instrument and the rest of the portfolio. This article provides an overview of how
one can calibrate loan-equivalent correlation parameters. Results from taking the
approach to the data suggest that structured instruments have far higher correlation
parameters than single-name instruments.
Incorporating
Systematic Risk in Recovery: Theory and Evidence
Amnon Levy and Zhenya Hu, May 4, 2008
This paper proposes a theoretical framework to account for systematic risk in recovery
and to address the correlation between the firm's underlying asset process and recovery.
Under the proposed framework, the expected value in default under the risk-neutral
measure can be expressed as a linear function of the expected value under the physical
measure. This allows for a simple mapping between expected recovery observed in
the data and a measure that can be applied when using risk-neutral valuation methods.
A Brief History of
Active Credit Portfolio Management
Brian Dvorak, March 26, 2008
The first commercial EDF™ credit measure model was released by KMV in 1990,
although its foundations in extending the Merton model date from the early 1980s.
The EDF model is now in use at hundreds of institutions worldwide, and Moody's KMV
EDF credit measures are produced daily on more than 30,500 listed firms in 58 countries.
This paper addresses the following questions: What are the origins of active credit
portfolio management? How did the practice start, how has it evolved, and what can
we see on the horizon?
The Distribution of Defaults and Bayesian Model Validation
Douglas W. Dwyer, March 11, 2008
Quantitative rating systems are increasingly being used for the purposes of capital
allocation and pricing credits. For these purposes, it is important to validate
the accuracy of the probability of default (PD) estimates generated by the rating
system and not merely focus on evaluating the discriminatory power of the system.
The validation of the accuracy of the PD quantification has been a challenge, fraught
with theoretical difficulties (mainly, the impact of correlation) and data issues
(eg, the infrequency of default events).Moreover, models - even “correct“
models - will over-predict default rates most of the time. Working within the standard
single-factor framework, we present two Bayesian approaches to the level validation
of a PD model. The first approach provides a set of techniques to facilitate risk
assessment in the absence of sufficient historical default data. It derives the
posterior distribution of a PD, given zero realized defaults, thereby providing
a framework for determining the upper bound for a PD in relation to a low default
portfolio. The second approach provides a means for monitoring the calibration of
a rating system. It derives the posterior distribution of the aggregate shock in
the macro-economic environment, given a realized default rate. By comparing this
distribution to the institution's view of the stage of the credit cycle its
borrowers are in, this approach provides useful insight for whether an institution
should revisit the calibration of its rating system. This method allows one to determine
that a calibration needs to be revisited even when the default rate is within the
95% confidence level computed under the standard approach.
Asset Correlation, Realized Default Correlation, and Portfolio Credit Risk
Jing Zhang, Fanlin Zhu, and Joseph Lee, March 2008
Asset correlation is a critical driver in modeling portfolio credit risk. Despite
its importance, there have been few studies on the empirical relationship between
asset correlation and subsequently realized default correlation, and portfolio credit
risk. This three three-way relationship is the focus of our study using U.S. public
firm default data from 1981 to 2006.
Valuation of Corporate
Loans: A Credit Migration Approach
Deepak Agrawal, Irina Korablev, and Douglas W. Dwyer, January 25, 2008
Banks and investors in loan assets have always had difficulty obtaining an unbiased
and consistent value for the assets they hold. With the growth of liquidity in the
loan market, the demand for a valuation method that can be consistently applied
has been growing. However, the problems of loan valuation are complex. In large
part this is because of the existence of embedded options and contractual conditions
that can significantly affect the value of a loan. In this paper, we present the
Moody's KMV methodology for valuing corporate loans, taking into account both embedded
options and credit state contingent cash flows.
Using Asset Values and Asset Returns for Estimating Correlations
Fanlin Zhu, Brian Dvorak, Amnon Levy, Jing Zhang, September 12, 2007
In the Moody's KMV Vasicek-Kealhofer (VK) model, asset values and asset returns
are calculated separately. Moody's KMV GCorr uses weekly asset returns directly
from the VK model to calculate asset correlations. As an alternative, asset returns
estimated from monthly asset values from Credit Monitor® can be used to estimate
asset correlations. This study shows that the asset returns backed out from asset
values are vulnerable to capital structure changes and other corporate activities,
especially for financial firms. The frequent capital structure changes in financial
firms make their correlations from asset values much smaller than the correlations
from VK asset returns. Moreover, it is demonstrated that confidence intervals for
correlation estimates from three years of monthly returns are much wider than correlation
estimates from three years of weekly VK asset returns.
Power and Level Validation of Moody's KMV EDF™ Credit Measures in North America,
Europe, and Asia
Douglas W. Dwyer & Irina Korablev, September 10, 2007
In this paper, we validate the performance of Moody's KMV EDF™ credit measures
in its timeliness of default prediction, ability to discriminate good firms from
bad firms, and accuracy of levels in three regions: North America, Europe, and Asia.
We focus on the period 1996?2006 for most of our tests. Wherever possible, we compare
the performance to that of other popular alternatives, such as agency ratings, Moody's
KMV RiskCalc® EDF credit measures, Altman’s Z-Scores, and a simpler version
of the Merton model. We find that EDF credit measures perform consistently well
across different time horizons, and different sub-samples based on firm size and
credit quality. Our tests indicate that EDF credit measures provide a very useful
measure of credit risk that can be applied throughout the world.
Analyzing the Subprime Market Fallout Using EDF Credit Measures
Douglas W. Dwyer & Sarah Woo, April 16, 2007
Recent turmoil in the subprime mortgage market claimed several victims, notably
New Century Financial Corporation (NEWC), which filed for bankruptcy on April 2,
2007. In a review of the credit risk of a group of over two hundred REITs and mortgage
lenders, we found several firms with high EDF credit measures, which is the one-year
probability of default. A look at the EDF credit measure for the group as a whole,
however, reveals that credit risk has not changed much for less-risky companies,
i.e., those falling within the 75th percentile and below. Clearly, market players
are able to distinguish between companies holding onto subprime mortgages and those
with higher-quality or highly-diversified portfolios. Prior to its default on April
2, 2007, NEWC had been materially deteriorating since 2006, when its EDF credit
measure crossed the 90th percentile of its peer group. Most significant in NEWC’s
spiral towards bankruptcy was its liquidity crisis, as the company received notices
of default from its lenders alongside accelerated demands that it complies with
mortgage loan repurchase obligations. This report provides an analysis as to how
a subprime mortgage lender such as NEWC entered into default.
EDF™ 8.0 MODEL ENHANCEMENTS
W. Dwyer & Shisheng Qu, January, 2007
The Moody's KMV Expected Default Frequency model of public firms is the pioneering
implementation of a structural model that gives investors the ability to monitor
credit risk across a broad range of firms. The release of the EDF? 8.0 model represents
a major recalibration of the model, which incorporates both a larger default dataset
and improved estimation techniques that derive the EDF term structure from credit
migration.
The EDF 8.0 model refines the mapping of the Distance-to-Default (DD) to the EDF
level. The resulting EDF value is a superior measure of both absolute and relative
risk. The EDF 8.0 model also provides improved granularity with a wider range of
EDF credit measures so that fewer credits hit the model cap and floor.
These refinements meet the increased demands that market participants are placing
on quantitative credit risk models. Market participants demand models that provide
more granular measure of credit risk. They also want models they can use to determine
the fair value spread on a given exposure. Models need to be transparent and validated.
The validity of the EDF level needs to be demonstrated given its importance in computing
both required economic and regulatory capital.
In this document, we describe the process of mapping the DD to an EDF credit measure.
Further, we show the impact of the mapping changes on the EDF level, required economic
capital, required regulatory capital, and the EDF Credit Categories, as well as
the implications for the EDF-implied spreads for both Bonds and CDS contracts. Finally,
we provide more details regarding the inner workings of the model.
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