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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 (e.g., 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.
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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