An Introduction to Through-the-Cycle Public Firm EDFTM ... · Through-the-Cycle Public Firm EDF...

An Introduction to Through-the-Cycle

Public Firm EDFTM Credit Measures

May 2011David T. Hamilton, PhD Managing Director, Capital Markets Research Group

2Through-the-Cycle Public Firm EDF Credit Measures

What are Through-the-Cycle EDF Credit Measures?

» Through-the-Cycle EDF (TTC EDF) credit

measures are one-year default

probabilities that are largely free of the

effect of the credit cycle

» TTC EDFs are useful in applications in

which the cost of adjusting credit

exposures outweighs the cost of negative

credit events (such as default); e.g.

required capital, fixed income portfolio

management guidelines

» TTC EDFs are derived from Moody’s

Analytics’ public firm EDFs, the industry-

leading structural credit risk model

» TTC EDFs are available at a daily

frequency for all 30,000+ firms in all

geographic regions for the past year, and

monthly back to 1992


Outline

1. The Distinction between PIT and TTC Credit Measures

2. Public Firm EDF Model Review

3. TTC EDF Model Mechanics

4. TTC EDF Metric Performance Statistics

5. Conclusion


The Distinction between PIT and

TTC Credit Measures1


What Do the Terms PIT and TTC Mean?

» A point-in-time (PIT) credit risk measure is one which utilizes all available and

pertinent information as of a given date to estimate a firm’s expected likelihood

of default

» PIT PDs are ideally suited for situations where the where the cost of defaults or

credit spread changes is high, and early detection of changes in credit risk at

both the single name and portfolio level is important

» The definition of through-the-cycle (TTC) credit risk measures is less precise,

but the predominant feature of TTC credit risk measures is their high degree of

stability and smoothness over the cycle

» The stability of TTC risk measures comes at the cost of reduced timeliness and

default prediction accuracy relative to PIT risk measures

» TTC PDs are valuable when portfolio adjustment costs or regulatory

compliance costs are high, such as meeting required capital and in fixed

income portfolio investment guidelines


The PIT-TTC Distinction is Important and Useful

» A complete risk management system requires both PIT and TTC EDFs

» Actions by a firm’s managers depend on whether a change in credit quality is

believed to be permanent or transitory.

– For example, a change in credit quality perceived to be permanent may induce a

change in capital structure (that in turn affects future credit quality)

» Risk management is often a constrained optimization problem

– E.g. maximize returns subject to portfolio limits; maximize ROA subject to capital

constraints

– Maximum model power (in terms of default prediction) is therefore not the sole or

sufficient goal

» From a policy maker’s perspective, the use of PIT measures in risk

management may exacerbate economic downturns because they tend to be

strongly pro-cyclical. TTC risk measures may potentially help stabilize the

financial system


What Properties Should TTC Risk Measures Have?

» A TTC risk measure is a PD derived from a PIT measure that reflects the credit

component that is largely free of the effect of the credit cycle

– The PIT risk measure contains all the information we need, it is just hidden

– Presupposes the existence of an aggregate cycle that affects all firm-level PDs

» The TTC smoothing method should attenuate the influence of the

credit/business cycle while minimizing the loss of firm-specific signal

– A TTC PD will not completely remove cyclical effects

– Peak-to-trough volatility (cyclical amplitude) should be significantly reduced

» TTC smoothing explicitly dampens early warning signal, and possibly biases

level calibration and reduces rank ordering power for reduced volatility

– Is the tradeoff acceptable?

– Given the cost of smoothing PIT PDs, one must have some theoretical basis for

smoothing – i.e. the smoothing intensity must be optimal with respect to some

definition of the cycle


Public Firm EDF Model Review2


Moody’s Analytics’ Public Firm EDF Model and Metrics

» Moody’s Analytics’ public firm EDF model is a variant of the Black-Scholes-

Merton structural credit risk modeling approach:

- There is a causal, economically motivated explanation for default

- Equity valuations, which largely ignore credit risk, may be used to infer the risk of

default

» Basic statistics and finance theory allow one to map fundamental credit

concepts, like firm leverage, into estimates of the probability of default (PD)

» Moody’s Analytics’ public firm model generates a PD called the Expected

Default Frequency (EDFTM) that ranges from 1 bp to 35% at a one-year

time horizon

» EDF credit measures are cardinal measures of risk:

- EDFs are expected default probabilities: an EDF of 1%, for example, means that

out of 100 exposures there is one expected default per year

- EDF levels have the same meaning through the economic/credit cycle: an EDF

of 1% has a constant meaning in both expansions and recessions


Default Process in a BSM-Type Default Model

Value of Assets / Liabilities

Timet = 0 T = 1 year

Notional value of liabilities

Xt

Distribution of market

value of assets (A)

E[AT] = μ

Probability that A<X

→ firm defaults

Distance to

default (DD)

measured in σ

Market value of assets

At If A<X then the firm has

negative net worth and

exercises its option to default


Distance-to-Default Summarizes Credit Risk

» Without loss of generality, DD at a one-year time horizon can be written

» The numerator is simply market leverage

» The denominator, the volatility of a firm’s assets, is its business risk

» The higher is market leverage or the higher is business risk, the lower the

DD and the higher the EDF

» We use DD and its drivers to derive TTC EDFs

A

TXADD

)ln()ln( 0


Calculating EDFTM Credit Measures from DDs

» EDF credit measures are

derived from an empirical

mapping of DDs to historical

default rates

» Public firm EDFs were

calibrated using US non-

financial firms from 1980 to

2007, including over 8,000

defaults

» In the BSM model, PDs for a

majority of firms tend to be too

low compared to realized

default rates

DD = 4 maps to a 0.003% PD in

the simple BSM model, but to

a 0.4% EDFTM metric

Note: the EDF-DD curve in the graph is a stylized representation

of the actual DD to EDF mapping function


TTC EDF Model Mechanics3


Much like music, an EDF credit measure consists of many sub-signals vibrating at

different frequencies, with its underlying credit quality moving at low frequencies and

its cyclical component moving at high frequencies

Estimating a TTC EDF metric from a raw EDF is like adjusting the sound of a song by

turning the bass and treble knobs on your stereo according to your preference

By turning the knobs, we can adjust – filter – the signal to contain only the desired

subset of frequencies in the music

The treble knob controls the strength of the high frequencies (the cyclical elements),

while the bass knob controls the low frequencies (the firm-specific elements)

So, if we wanted to filter out the cyclical component in an EDF metric (i.e. keep the

low-frequency, firm-specific signal), we would need to turn down the treble

Filtering the Cyclical Signal from EDF Metrics


Filtering the Cyclical Signal from EDF Metrics

)( ,tiddf

tidd ,

][][ ddEddE

dddd

)( ,tiddg

)(ddG

tiiiti dddd ,,

tidd ,

The goal is to find a function G(dd) that preserves the expected value of dd while

reducing the amplitude (long-run volatility) of dd

A linear filter has this property for appropriately chosen α and β

The parameters of the filter can be estimated through linear regression if we know dd

and dd’


From EDFs to Through-the-Cycle EDFs

» Two key modeling challenges in deriving a TTC credit measure are:

– What is the “C” in TTC? Do we really want to smooth EDF metrics with respect to

output (e.g. GDP) fluctuations, or credit fluctuations (which tend to occur less

frequently)?

– Once we have defined the cycle, how do we measure and filter it out of each firm’s

raw EDF credit measure?

» We define the credit cycle as the periodic fluctuations in EDFs that affect all

firms

» As point-in-time measures, EDFs include the effects of firm-specific and

cyclical credit risk components

– The cyclical effect we want to filter out are embedded within each firm’s EDF; we do

not need to utilize external macroeconomic data

– The cyclical effect is not directly observable, so we need a method to estimate it


Mean US EDFs, Industrial Production, and Recessions

US EDFs are correlated with changes in US industrial production, but not perfectly


A Trend-Cycle Approach to TTC Estimation

» A firm’s DD (yt) may be modeled as consisting of two additive elements:

yt = μt + ct

where μt is the firm-specific trend component and ct is the cyclical component

» The firm-specific trend of credit risk for a firm is usually thought of as relatively

slow moving, enduring (long term), smooth, and positively auto-correlated

» The cyclical component is typically considered high-frequency, transient (short

term), volatile, and relatively less positively (or negatively) auto-correlated

» If we can estimate μt, then we have the data we need to estimate the

parameters in the linear regression to the filter each firm’s raw DD and

calculate a TTC EDF

» We use the Hodrick-Prescott Filter to estimate μt and ct


Trend-Cycle Decomposition of DD

The HP filter trend-cycle decomposition bears a resemblance to the classic asset value

dynamics model

yt

ct

μt = yt - ct

The cyclical

component is

mean zero and

stationary

The trend

component

(“drift”) evolves

smoothly


TTC EDF Estimation Process

Step 1: For each firm, estimate the HP filter

trend component from its DD history

Step 2: For each firm, regress HPDD on

DD to get parameters α and β

For firms with insufficient DD history we

estimate α and β from firms with similar

characteristics, based on firm size, industry

sector, region, asset volatility, and leverage


TTC EDF Estimation Process (continued)

Step 3: Using parameters α and β from step 2,

calculate TTC DD for each firm

Step 4: Using the DD-to-EDF mapping,

calculate TTC EDF from TTC DD

Honeywell Corp.


Remarks on TTC EDF Methodology

» Our methodology is agnostic with respect to the definition of the credit cycle; we

interpret credit cycles simply as deviations from estimated long-run trend

» Our model does not depend on an assumption that credit cycles are periodic or

regular; it does not require us to know where we are in the credit cycle nor to

forecast the future

» Our TTC EDF filtering methodology is based on data for over 20,000 firms from

1969 to 2010, including 5 full credit cycles, including the severe downturn of 2008-

2010

» Our methodology is very parsimonious and relies on just a few parameters; i.e.

there is less model risk relative to other methods

» TTC EDFs are a derivative of EDFs; i.e. the raw EDF model is not tampered with

» TTC EDFs can be calculated daily for all firms and are not subject to ex-post

revision


Example: Goldman Sachs


Example: France Telecom


Example: Siemens AG


Example: Ferrovial SA


TTC EDF Metric Performance Measures4


TTC EDF Performance Measures

We evaluate Through-the-Cycle EDF credit measures using five criteria:

1. EDF cyclical volatility

– How much is EDF cyclical amplitude (the range of EDF, or max - min) reduced?

2. Rank order power

– How much does smoothness reduce rank order power (AR) of default prediction?

3. Level calibration

– Does TTC smoothing bias the level of EDFs relative to realized default rates?

4. Rating transition probabilities implied by TTC EDFs vs. EDFs

– Do TTC EDFs yield implied ratings that are more stable than those based on EDFs?

5. Performance in a portfolio: required capital

– How much do TTC EDFs reduce the procyclicality of required capital?

The data suggests that the smoothness benefits of TTC EDFs (at the single-name level as

well as the portfolio level) generally outweigh the costs of the loss of rank order power and

level calibration by a significant margin


Cyclical Amplitude of TTC EDFs is Significantly Lower than EDF for Most Firms

» Cyclical volatility

(amplitude) is measured

by the range (max-min) of

each firm’s EDF time

series

» 86% of firms’ EDF

amplitude is reduced by

50% or more

» Almost 50% of firms’ EDF

amplitude is reduced by

at least 80%

Distribution of TTC EDF / EDF range ratios, 1992-2011


TTC EDFs Retain Strong Rank Order Default Prediction Power while Achieving High Stability


By Design TTC EDF Levels Are Compressed, Especially for High and Low EDF Levels

North American Corporates » The graph shows the

average EDF for each EDF

percentile bucket and

compares it to the average

realized default rate for the

same bucket

» The lines for TTC EDF are

flatter than the lines for

EDF

» Between the 20th and 90th

percentiles TTC EDFs

exhibit the same or better

consistency with realized

default rates as EDFs


Ratings Implied by TTC EDFs are Much More Stable than those Based on EDFs

Aaa Aa1 Aa2 Aa3 A1 A2 A3 Baa1 Baa2 Baa3 Ba1 Ba2 Ba3 B1 B2 B3

EDF 61.5 9.1 12.6 18.4 25.5 26.8 23.9 21.0 18.9 17.2 16.5 15.9 15.6 15.5 15.9 16.8

TTCEDF 99.9 89.6 77.6 66.3 60.9 59.6 57.7 55.1 52.3 49.4 48.2 47.0 45.7 46.3 47.3 49.1

MOODYS 86.2 74.9 74.2 74.9 75.4 75.8 73.4 72.6 73.6 70.0 63.0 62.5 63.9 63.9 61.6 59.1


TTC EDFs Reduce the Procyclicality of Required Capital

Required capital using DJIA portfolio of 30 firms (as of 31 March)

» We calculated required

capital using the Basel II

formula and a 45% recovery

rate

» The average Moody’s rating

is Aa3, the average EDF is

0.1%, and the average TTC

EDF is 0.06% for firms in the

portfolio

» The change in required

capital during the financial

crisis falls from 9.2X using

unadjusted EDFs to 1.5X

using TTC EDFs; for

Moody’s ratings the change

is 1.1X


Conclusion5


Key Take-Aways

» Through-the-Cycle EDF (TTC EDF) credit measures are one-year default

probabilities that are largely free of the effect of the credit cycle

» TTC EDFs are useful in applications in which the cost of adjusting credit exposures

outweighs the cost of negative credit events (such as default); e.g. required capital,

fixed income portfolio management guidelines

» A complete risk management system requires both EDFs and TTC EDFs; they are

complements, not substitutes

» TTC EDFs are derived from EDFs; we do not tamper with the EDF model, but we

use its drivers

» A high degree of stability is achieved for acceptable loss of forward looking default

prediction power (in terms of rank ordering and level calibration)


David T. Hamilton

Managing Director

Quantitative Credit Research

Capital Markets Research Group

Moody’s Analytics

7 World Trade Center

New York, NY 10007

+1 212 553-1695

[email protected]

moodys.com


© 2011 Moody’s Analytics, Inc. and/or its licensors and affiliates (collectively, “MOODY’S”). All rights reserved. ALL INFORMATION CONTAINED HEREIN IS PROTECTED BY

COPYRIGHT LAW AND NONE OF SUCH INFORMATION MAY BE COPIED OR OTHERWISE REPRODUCED, REPACKAGED, FURTHER TRANSMITTED, TRANSFERRED,

DISSEMINATED, REDISTRIBUTED OR RESOLD, OR STORED FOR SUBSEQUENT USE FOR ANY SUCH PURPOSE, IN WHOLE OR IN PART, IN ANY FORM OR MANNER OR

BY ANY MEANS WHATSOEVER, BY ANY PERSON WITHOUT MOODY’S PRIOR WRITTEN CONSENT. All information contained herein is obtained by MOODY’S from sources

believed by it to be accurate and reliable. Because of the possibility of human or mechanical error as well as other factors, however, all information contained herein is provided “AS

IS” without warranty of any kind. Under no circumstances shall MOODY’S have any liability to any person or entity for (a) any loss or damage in whole or in part caused by, resulting

from, or relating to, any error (negligent or otherwise) or other circumstance or contingency within or outside the control of MOODY’S or any of its directors, officers, employees or

agents in connection with the procurement, collection, compilation, analysis, interpretation, communication, publication or delivery of any such information, or (b) any direct, indirect,

special, consequential, compensatory or incidental damages whatsoever (including without limitation, lost profits), even if MOODY’S is advised in advance of the possibility of such

damages, resulting from the use of or inability to use, any such information. The credit ratings, financial reporting analysis, projections, and other observations, if any, constituting part

of the information contained herein are, and must be construed solely as, statements of opinion and not statements of fact or recommendations to purchase, sell or hold any

securities. NO WARRANTY, EXPRESS OR IMPLIED, AS TO THE ACCURACY, TIMELINESS, COMPLETENESS, MERCHANTABILITY OR FITNESS FOR ANY PARTICULAR

PURPOSE OF ANY SUCH RATING OR OTHER OPINION OR INFORMATION IS GIVEN OR MADE BY MOODY’S IN ANY FORM OR MANNER WHATSOEVER. Each rating or

other opinion must be weighed solely as one factor in any investment decision made by or on behalf of any user of the information contained herein, and each such user must

accordingly make its own study and evaluation of each security and of each issuer and guarantor of, and each provider of credit support for, each security that it may consider

purchasing, holding, or selling.

An Introduction to Through-the-Cycle Public Firm EDFTM ... · Through-the-Cycle Public Firm EDF...

Documents

Transcript of An Introduction to Through-the-Cycle Public Firm EDFTM ... · Through-the-Cycle Public Firm EDF...