measuring & managing credit risk edf credit measures for public firms october 2006

Measuring & Managing Credit RiskEDF™ Credit Measures for Public Firms

October 2006

2 Measuring & Managing Credit Risk - EDF™ Credit Measures Copyright © 2006 Moody’s KMV Company. All Rights Reserved.

Session Objectives

1. What is the EDF credit measure?

2. When does a firm Default?

3. What drives the EDF credit measure?

4. How are the EDF Drivers calculated?

5. How is the EDF measure calculated from the EDF Drivers?

6. EDF methodology summary

7. EDF validation

8. Conclusion

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EDF Credit Measure for Public Firms

EDF stands for Expected Default Frequency – the probability that a firm will

default within a given time horizon by failing to make an interest or principal

payment.

We provide EDF measures for time horizons of 1, 2, 3, 4, and 5 years.

EDF Ranges from .02% to 20%, i.e., 2 to 2000 basis points.

Say we create a portfolio of 100 firms, each with a 2% EDF. On average, 2

out of the 100 firms will default over the next year, and 98 will not default.

A firm with a 2% EDF is 10 times more likely to default than a firm with a

0.2% EDF.

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N-COLLINS & AIKMAN CORP-EDF N-COLLINS & AIKMAN CORP-S&P

1-Year EDF

S&P Rating

Source: Credit Monitor

Default Example: Collins & Aikman Corp

1-Year EDF S&P Rating

DefaultedMay 2005

1 2 3 4 5 6 7 8

The value of EDF: Measures credit risk in terms of absolute default probabilities rather than relative rankings.

Provides the most accurate forward-looking, causal model.

Provides frequent updates and early warning of changes in credit quality.


Agency Ratings: An Example

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Agency Ratings: Another Example

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Differentiating EDF Credit Measures from Traditional Ratings

EDF Credit Measures Objective, Market driven Quantitative Method

Quantitative Output

EDF = 0.02% (An actual probability of default)

Absolute (Cardinal) Precise and continuous, providing full

granularity (high resolution) Specific time horizon Reflects current assessment of future

prospects of the firm/economy Dynamic, updated daily or monthly Reflects issuer’s default probability

(PD), and not issue-specific LGD

Traditional Ratings Subjective, driven by fundamental analysis Qualitative Method

Qualitative Output

AAA = “Obligor’s capacity to meet its financial commitment on the obligation is extremely strong.”

Relative (Ordinal) Distinct risk buckets without specifying or

targeting a specific default rate No specific time horizon (“long term”) Supposed to reflect average economic

conditions – “through the cycle” Stable (low ratings volatility) Opinion on Expected Loss – combines the

effect of PD and LGD (Loss Given Default)1 2 3 4 5 6 7 8


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N-TROPICAL SPORTSWEAR INTL CP-EDF

N-TROPICAL SPORTSWEAR INTL CP-S&P

Default Example: Tropical Sportswear intl.

1-Year EDF

DefaultedDecember 2004

S&P Rating


1-Year EDF

S&P Rating

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When does a firm Default?

A firm defaults when the value of its business falls below what it owes.

If the firm value is greater than what it owes, the equity holders have the ability and incentive to pay the debt obligations and keep the firm alive.

A firm’s ability to pay its debt depends more on the Market Value of its Assets, and less on its cash position.

If the assets of the firm have sufficient market value, the firm can raise cash by selling a portion of its assets - or by issuing additional equity or debt.

EDF is the probability that a firm’s future market value will be insufficient to meet its future debt obligations.

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N-TROPICAL SPORTSWEAR INTL CP-AVL N-TROPICAL SPORTSWEAR INTL CP-DPT


Market Value of Assets

Default Point(Liabilities Due)

Default Example: Tropical Sportswear Intl.



• EDF at T1 is greater than EDF at T2.

• Higher Leverage implies Higher EDF.

• Asset Value and Liabilities drive EDF.

• What else drives EDF?

T2

?

T1

?

Market Value of Assets Default Point

$ Million

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20000

40000

60000

80000

100000

120000

140000

05/99 10/99 04/00 10/00 04/01 10/01 04/02 10/02 04/03 10/03 04/04

N-PEPSICO INC-AVL N-PEPSICO INC-DPT

N-DELL INC-AVL N-DELL INC-DPT

Does similar Leverage imply similar EDF?

Pepsi’s Market Value of Assets

Dell’s Market Value of Assets Pepsi’s Default Point

Dell’s Default Point

Pepsi’s Market Value of Assets

Dell’s Market Value of Assets

Dell’s Default Point Pepsi’s Default Point

February 2003: Dell and Pepsi had similar Market Leverage.

Did they have similar EDF?

$ MillionSource: Credit Monitor


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N-PEPSICO INC-EDF N-DELL INC-EDF

Pepsi’s EDF

Dell’s EDF

0.02

0.69

• Why is Dell’s EDF substantially higher?

• Asset Volatility: 46% (Dell) vs. 19% (Pepsi)

• Asset Volatility and Leverage drive EDF

Pepsi and Dell in Feb 2003: Similar Leverage but different EDF


Pepsi’s EDF Dell’s EDF


EDF Drivers

1. Market Value of Assets (or Business Value)

Market assessment of the future cash flows of the business

Value of the firm as a “going concern”

2. Default Point (or Liabilities Due)

The liabilities due in the event of distress

3. Asset Volatility (or Business Risk)

The variability of the market value of assets

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ssetValue

Value

EDF Drivers: A Pictorial ViewDistribution of Market Value of Assets at Horizon (1 Year)

EDF™

Expected Market Value of Assets

Asset olatility(1 Standard Deviation)

efault PointD

A

V

Today Time1 Year

Note: The symbol “~” stands for “increasing function of” or “directionally equivalent to”. 1 2 3 4 5 6 7 8

DA

VAsset olatility

efault Point ]log [ sset Value /EDF ~


Impact of the EDF Drivers on EDF

Default Point goes up………………….….………….EDF goes

Market Value of Assets goes up……….……………EDF goes DOWN

Market Leverage (Default Point / Market Value of Assets) goes up………………………………………...….…...EDF goes

Asset Volatility goes up………….…..….……………EDF goes UP

UP

UP

DA

VAsset olatilityEDF is an increasing function of : efault Point ]log [ sset Value /

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Estimating Market Value of Assets

Market Value of Assets is the total market value of the firm as a “going concern.”

Market Value of Assets is the Net Present Value of the firm’s future cash flows.

Market Value of Assets is NOT the Book Value of Assets.

Market Value of Assets is NOT the Market Capitalization, which is equal to the Market Value of Equity.

Even though the Equity of a public firm is traded in the markets, the firm’s Assets are not traded. Market Value of Assets is not directly observable.

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Value

ValueAssets*

A firm derives value from the cash flows it is expected to generate.

For most firms, we cannot find

Market Value of Assets by adding

Market Value of Liabilities and

Equity as the total amount of

market value of liabilities is not

available (most debt is not traded).

Moreover, Market Value of liabilities

is not equal to the Book Value of

Liabilities, because the Market

Value of Liabilities changes with

credit quality.

Estimating Market Value of Assets: Capital Structure of a Firm

Liabilities*

Senior claim on the Assets.

Upside limited to principal and

interest.

Equity*Junior claim on

the Assets.Unlimited upside

and limited downside.

* Asset, Liability, and Equity depicted above are market values and not book values.

Claim

Future Cash Flowproduced by Assets

Claim

Liabilities and Equity represent a complete set of claims on the asset value.

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What is the relationship between Equity and Market Value of Assets?

Equity holders have the right, but not the obligation, to “buy” the firm’s assets from the lender by re-paying the debt.

When the Market Value of Assets is above what is owed, Equity holders can exercise the above right. As the Asset Value increases beyond what is owed, Equity Value continues to increase: Unlimited upside.

When the Market Value of Assets is below what is owed, Equity holders can choose not to exercise the above right. As the Asset Value goes below what is owed, Equity Value approaches zero - but never goes negative: Limited downside (limited liability).

Key insight from Black, Scholes, and Merton (1973,74):

Equity is a Call Option on the firm’s Assets.

Derivative Pricing Theory (Black, Scholes, etc.) provides a mathematical relationship between Market Value of Assets (Underlying) and Equity Value (Derivative).

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Strike Price(Contractual Amount)

Underlying

Cal

l O

pti

on

Val

ue

Estimating Market Value of Assets: Equity as a Call Option on the Assets

Liabilities(Contractual Amount)

Market Value of

Assets

Eq

uit

y V

alu

eGeneric Call OptionEquity as a Call

Option on the firm’s Assets

Strike Price Liabilities

Underlying Market Value of Assets

Call Option Value Equity Value

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Equity as a Call Option on the Assets

Equity is a Call Option on the

Market Value of Assets.

Option Pricing Theory provides an

extensively validated relationship

between Equity Value and Market

Value of Assets.

Given an Equity Value, this

relationship can be used to solve

for the Market Value of Assets.

Liabilities(Contractual Amount)

Market Value of

Assets

Eq

uit

y V

alu

e

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MKMV Public EDF Model: An Extension of the Merton Model

Merton MKMV Public EDF Model

Two classes of Liabilities: Short Term Liabilities and Common Stocks

Five Classes of Liabilities: Short Term and Long Term Liabilities, Common Stocks, Preferred Stocks, and Convertible Stocks

No Cash Payouts Cash Payouts: Coupons and Dividends (Common and Preferred)

Default occurs only at Horizon. Default can occur at or before Horizon.

Equity is a call option on Assets, expiring at the Maturity of the Short Term Liabilities.

Equity is a perpetual call option on Assets; it never expires.

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Default Point

The amount of Liabilities due in the event of distress

The threshold level of Market Value of Assets, below which the firm defaults

Default Point is a function of the firm’s Liability structure, as described by the balance sheet - specifically the short/long term breakdown of Liabilities.

MKMV empirical research: Default Point lies between the Short Term Liabilities and the Total Liabilities.

Default Point ≈ Short Term Liabilities + ½ of Long Term Liabilities

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N-TROPICAL SPORTSWEAR INTL CP-AVL N-TROPICAL SPORTSWEAR INTL CP-LBS

N-TROPICAL SPORTSWEAR INTL CP-DPT

Default Point



Total LiabilitiesDefaulted

December 2004


Default Example: Tropical Sportswear Intl.


Default Point

Total Liabilities

$ Million


Asset Volatility

A measure of the variability in the firm’s future Market Value of Assets.

Reflects the degree of uncertainty in the firm’s future earnings.

Quantifies business risk: Firms in the same industry/country and of similar

size tend to have similar asset volatilities.

Neither the Market Value of Assets, nor the Asset Volatility is directly

observable. They can be implied from the Equity Value and Equity Volatility.

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Asset 100Liability 80

Equity 20

Estimating Asset Volatility and the Role of Leverage

+20 +20

5

Leverage

Change in Equity = +100% (20/20)Change in Asset Value = +20% (20/100)

Home originally worth:100Down Payment:20

Bank Loan:80Home now worth:120

De-Leverage

1/5Change in Asset Value = +20% (20/100) Change in Equity = +100% (20/20)

A measure of the variability in the firm’s future Market Value of Assets (business risk).

Measured as the standard deviation of the Annual % Change in the Market Value of

Assets. Example: Asset Volatility of 30% indicates that a typical change in the business

value is plus or minus 30% over the next year.

Volatility Volatility

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Asset Return Equity Return

Estimating Asset Volatility using the Options Framework

The same Options Framework that links Equity Value to the Market Value of Assets

also links Equity Volatility to Asset Volatility. Equity Returns are de-levered to obtain

Asset Returns.

Asset Returns are then used to calculate the Empirical Asset Volatility.

The Empirical Asset Volatility (historical) gains predictive power when blended with a

comparables-based (along size, profitability, country, industry) volatility measure

(Modeled Asset Volatility).

Empirical Asset Volatility

Modeled Asset VolatilityAsset Volatility

… … …

1 2 3 4 5 6 7 8

Standard Deviation


Estimating Asset Volatility

Asset Volatility is NOT equal to Equity Volatility.

Leverage amplifies the Volatility of the underlying Assets to produce a higher Volatility at the Equity level.

The same Options Framework that links Equity Value to the Market Value of Assets also links Equity Volatility to Asset Volatility.

Equity Returns are de-levered to obtain Asset Returns, which are then used to calculate an historical Asset Volatility.

The historical Asset Volatility is combined with volatility information from comparable firms (of similar size, profitability, industry, country) to estimate each firm’s final Asset Volatility.

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0%

5%

10%

15%

20%

25%

30%

35%

200 500 1,000 10,000 50,000 100,000 200,000

Total Assets ($m)

Ann

ualiz

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olat

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COMPUTER SOFTWARE

AEROSPACE & DEFENSE

FOOD

UTILITIES, ELECTRIC

BANKS AND S&LS

Asset Volatility: Measure of Business Risk

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Time

Rising Equity Market Cap

Because of rising Asset Volatility

But a Dramatically Higher EDF

Asset Volatility: A Critical EDF Driver


Calculating EDF from EDF Drivers and Distance to Default

Distance to Default (DD) ≈ The number of Standard Deviations the Market Value of Assets is away from Default Point

Why is the relationship between EDF and the three drivers defined as above?

Expected Default Frequency = Probability that the Market Value of Assets in 1 Year falls below

the Default Point.

= Solid Area under the Probability Curve. For example, N (-DD) is the Probability that a Standard

Normal Variable will be DD or farther below the mean.

(Normality was Merton’s assumption, but is not used by MKMV)

AssetValue

TodayTime

Value

EDF

1 Year


Asset Volatility(1 Standard Deviation)

Default Point

Asset VolatilityEDF ≈ Default Point

Market Value of AssetsX

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Calculating EDF from EDF Drivers and Distance to Default

Distance to Default (DD) ≈ The number of Standard Deviations the Market Value of Assets is away from Default Point

AssetValue

TodayTime

Value

EDF

1 Year


Asset Volatility(1 Standard Deviation)

Default Point

DD is the distance between the (log of) Market Value of Assets and Default Point,

expressed as a multiple of Asset Volatility.

EDF is an increasing function of 1/DD and a decreasing function of DD.

Distance to Default (DD) ≈ log [Market Value of Assets

Default point Asset Volatility

1] X

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Distance to Default (DD)

DD represents the cushion between Market Value of Assets and Default

Point, expressed as a multiple of Asset Volatility.

The Larger the DD, the Larger the cushion, and the Lower the EDF.

The Smaller the DD, the Smaller the cushion, and the Higher the EDF.

EDF moves inversely with DD.

It provides a relative rank ordering of Default Risk.

We must transform DD into EDF to get an absolute probability of default

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Transforming DD to EDF: Classic Merton Approach

The classic Merton approach uses Normality and other simplifying assumptions to

map DD to EDF, using a Cumulative Normal Distribution transformation:

Merton EDF = N(-DD), where N is the Cumulative Normal Distribution function.

EDFs calculated using the above approach (i.e., simplifying assumptions) dramatically

understate the default probability.

Example: Firms with DD = 4 are predicted to have a default rate of 0.003% under the

Normal distribution assumption. But, in reality, firms with DD = 4 are found to

have a default rate of 0.6%: 200 times that predicted by Normality assumptions!

Normality or other simplifying assumptions CANNOT be used in mapping DD to EDF.

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Realized PD

Assumptions vs. Reality: Firms tend to change Liabilities as they approach distress.

Firms tend to change (increase) Liabilities as they approach distress.

Reality

Merton PD

Liabilities are assumed to be stable over time.

Merton Model

Default Point

Increase in Liabilities can be proxied, say, by a higher Default Point, causing a higher PD.

Horizon

AssetValue

Time

AssetValue

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Assumptions vs. Reality: Default can happen anytime before Horizon.

Defaulting Path

Default occurs the first time Asset Value falls below Default Point.

Reality

Merton PD

Default Point

Non-Defaulting Path

?

Merton Model: Non-Defaulting PathReality: Defaulting Path

Realized PD

Default occurs when Asset Value at Horizon is below Default Point.

Merton Model

Horizon

AssetValue

AssetValue

Time


Assumptions vs. Reality: Asset Return Distribution is Fat Tailed.

Asset Return Distribution is Fat Tailed.

Reality

Asset Return Distribution is Normal.

Merton Model

Merton PD

Realized PD

Default Point

Horizon

AssetValue

Time

AssetValue


Modeling the Default Process is difficult. How do we overcome it?

We cannot use the Normal Distribution to map DD to EDF. Reasons include:

Firms change Liabilities as they approach distress; Default Point is not constant.

Default can happen anytime before Horizon; Default Point is an absorbing boundary.

Asset returns are fat-tailed relative to the Normal Distribution.

The default processes of actual firms are difficult to model analytically.

We overcome the above challenges by empirically mapping DD to EDF.

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Empirically mapping DD to EDF

DD is empirically mapped to EDF by tracking the default experience of thousands of firms from MKMV’s extensive Default Database.

MKMV uses actual default rates for companies in similar risk ranges (DD buckets) to determine a one-to-one relationship between DD and EDF.

Distance to Default

ED

F

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MKMV Database

MKMV Public Firm Default Database (Global)1973-2005

(7,600 + defaults)

Def

aults

Quarter

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1 2 3 4 5 6 7 8

1) Search the Default Database for all

instances of firms having a DD of 6.

2) 42,000 such instances (of firms having a

DD of 6) were found.

3) 17 out of these 42,000 instances resulted

in Default in the next 1 year.

4) Empirical Default Rate corresponding to a

DD of 6 is 17/42000 = .04% = 4bp

5) Map DD of 6 to an EDF of .04% = 4bp

6) Repeat above steps for other DD buckets.

DD = 6

42,000 Instances of DD = 6

17 Defaults over the next 1 year

1-Year EDF™ =17 / 42,000 = 4bp



DD =1

DD = 4

DD = 2

DD = 5

DD = 3

DD = 6

9000 Instances 15000 Instances 20,000 Instances

35000 Instances 40,000 Instances 42,000 Instances

720 Defaults 450 Defaults 200 Defaults

150 Defaults 28 Defaults 17 Defaults

EDF™ =800bp EDF™ =300bp EDF™ =100bp

EDF™ =43bp EDF™ =7bp EDF™ =4bp

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Distance to Default

ED

F

EDF = 0.43%

Calculating EDF using the DD to EDF Mapping

EDF = 20%

EDF = 0.02%

DD = 4

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DD to EDF: One-to-One Relationship

Two firms with the same DD will have the same EDF - even if they differ with respect to Size, Industry, Geography, or the EDF Drivers.

Size, Industry, and Geography do affect Default Risk. The effects of Size, Industry, and Geography are already embedded in DD via the three EDF Drivers: Market Value of Assets, Asset Volatility, and Default Point.

Distance to Default

ED

F

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EDF methodology summary

Asset VolatilityMarket Value

of AssetsDefault Point

Distance to Default

DD-EDF Mapping

EDF

Equity is a Call Option on the Assets.Solve for Market Value of Assets and

Asset Volatility.

Market Value of Equity

Amount of Short and Long Term Liabilities

Amount of Short/Long Term Liabilities determine Default Point

Distance to Default is the cushion between Market Value of Assets

and Default Point, expressed as a multiple of Asset Volatility.

MKMV’s Default Database is used to empirically map DD to EDF.

EDF is the probability that the firm will default within the specified time horizon.

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1 Yr

AssetValue

1-YearEDF™


Today Time

Value

EDF Methodology: EDF for Horizon beyond 1 Year

2 Yrs

Distribution of Market Value of Assets at Year 1

1-YearDistance-to-Default

2-YearCumulative EDF

Distribution of Market Value of Assets at Year 2

1-YearAsset Volatility

1-Year Default Point

2-Year Default Point

2-YearAsset Volatility

2-YearDistance-to-Default

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N-TROPICAL SPORTSWEAR INTL CP-AVL N-TROPICAL SPORTSWEAR INTL CP-DPT

N-TROPICAL SPORTSWEAR INTL CP-EDF N-TROPICAL SPORTSWEAR INTL CP-ASG

Tropical Sportswear Intl.: EDF along with the three EDF Drivers

1-Year EDFMarket Value of Assets

Default Point

Asset Volatility


Ass

et V

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Mil

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D

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ED

F (%

), Asset V

ola

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Asset Volatility

Default Point

EDF


Early Warning Power of EDF Measures

Months Before and After Default

ED

F,

Rat

ing

MKMV EDFMoody’s Rating

Median EDF and Rating-Implied EDF for Defaulted FirmsUnited States Data: 1996-2004

• Median EDF tends to start rising 24 months before default.

• Median Rating tends to stay flat until a year before default, showing a steep rise about 4 months before default.

• EDF tends to lead the Ratings.

• EDF provides early warning power.

• EDF is dynamic and continuous, while Ratings move in discrete steps.

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Does the Predicted Default Rate (EDF) match the Actual Default Rate?

Predicted and Actual Number of DefaultsUS Public Non-Financial Firms w/ Sales > 300 M

Years 1991-2004

EDF < 20%

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Does the Predicted Default Rate (EDF) match the Actual Default Rate?

EDF = 20%

Predicted and Actual Number of DefaultsUS Public Non-Financial Firms w/ Sales > 300 M

Years 1991-2004

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Do EDF Measures provide Discriminatory Power over that provided by Agency Ratings?

Study Performed by 3rd Party on behalf of prospective client, published in Risk Magazine

103 Non-Financial Single B firms on 12/31/92 were sorted by their EDF, as shown on the next slide.

Observed wide range of risk (as measured by EDFs) from 0.15% to 20%.

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103 B-Rated Firms as of 31/12/92

Number

of Firms

0

2

4

6

8

10

12

14

0.15-0.65

0.67-1.14

1.15-2.04

2.16-2.63

2.69-3.33

3.69-5.32

5.64-8.49

8.84-20.00

EDF RangeEDF Range High RiskLow Risk


Defaults 6 Months Later

Number

of Firms

0

2

4

6

8

10

12

14

0.15-0.65

0.67-1.14

1.15-2.04

2.16-2.63

2.69-3.33

3.69-5.32

5.64-8.49

8.84-20.00



Defaults 1 Year Later

Number

of Firms

0

2

4

6

8

10

12

14

0.15-0.65

0.67-1.14

1.15-2.04

2.16-2.63

2.69-3.33

3.69-5.32

5.64-8.49

8.84-20.00



Defaults 2 Years Later

Number

of Firms

0

2

4

6

8

10

12

14

0.15-0.65

0.67-1.14

1.15-2.04

2.16-2.63

2.69-3.33

3.69-5.32

5.64-8.49

8.84-20.00




Number

of Firms

0

2

4

6

8

10

12

14

0.15-0.65

0.67-1.14

1.15-2.04

2.16-2.63

2.69-3.33

3.69-5.32

5.64-8.49

8.84-20.00




Number

of Firms

0

2

4

6

8

10

12

14

0.15-0.65

0.67-1.14

1.15-2.04

2.16-2.63

2.69-3.33

3.69-5.32

5.64-8.49

8.84-20.00


• Equal rated firms do not have the same risk• EDF adds significant discriminatory power


Benefits of the EDF™ Credit Measure

Evaluate Default Risk with a greater degree of accuracy and objectivity.

Quantify Default Risk, to:

1. Price appropriately

2. Improve portfolio performance.

Focus resources where they add the most value.

EDF is updated frequently and provides early warning of changes in credit quality.

Cause-and-Effect model facilitates What If and Pro-Forma Analysis.

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Summary

1. What is the EDF credit measure?

Forward-looking Probability of Default over a defined time horizon

2. When does a firm Default?

Market Value of Assets < Default Point

3. What drives the EDF credit measure?

Market Value of Assets, Default Point, and Asset Volatility

4. How are the EDF Drivers calculated?

5. How is the EDF measure calculated from the EDF Drivers?

Distance to Default is empirically mapped to EDF via the Default Database

6. EDF methodology summary

7. EDF validation

The EDF measure is accurate and powerful; it provides significant early warning.

8. Conclusion

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measuring & managing credit risk edf credit measures for public firms october 2006

Documents

edf measures

measures credit risk

edf drivers

value of edf

edf validation

edf ranges

credit quality

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