Measuring & Managing Credit Risk EDF™ Credit Measures for Public Firms

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Measuring & Managing Credit Risk EDF™ Credit Measures for Public Firms
October 2006

Session Objectives What is the EDF credit measure?
When does a firm Default? What drives the EDF credit measure? How are the EDF Drivers calculated? How is the EDF measure calculated from the EDF Drivers? EDF methodology summary EDF validation Conclusion 1 2 3 4 5 6 7 8

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. 1 2 3 4 5 6 7 8

Default Example: Collins & Aikman Corp
Defaulted May 2005 1-Year EDF S&P Rating 1-Year EDF S&P Rating 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. Source: Credit Monitor 1 2 3 4 5 6 7 8

Agency Ratings: An Example
1 2 3 4 5 6 7 8

Agency Ratings: Another Example
1 2 3 4 5 6 7 8

Differentiating EDF Credit Measures from Traditional Ratings
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

Default Example: Tropical Sportswear intl.
Defaulted December 2004 1-Year EDF S&P Rating S&P Rating 1-Year EDF Source: Credit Monitor 1 2 3 4 5 6 7 8

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. 1 2 3 4 5 6 7 8

Default Example: Tropical Sportswear Intl.
Market Value of Assets Default Point \$ Million EDF at T1 is greater than EDF at T2. Higher Leverage implies Higher EDF. Asset Value and Liabilities drive EDF. What else drives EDF? Source: Credit Monitor Market Value of Assets T2 ? T1 ? Defaulted December 2004 Default Point (Liabilities Due) 1 2 3 4 5 6 7 8

Does similar Leverage imply similar EDF?
Pepsi’s Market Value of Assets Dell’s Default Point Dell’s Market Value of Assets Pepsi’s Default Point \$ Million Source: Credit Monitor Pepsi’s Market Value of Assets February 2003: Dell and Pepsi had similar Market Leverage. Did they have similar EDF? Dell’s Market Value of Assets Dell’s Default Point Pepsi’s Default Point

Pepsi and Dell in Feb 2003: Similar Leverage but different EDF
Pepsi’s EDF Dell’s EDF Source: Credit Monitor Why is Dell’s EDF substantially higher? Asset Volatility: 46% (Dell) vs. 19% (Pepsi) Asset Volatility and Leverage drive EDF 0.69 Dell’s EDF Pepsi’s EDF 0.02

EDF Drivers 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” Default Point (or Liabilities Due) The liabilities due in the event of distress Asset Volatility (or Business Risk) The variability of the market value of assets 1 2 3 4 5 6 7 8

EDF Drivers: A Pictorial View
Distribution of Market Value of Assets at Horizon (1 Year) Value Expected Market Value of Assets Asset olatility (1 Standard Deviation) V A sset Value D efault Point EDF™ Today Time 1 Year Asset olatility V EDF ~ log [ sset Value / A efault Point ] D Note: The symbol “~” stands for “increasing function of” or “directionally equivalent to”. 1 2 3 4 5 6 7 8

Impact of the EDF Drivers on EDF
Asset olatility V EDF is an increasing function of : log [ sset Value / A efault Point ] D Default Point goes up………………….….………….EDF goes UP Market Value of Assets goes up……….……………EDF goes DOWN Market Leverage (Default Point / Market Value of Assets) goes up………………………………………...….…...EDF goes UP Asset Volatility goes up………….…..….……………EDF goes UP 1 2 3 4 5 6 7 8

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. 1 2 3 4 5 6 7 8

Estimating Market Value of Assets: Capital Structure of a Firm
Claim 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. Assets* A firm derives value from the cash flows it is expected to generate. Liabilities* Senior claim on the Assets. Upside limited to principal and interest. Future Cash Flow produced by Assets Value Value Equity* Junior claim on the Assets. Unlimited upside and limited downside. Claim Liabilities and Equity represent a complete set of claims on the asset value. * Asset, Liability, and Equity depicted above are market values and not book values. 1 2 3 4 5 6 7 8

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). 1 2 3 4 5 6 7 8

Liabilities (Contractual Amount) Strike Price (Contractual Amount)
Estimating Market Value of Assets: Equity as a Call Option on the Assets Equity as a Call Option on the firm’s Assets Generic Call Option Call Option Value Equity Value Market Value of Assets Underlying Liabilities (Contractual Amount) Strike Price (Contractual Amount) Call Option Value Equity Value Strike Price Liabilities Underlying Market Value of Assets 1 2 3 4 5 6 7 8

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. Equity Value Market Value of Assets Liabilities (Contractual Amount) 1 2 3 4 5 6 7 8

MKMV Public EDF Model: An Extension of the Merton 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. 1 2 3 4 5 6 7 8

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 1 2 3 4 5 6 7 8

Default Example: Tropical Sportswear Intl.
Market Value of Assets Total Liabilities Default Point \$ Million Source: Credit Monitor Market Value of Assets Total Liabilities Defaulted December 2004 Default Point

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. 1 2 3 4 5 6 7 8

Estimating Asset Volatility and the Role of Leverage
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. Home originally worth:100 Down Payment:20 Bank Loan:80 Home now worth:120 +20 Asset 100 Equity 20 Liability 80 Leverage 5 Change in Asset Value = +20% (20/100) Change in Equity = +100% (20/20) De-Leverage 1/5 Change in Asset Value = +20% (20/100) Change in Equity = +100% (20/20) Volatility Volatility 1 2 3 4 5 6 7 8

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). Asset Return Equity Return Standard Deviation Empirical Asset Volatility Asset Volatility Modeled Asset Volatility 1 2 3 4 5 6 7 8

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. 1 2 3 4 5 6 7 8

Asset Volatility: Measure of Business Risk
0% 5% 10% 15% 20% 25% 30% 35% 200 500 1,000 10,000 50,000 100,000 200,000 Total Assets (\$m) Annualized Volatility COMPUTER SOFTWARE AEROSPACE & DEFENSE FOOD UTILITIES, ELECTRIC BANKS AND S&LS 1 2 3 4 5 6 7 8

Asset Volatility: A Critical EDF Driver
Rising Equity Market Cap But a Dramatically Higher EDF Because of rising Asset Volatility Time

Calculating EDF from EDF Drivers and Distance to Default
Expected Market Value of Assets Value Asset Volatility (1 Standard Deviation) Asset Value Distance to Default (DD) ≈ The number of Standard Deviations the Market Value of Assets is away from Default Point Default Point EDF Today 1 Year Time Asset Volatility EDF ≈ Default Point Market Value of Assets X 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) 1 2 3 4 5 6 7 8

Calculating EDF from EDF Drivers and Distance to Default
Expected Market Value of Assets Value Asset Volatility (1 Standard Deviation) Asset Value Distance to Default (DD) ≈ The number of Standard Deviations the Market Value of Assets is away from Default Point Default Point EDF Today 1 Year Time Market Value of Assets 1 Distance to Default (DD) ≈ log [ ] X Default point Asset Volatility 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. 1 2 3 4 5 6 7 8

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 1 2 3 4 5 6 7 8

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. 1 2 3 4 5 6 7 8

Assumptions vs. Reality: Firms tend to change Liabilities as they approach distress.
Liabilities are assumed to be stable over time. Merton Model Firms tend to change (increase) Liabilities as they approach distress. Reality Asset Value Increase in Liabilities can be proxied, say, by a higher Default Point, causing a higher PD. Asset Value Realized PD Default Point Merton PD Time Horizon 1 2 3 4 5 6 7 8

Assumptions vs. Reality: Default can happen anytime before Horizon.
Default occurs when Asset Value at Horizon is below Default Point. Merton Model Default occurs the first time Asset Value falls below Default Point. Reality Asset Value Defaulting Path Asset Value Non-Defaulting Path Merton Model: Non-Defaulting Path Reality: Defaulting Path Realized PD Default Point Merton PD ? Time Horizon

Assumptions vs. Reality: Asset Return Distribution is Fat Tailed.
Asset Value Asset Return Distribution is Normal. Merton Model Asset Return Distribution is Fat Tailed. Reality Asset Value Default Point Merton PD Realized PD Time Horizon

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. 1 2 3 4 5 6 7 8

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 EDF 1 2 3 4 5 6 7 8

MKMV Database MKMV Public Firm Default Database (Global) (7,600 + defaults) Defaults Quarter 1 2 3 4 5 6 7 8

Empirically mapping DD to EDF
Search the Default Database for all instances of firms having a DD of 6. 42,000 such instances (of firms having a DD of 6) were found. 17 out of these 42,000 instances resulted in Default in the next 1 year. Empirical Default Rate corresponding to a DD of 6 is 17/42000 = .04% = 4bp Map DD of 6 to an EDF of .04% = 4bp Repeat above steps for other DD buckets. 42,000 Instances of DD = 6 17 Defaults over the next 1 year 1-Year EDF™ =17 / 42,000 = 4bp DD = 6 1 2 3 4 5 6 7 8

Empirically mapping DD to EDF
9000 Instances Instances 20,000 Instances 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 DD =1 DD = 4 DD = 2 DD = 5 DD = 3 DD = 6 1 2 3 4 5 6 7 8

Calculating EDF using the DD to EDF Mapping
Distance to Default 1 2 3 4 5 6 7 8

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 EDF 1 2 3 4 5 6 7 8

EDF methodology summary
Market Value of Equity Amount of Short and Long Term Liabilities Equity is a Call Option on the Assets. Solve for Market Value of Assets and Asset Volatility. Amount of Short/Long Term Liabilities determine Default Point Asset Volatility Market Value of Assets Default Point Distance to Default is the cushion between Market Value of Assets and Default Point, expressed as a multiple of Asset Volatility. Distance to Default MKMV’s Default Database is used to empirically map DD to EDF. DD-EDF Mapping EDF is the probability that the firm will default within the specified time horizon. EDF 1 2 3 4 5 6 7 8

EDF Methodology: EDF for Horizon beyond 1 Year
Distribution of Market Value of Assets at Year 2 Distribution of Market Value of Assets at Year 1 Value Expected Market Value of Assets 2-Year Asset Volatility 1-Year Asset Volatility 2-Year Distance-to-Default Asset Value 1-Year Distance-to-Default 2-Year Default Point 2-Year Cumulative EDF 1-Year Default Point 1-Year EDF™ Today Time 1 Yr 2 Yrs 1 2 3 4 5 6 7 8

Tropical Sportswear Intl.: EDF along with the three EDF Drivers
Asset Value (\$ Million), Default Point (\$ Million) Market Value of Assets Default Point EDF Asset Volatility EDF (%), Asset Volatility (%) Market Value of Assets 1-Year EDF Asset Volatility Defaulted December 2004 Default Point

Early Warning Power of EDF Measures
Months Before and After Default EDF, Rating MKMV EDF Moody’s Rating Median EDF and Rating-Implied EDF for Defaulted Firms United States Data: 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. 1 2 3 4 5 6 7 8

Does the Predicted Default Rate (EDF) match the Actual Default Rate?
Predicted and Actual Number of Defaults US Public Non-Financial Firms w/ Sales > 300 M Years EDF < 20% 1 2 3 4 5 6 7 8

Does the Predicted Default Rate (EDF) match the Actual Default Rate?
Predicted and Actual Number of Defaults US Public Non-Financial Firms w/ Sales > 300 M Years EDF = 20% 1 2 3 4 5 6 7 8

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%. 1 2 3 4 5 6 7 8

103 B-Rated Firms as of 31/12/92 Number of Firms EDF Range High Risk
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 EDF Range High Risk Low Risk

Defaults 6 Months Later Number of Firms EDF Range High Risk Low Risk 2
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 EDF Range High Risk Low Risk

Defaults 1 Year Later Number of Firms EDF Range High Risk Low Risk 2 4
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 EDF Range High Risk Low Risk

Defaults 2 Years Later Number of Firms EDF Range High Risk Low Risk 2
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 EDF Range High Risk Low Risk

Defaults 3 Years Later Number of Firms EDF Range High Risk Low Risk 2
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 EDF Range High Risk Low Risk

Defaults 4 Years Later Equal rated firms do not have the same risk
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 Range High Risk Low Risk Equal rated firms do not have the same risk EDF adds significant discriminatory power Number of Firms

Benefits of the EDF™ Credit Measure
Evaluate Default Risk with a greater degree of accuracy and objectivity. Quantify Default Risk, to: Price appropriately 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. 1 2 3 4 5 6 7 8

Summary What is the EDF credit measure? Forward-looking Probability of Default over a defined time horizon When does a firm Default? Market Value of Assets < Default Point What drives the EDF credit measure? Market Value of Assets, Default Point, and Asset Volatility How are the EDF Drivers calculated? How is the EDF measure calculated from the EDF Drivers? Distance to Default is empirically mapped to EDF via the Default Database EDF methodology summary EDF validation The EDF measure is accurate and powerful; it provides significant early warning. Conclusion 1 2 3 4 5 6 7 8

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