CONTEMPORARY CREDIT RISK MODELS

Tilburg University Faculty of Economics and Business Administration Department of Finance Thesis supervisor: Muhammad Ather Elahi Thesis author: Dmitrii Izgurskii ANR: 570544 URL electronic version: http://homepage.uvt.nl/~s570544/thesis.pdf June 20th, 2008

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Index1. Introduction 3

2. Building blocks of credit risk 2.1. Default Risk 2.2. Concentration Risk 2.3 Downgrade Risk 2.4 Spread Risk

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3. Credit risk measurement

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4. History of credit risk measurement

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5. Credit-rating agencies 6. The CreditRisk+ model 7. The CreditMetricsTM model

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8. KMV Portfolio Manager

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9. McKinseys CreditPortfolioView

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10. Summary and implications of the models 10.1. Summary of models characteristics 10.2. Ratings of credit-rating agencies 10.3. Survey at major global banks 10.4. Backtesting the models

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11. Conclusion

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Works Cited

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Izgurskii 3 1. Introduction The credit quality problems of the last two-and-half decades posed a challenge for the financial institutions (FIs) to say the least. Loans that are not or partially repaid drain FIs working capital very quickly, resulting in lower profits and in worst case a bankruptcy of the FI itself. The credit quality problems of 1980s were characterized by less developed countries not being able to repay loans to commercial banks (FDIC, Saunders and Cornett). The 1990s brought about deteriorating commercials real estate loans, followed by consumers disproportionate failure on car loans and credit card payments. The new millennium saw numerous failures of technology companies, with the two biggest being Enron and WorldCom. In addition, FIs all over the world saw a rapid growth in trading and development of derivatives. These financial derivatives, most often in the form of options and swaps, created additional source of credit risk to an FI (Saunders and Cornett). Quantification of credit risk inherent in these derivatives is complex and requires sophisticated quantitative tools. These macroeconomic developments stressed the industrys prevailing credit risk management methods to the fullest and were key driving forces behind the developments of latest credit risk models (Wolf and Vogel 13). This paper will describe the latest credit risk models (CRMs) widely used in the financial industry for managing credit portfolios. In addition we will determine which model is suited for what conditions.

2. Building blocks of credit risk The majority of literature defines credit risk the risk of the obligor not being able to fulfil the contractually promised payment, the so-called state of default. In this state the value of the loan made to the firm in default decreases, since payments, on which this value depends, are missed (Saunders and Cornett 300). Understandingly, credit risk is often assumed to be represented by default risk. However, the true credit risk would be undervalued if we only adhere to that definition. This is because in addition to default risk, other non-market risks also contribute to the uncertainty of the bonds and loans value. Excluding them would only give a partial measure of credit risk. The risks comprising the credit risk, as managed and measured by FIs, are discussed below.

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2.1. Default risk As mentioned earlier, default risk is the risk that the borrower fails to fulfil its contractual obligations. The presence of default risk implies that the lender will receive on average less than what is stated in the loan contract. Formally this can be stated as

ROA = [1 P(default)] (1 + r ) 1 ,

(1)

where ROA signifies return on assets that the lender transfers to the borrower and r is the contractual interest rate (Saunders and Cornett 300). This equation plays key role in pricing loans. When a borrower inquires for the pries of loans, i.e. interest rate r, a lender estimates this particular borrowers probability of default and the desired ROA he or she wishes to achieve on the loan. Using these as independent variables, the lender then calculates the loans interest rate and communicates it to the borrower. Consider for example a lender facing a firm wanting to borrow funds. The internal credit rating department estimates this borrowers probability of default (PD) to be 8 percent. Additionally, other projects with attractive ROAs are available to the lender, and so it requires a minimum of 13 percent ROA on this particular loan. Using (1), the interest rate quoted to this particular borrower is 22.83%, as calculated below. 0.13 = 0.92(1 + r ) 1 r= 1.13 1 = 0.2283 0.92

There is one caveat when pricing a loan using this method: probability of default is often hard to estimate accurately because not all required information is available. Default occurs when a firm has not enough funds to repay its debt obligation. By monitoring firms assets and liabilities, a clearer picture arises of the firms financial situation. However, accounting statements containing this information are released on quarterly basis or even less often. By the time the information is extracted from these statements it is already obsolete and gives just a snapshot of firms historical value. When pricing a loan the lender transfers the default risk to the borrower through loan prices and it will always want to err on the upside of the PD estimate, which implies higher interest rates to the borrower. However, the borrower wishes to get finances as cheap as possible, so it is also in her interest to have its PD estimated not higher than it actually is. The borrower

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Izgurskii 5 tries to achieve this by providing additional information about its finances and operations to the lenders credit analysts. Additionally, it can acquire a rating from S&Ps if it deems it as a good investment in a sense that the total cost of funds and the rating service will be less than if the firm borrowed funds while being unrated.

2.2. Concentration risk Concentration risk refers to the risk of having solvency-threatening losses due to loans being unevenly distributed between counterparties, or concentrated in a specific region or industry sector. The concentration of loans to individual counterparties is coined granularity, whereas concentration of loans in specific industry and/or region is referred to as sectoral concentration (Deutsche Bundesbank 35-37). The correlations between borrowers under different macroeconomic scenarios determine the intensity of the losses due to concentration risk. In a 2004 study by the Basel Committee, it was found that 9 out of 13 major financial institution collapses were caused by exposure to excessive levels of concentration risk. (York 57). This might explain why the focus of contemporary CRMs is predominantly on concentration risk of a credit portfolio, measurement of which is cumbersome since subjective estimates based on asset correlations need to be made. Once the concentration risk for a portfolio is determined with the help of a CRM, one can neutralize it by diversifying the credit portfolio.

2.3. Downgrade risk Another type of risk is the downgrade risk, a risk that a loans or portfolios present value (PV) drops as an effect of an increased PD. A rise in the PV should not be considered as a risk since it increases ones utility, to which rational agents will never object, unless the portfolio contains credit derivatives whose value is inversely correlated with the underlying. To hedge against downgrade risk a corporation needs to hold a position in derivatives whose value moves up as the value of bonds drops.

2.4. Spread risk Lastly, an FI might be subject to spread risk, also known as basis or margin risk. This is the risk of being exposed to a spread in interest rates. It usually occurs when an FI tries to neutralize the uncertain movements in interest rates by letting the loan rate float with some other rate it is based on, like prime rate, while financing the loan with another floating rate, like LIBOR.

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Izgurskii 6 For example, consider a bank that made such a commitment while present prime and LIBOR rates are 8 and 4 percent respectively. This bank will then realize a 4 percent gross profit on the next horizon by receiving 8 percent and paying back 4 percent. However, at the second and subsequent horizons, the spread between these two rates might be different from the initial 4 percent. This uncertainty is the spread risk (Riskglossary.com, Saunders and Cornett 366). Not unexpectedly, there is some argument about whether spread risk is market risk or credit risk. If the financing of a FI is obtained in the market, then movements in these rates are coined as market risk. On the other hand, movements in the debt values represent credit risk.

3. Credit risk measurement Financial institutions measure credit risk for several reasons. First, by quantifying counterpartys credit risk in monetary terms, the lender can price a loan accordingly. Commercial and Industrial loan interest rates are often quoted in two parts. The first part is the base lending rate, often being set to equal the LIBOR or prime lending rate. The second part, coined the credit risk premium or margin, is the rate that the bank demands for a particular borrower. For example, a start-up company might pay current LIBOR of say 8% and 5% credit risk premium on a one-year $1m loan, while an AAA-rated corporation is charged 8% LIBOR and 0.5% credit risk premium for the same loan. The second reason is that FIs often want to limit their potential loss exposure to a particular borrower or group of borrowers possessing some characteristic, the so-called practice of credit portfolio diversification. A recent example is that of Japanese FIs incurring large losses on their over-concentrated investments is real estate in Asia (Saunders, Cornett 2006). Arguably, this could have been prevented by applying principles of diversification. Lastly, regulatory powers require banks to maintain certain levels of capital to ensure stability in banks operations. The required capital designated to cover exposure to credit risk is generally lower than that assigned by standardized set of rules. The Bank for International Settlements (BIS) tries to address this issue through its publications of proposed regulatory rules. The BIS is an institution that acts as the central bank for central banks of member countries. Its members, mostly commercial banks, are advised to maintain certain levels capital depending the banks assets. The purpose of this capital adequacy policy is to ensure stable financial environment. The required minimum levels of capital are often given as the ratio of the total exposure to certain market risk. As of 1998, BIS capital requirements could be calculated

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Izgurskii 7 in two ways, either by using the BIS Standardized Framework or by using own internal models of risk assessment. Although internal models provide greater degree of freedom they are still subject to strict regulatory supervision (Saunders and Cornett 575-601). Additionally, in 2001 the BIS issued regulatory document which specified two methods for calculation of capital requirements for exposures to credit risk. The choice was between the Standardized Approach and the strictly audited Internal Rating-Based (IBR) approach. The IBR approach allows FIs to use their own credit risk assessment tools to estimate capital requirements (Saunders and Cornett 579, Basel Committee on Banking Supervision, 31 May 2001).

4. History of credit risk measurement Up to the late 1970s the credit risk assessment was analyzed using predominantly qualitative models. Qualitative models, also called expert systems, rely on FIs experts to use their skills and insights to make a decision whether to grant credit or what the loan price should be. The focal points of the analysis are borrowers reputation, capital structure, volatility of earnings and collateral. For todays risk management qualitative models prove to be unsuitable. Assessing the risk of a single obligor takes a lot of experts time and it would be impractical to assess all banks credit transactions. Exceptions are made when the counterparty represent significantly large exposure, so that the expensive analysts time is justified in monetary terms. J.P. Morgan and U.S. banks in general still consider that additional expert evaluation will outperform existing quantitative models (J.P. Morgan I, Federal Reserve 898). In addition, the sophistication of present credit instruments demands assessment methods based on numerical analysis. Hence the banks shift towards quantitative models presented opportunities to save costly time and offer objective evaluation of credit instruments. For the above mentioned reasons, quantitative models are considered the better alternative to qualitative models due to their fast processing time and objective predictions. Moreover, these models incorporate widely recognized modern financial theory and widely available financial data. The latest CRMs focus on predicting the distribution of credit losses through either Monte Carlo simulations or analytical methods. Additionally, besides default risk, the new breed CRMs also weigh in concentration risk, downgrade risk and spread risk in the overall assessment result. The existence of the quantitative CRMs is predominantly the result of technological

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Izgurskii 8 developments and improved financial data availability and regulations (Wolf and Vogel 13-17, Altman 190-96).

5. Credit-rating agencies Credit-rating agencies are in effect outsourced credit-risk assessment analysts. The costs of credit risk assessment on a bond issue are incurred by the borrower of the funds instead of the lender. Bond rating agencies, most notable are Moodys KMV, Fitch and Standard and Poors, offer a wide variety of fee-based credit-ratings services to corporate and government clientele. One of these services is when a debt issuer acquires a credit-rating for its newly issued debt, because he or she estimates that the monetary gain from it is greater than cost of acquiring such a rating. The rating-agencies use proprietary quantitative credit risk models in conjunction with large databases of financial and management data to assign a rating to a bond. Additionally, the agencies financial experts review the ratings using qualitative analysis techniques (Standard and Poors). Standard and Poors, the current market leader in global credit ratings (Standard and Poors June 2008), uses seven categories to rate bonds based on their default probability, with each rating representing a range of PDs. The AAA category represents debt that is least probable to default and CCC category being the most likely to default. Exhibit 1 shows a transition matrix. For example, bonds graded AAA had a beginning-of-the-year PD of 0.00% to default at yearend. In contrast, junk-bonds, rated CCC, had a PD of 14.55% to default in at the horizon. The last column of the table, titled NR lists the probability of a bonds rating to be withdrawn.

2007 Global Transition Rates (%) From/to AAA AA A BBB BB B CCC AAA 95.60 0.60 0.00 0.00 0.00 0.00 0.00 AA 2.20 91.37 2.90 0.26 0.00 0.00 0.00 A 0.00 3.21 86.6 3.81 0.00 0.00 0.00 BBB 0.00 0.00 2.75 83.69 6.72 0.08 0.00 BB 0.00 0.00 0.22 2.70 75.26 7.43 0.00 B 0.00 0.00 0.30 0.66 6.44 75.0 20.0 CCC 0.00 0.00 0.07 0.07 0.09 2.56 45.45 D 0.00 0.00 0.00 0.00 0.19 0.24 14.5 NR 2.20 4.82 7.50 8.81 11.3 14.3 20.0

Exhibit 1. Transition rates of rated bonds for the year 2007 (Source: Standard and Poors, 2007).

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Izgurskii 9 6. The CreditRisk+ model The CreditRisk+ model was published by Credit Suisse Financial Products in 1997. It belongs to the default-only type of models since changes in credit quality, as measured by credit ratings of S&Ps, are not modeled. The model estimates distribution of credit-portfolio losses with the purpose of using it to calculate economic capital. Economic capital are funds used to cover unexpected losses up to some degree, say 1 percent; meaning that 1 percent of the time the losses will deplete all economic capital. The nature of assumptions that the model makes about the inputs, makes it best suitable for analysis of credit-portfolios comprising many small loans, like mortgages, consumer loans and small business loans (Saunders and Cornett 339-341). The LGD denotes the rate of one unit of currency that is recovered given that the obligor is in default. A specific obligors LGD will largely depend on how efficient the assets of the defaulted firm will be transferred to the creditor, the liquidity of the assets and tangibility of the assets. A loan to a firm with relatively large share of intangible and illiquid assets, for example stored in research and development, will have relatively high LGD and is therefore riskier. Estimates of LGDs stem from different sources, like FIs own experts or credit rating agencies. Although the model assumes initially that LGDs are constant, this conjecture can be relaxed by allowing LGDs to follow some distribution. This relaxation will result in multiple values of LGD for a single loan, just like in the real world. Multiple LGD values lead to improved predictions about portfolios PDF, but only if the distribution underlying the LGD is estimated accurately (Saunders Cornett 339-41). The default rate of a single loan is assumed to be random and uncorrelated to other rates in the portfolio. As a result, the defaults in the credit-portfolio can be approximated with the Poisson distribution, which is a key factor in determining the allocation of economic capital (Credit Suisse First Boston). CreditRisk+ is very fast in terms of computing speed due to its analytical estimation methods. Additional advantage is that the model does not suffer from ambiguity -- a particular set of input values will always result in same portfolio loss distribution. As the size of credit-portfolio grows, the computation speed decreases rapidly up to the point that the model is on par with a simulation model. Another consequence of the analytical approach is that estimation process of certain statistics requires non-analytical techniques that are out of CreditRisk+s scope (Saunders and Cornett 339-41).

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Izgurskii 10 7. The CreditMetricsTM model The CreditMetrics model was made public in the form of a document titled CreditMetrics - technical document, released by J.P. Morgan in April 1997. The banks reasons for the publication were (a) to provide a common benchmark model of credit risk; (b) to increase transparency in credit risk management; (c) to give its clients a tool for evaluation of the banks credit risk advice. (J.P. Morgan I). CreditMetrics is a quantitative model that enables a financial practitioner to calculate credit Value-at-Risk based on portfolios loss distribution at horizon. The only required input is historical data. Other possible inputs, like macroeconomic variables, are ignored and therefore the model belongs to the type of unconditional models in which the transition matrix does not depend on current state of the economy. The credit Value-at-Risk calculation process starts with inference of debt market-values from debts quality rating assigned by credit-rating agency or internal ratings department. In the next step, the portfolio-loss distribution is constructed from individual debt market-values at horizon and their correlations. Once portfolio-loss distribution is determined, the model computes Value-at-Risk figure. This figure is key factor in assignment of economic capital and/or regulatory capital to the specific portfolio. CreditMetrics accounts for three of the four risks that comprise credit risk. Specifically, derivation of concentration risk is possible from the correlation matrix of credit rating movements. Such table specifies for every obligor in the portfolio the probability of a credit rating movement given that a movement in credit rating of other obligor has occurred. Downgrade and default risks figures are found in transition matrices, which simply list the probability of movement to a different rating class in the next period. The models scope are traditional credit instruments like fixed-income securities, loans, forwards and swaps and other contracts because of its assumption that credit facilities are based on deterministic, i.e. fixed, interest rate. Credit risk measurement of derivatives based on floating interest rates is beyond scope of the model. Most of the fixed income instruments are traded in the OTC market and so their value and volatility cannot be observed directly as with exchange traded instruments. In order to calculate credit-Value-at-Risk for these bonds/loans, their value and volatility must be estimated from their credit rating, the rating transition matrix, LGD and credit spreads. However, the more estimations required, the greater the chance that the outcome of the model will be inaccurate.

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Izgurskii 11 8. KMV Portfolio Manager The KMV Credit Portfolio model of credit risk assessment was released in 1993. This credit risk tool estimates the asset-value of a firm using the Mertons option-valuation approach. The results were then transformed into the so-called Distance-to-Default (DtD) rating which is used to calculate the models main output, the Expected Default Frequency (EDF). Instead of using transition matrices from other vendors, the model uses the EDFs to develop its own transition matrix. The loss correlations between firms are calculated based on the common risk factors of firms assets. Then using the transition matrix and the correlations, the KMV model is able to estimate the distribution of portfolio losses. As seen in previous models, the economic and regulatory capitals are derived from this distribution (Wolf and Vogel 13-17). Unfortunately the information about firms liabilities is not always as transparent as is desired. The trading of corporate debt happens for the most part in the OTC market, which is not transparent to the public. Therefore, we cannot derive the firms value and volatility from these unobservable figures. To bypass this issue, the KMV model utilizes Robert Mertons optionvaluation model to price firms liabilities. In order to employ it, several simplifying assumptions about firms capital structure need to be made. Specifically, the capital structure of the firm is composed of equity, short-term debt, long-term debt (assumed to be a perpetuity) and convertible preferred shares. The value and volatility of equity are functions of assets value, assets volatility, the leverage ratio of the firm, average coupon paid on long-term debt and the risk free rate. The value of equity is directly observable in the stock market and so the asset value can be found by rearranging the function. From the time series of asset value we then derive the asset volatility. According to the Mertons option-valuation framework, default occurs when assets value falls below the value of firms liabilities. However, in practice, KMV has observed different thresholds of asset value below which firms default. This threshold lies between the value of short-term debt and the value of total liabilities. In order to produce more accurate estimate of EDF the DtD ranking is calculated first. In effect, DtD tells us how many standard deviations (volatilities) a firm is away from default implying that for larger DtD the firm is less likely to default. The figure below helps to visualize the DtD concept.

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Exhibit 2. The Distance-to-Default concept (Source: Crouhy et al. 2000)

In the last phase, the model maps DtDs to the EDFs. This is by looking into historical data Moodys KMV has worlds largest database for that purpose and finding what percentage of firms with a specific DtD ranking did default. The EDF measure accounts only for default risk component within the encompassing credit risk. In case of large portfolio of credit instruments, a bank wants to also assess the concentration risk. In order to do that, it needs to estimate the correlations of these credit instruments comprising the portfolio. KMV Credit Portfolio relies on multi-factor model of asset returns to find correlations between the assets. Using correlations based on historical asset prices is impractical when dealing with large portfolios. A portfolio consisting of N debt instruments would require estimation of N(N-1)/2 correlations. If N is 1000 then we need to estimate 499500 correlations. In addition, the correlations might be inaccurate due to sampling errors in historical asset prices. The multi-factor model neutralizes these imbalances. This model assumes two categories of risk factors that drive asset returns: systematic factors and non-systematic factors. Asset correlations are result of systematic risk factors inherent in all bonds comprising the portfolio. Global economic, regional and industrysector factors are considered to be common factors. In a model of asset returns with only two common factors, the correlation between assets returns in a portfolio would require us to estimate KN+K(K1)/2 parameters. Here, N stands for number of assets in the portfolio and K stands for number of common factors. Again, in case of 2 common factors and 1000 bonds,

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Izgurskii 13 estimation of 2003 parameters is needed compared to 499500 parameters, had we used historical correlations method. Using the correlation numbers in calculation of asset returns, and subsequently the distribution of future portfolio loss, ensures that concentration risk is accounted for. Unlike CreditMetrics model, the Credit Portfolio does not simulate the values of a loan portfolio at credit horizon. Instead an inverse gaussian distribution is derived which represents the future possible losses of the portfolio. But for that to be the case we have to assume that a portfolio is well deversified. Then it can be shown that its loss (represented by random variable L) at time t (assumed to be less than maturity T) equals the difference between its future value in a world with no defaults and its future value in world with defaults. Formally:

L = Vt , ND Vt

The distribution of L is approximated by inverse Gaussian distribution which is skewed, leptokurtic and non-normal. Once this distribution is established, an FI is able to estimate the required capital cushion necessary to absorb an -% worst case loss. The following example illustrates how the assumption about the distribution of portfolio loss affects the economic capital. Assume many obligors with the same loss correlations of 0.4 and EDFs of 1%. Capital cushion against 1% worst case loss would require us to hold 4.5 times the volatility of the portfolio loss. Had we used standard normal distribution as the approximation of the distribution of portfolio loss, than already 2.3 times the portfolio loss volatility would suffice.

9. McKinseys CreditPortfolioView The CreditPortfolioView model is based on research papers of Tom Wilson published in 1987 and 1997. At the time of the publication of second paper he was Chief Risk Officer at McKinsey & Company and it is this company that employed the model. However at the present time it seems that McKinsey no longer supports the model. CreditPortfolioView assumes that default and migration probabilities are influenced by the macroeconomic factors. The main drivers behind economys health are the GDP growth rate, interest rates, unemployment rate, foreign exchange rate, government expenditures, and savings rate. The model takes a starting-point-matrix based on Moodys KMV or S&Ps historical data.

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Izgurskii 14 Next, taking the prevailing macroeconomic conditions as inputs, the model utilizes Monte Carlo simulation methods to output the conditional transition matrix. This matrix shows the default and migration probabilities of firms belonging to a particular industry sector to which earlier defined macroeconomic variables apply. Subsequently the conditional transition matrices can be used to either price a loan or calculate portfolios credit-VaR (Crouhy et al.). As Crouhy et al. point out (2000), the calibration process (the reverse of linear regression) requires that the initial transition matrix with the unconditional probabilities is very closely aligned with the real world; otherwise estimates based on it will be too inaccurate to be meaningful. Furthermore they point out that older and simpler Bayesian model in conjunction with analysts expertise might perform just as good.

10.

Summary and implications of the models

10.1. Summary of models characteristics Exhibit 3 provides a quick reference for the models main characteristicsCreditRisk+

KMV Portfolio Manager Risk driver Asset values

CreditMetrics

CreditPortfolioView

Asset values

Expected default rates

Macroeconomic factors Market-value change

Definition of risk

Default losses

Market-value change

Default losses

Credit events

Continuous default probabilities

Downgrade/default

Default

Downgrade/default

Transition probabilities Loss correlations

EDF (based on assetvalue) Asset-return factors

Constant, historical

N/A

Macroeconomic factors

Equity-return factors

Conditional on common risk factors

Conditional on macroeconomic factors Historical distribution

Recovery rates (equal to 1-LGD) Output computation method

Random distribution

Random distribution

Constant

Analytical/simulation

Simulation/analytical

Analytical

Simulation

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Izgurskii 15Exhibit 3. Main characteristics of the 4 main models (Source: Wolf and Vogel)

CreditRisk+, as seen in the table, does not use transition probabilities. This implies that the changes in value due to an obligors deteriorating credit quality will not be used in the model. Hence, this model less suitable for corporate bonds which often have fluctuating probabilities of default, but not an actual default, causing their values to fluctuate. Portfolios that this model is suitable for are rather small and consist of identical loans, often made to retail consumers and small firms that are not publicly traded. In general, recovery rates modelled by random distribution, rather than being constant, offer a better approximation of the real world. Historical recovery rates are better than constant rates, but still worse than random distribution recovery rates, because of the probability that the actual distribution underlying these rates has changed. Although KMV and CreditMetrics models make use of random distribution to model recovery rates, it still should be remembered that these need to be defined correctly for any output to have a meaningful result. The models are highly sensitive to even slight changes in numerical data and so any misspecification results in erratic numbers. The two models from the previous paragraph also have the best of both worlds in output generation. Analytical method is accurate and fast for small portfolios, but cannot always be applied. As an alternative, Monte Carlo simulation methods offer a means for output calculation especially in case of large portfolios and random input data. One of the major strengths of KMV model is that it is based on continuous credit events. Daily updates of credit portfolio risks are possible due to availability of equity price data and this process is integrated in KMV. The acquisition of KMV by Moodys, a firm specialized in collecting market data and rating firms, certainly made that process a lot easier. 10.2. Credit-VaR estimation process with CreditRisk+ As mentioned earlier, CreditRisk+ can readily be used with small portfolios of small loans. Consider the following example, based on the example in Saunders and Cornett (33941). Assume that FIs portfolio consists of 100 loans of $10,000, for a total of $1m. The EDF and LGD are estimated at 2.5% and 50% respectively, for each loan in the portfolio. Then the Poisson distribution is used to generate frequency distribution of defaults for the 100 loans portfolio. The distribution of portfolio losses is easily derived from the distribution of defaults. Each default represents a loss of (1 LGD) times the loan value of $10,000 which equals

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Izgurskii 16 $5,000. Then the number of defaults is simply multiplied by loss per default. This produces the CreditRisk+ models main output, the frequency distribution of portfolio losses seen in exhibit 4.

Ehibit 4. Distribution of portfolio loss (Based on Saunders and Cornett 341)

Now that the FI has the required numbers, it can calculate the required economic capital to hold in order to protect itself from unexpected losses. The bank expects to lose on average $10,000 and this amount in already incorporated in loan prices and loan loss provisions. Additionally, the FI itself decides or is given regulatory mandate to insure itself against some very unlikely unexpected losses. If the FI is required to be able to cover losses in 95% of all possible cases then it must hold so much economic capital that when a loss of probability of 5% occurs, the economic capital covers that loss precisely up to a dollar. On the other hand, a 4% worst-case scenario loss could not be covered with the economic capital. In this example, a 5% worst-case loss equals roughly $25,000 which corresponds to the default of 5 loans in the 100loans portfolio. Since the bank already holds $10,000 in required capital to cover expected losses, it only needs to account for the difference between the amount needed to cover unexpected loss and amount needed to cover expected loss, which is $15,000. Economic capital in fact is nothing more than the cut-off point with the desired worst-case scenario probability being the are to the right of that point. See exhibit 5 below.

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Exhibit 5. Economic capital is the cut-off point at 99th percentile (Source: CSFB 24)

10.2. Ratings of credit-rating agencies For the sake of accuracy of the predictions it is best not to use transition matrices of credit rating agencies because their ratings are not continuous but rather discrete. By the time a certain rating is used, the state of the firm it belongs to has already changed, and a new estimate should be made. The model that suffers the most from is CreditMetrics, precisely for the fact that it uses transition matrices of credit rating agencies. The KMV Portfolio Manager on the other hand avoids this issue by constructing its own, EDF based transition matrix. The EDFs are updated continuously as new stock price and accounting data flows in. For portfolios of exchange listed credit instruments, the KMV Portfolio Manager clearly is superior to any other model.

10.3. Survey at major global banks Smithson et al. provide a report (2002) of international survey amongst 41 global banks about their practices of credit portfolio management. Most notable points are that the largest exposures in the credit portfolios of the surveyed banks are attributed to large and middlemarket corporations and banks. The instruments behind these exposures are mainly undrawn lines of credit, bilateral bank loans and syndicated bank loans. Since the obligors of these credit

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Izgurskii 18 facilities are very often listed on stock exchanges, one would expect that a credit risk model that incorporates public equity and bond prices would be a dominant contender. As it shows, this is case. The KMV Portfolio Manager is used at 69% of banks as the primary model of formal credit portfolio management. It is followed by CreditMetrics based CreditManager, which accounts for 20%. 17 percent of respondents use internally developed CRMs and only 6 percent manage the portfolio with a macro-factor model, perhaps such as CreditPortfolioView. The results need to be interpreted carefully, because they only represent global trend in portfolio management. Nevertheless, it seems that CreditPortfolioView has lost the battle in the credit risk management arena to a degree that almost all public information regarding it, including the main technical document, is nowhere to be found.

10.4. Backtesting the models Backtesting refers to the practice of using historical data as inputs into the model and evaluate its ability to predict the defaults which are of course already known. If needed, the models weights for different factors can then be adjusted so that it predicts the defaults with greater accuracy. Backtesting requires large samples of default data in order to conclude with sound statistical proof that a CRM is indeed useful in default prediction. However, the majority of credit instruments that the CRMs are intended for are either illiquid or their prices are hidden from the public. As a consequence, the price data on these instruments is sparse, forcing a researcher to engage in small-sample-statistics, a highly unreliable practice. The large proprietary Credit Research DatabaseTM of Moodys KMV surpasses this hurdle and offers opportunities significant backtesting research that benefits their model (Crouhy et al., Lopez 163).

11. Conclusion In this paper we have studied the four major credit risk models that are used for pricing of loans and estimation of economic capital. In the near future, when the Basel Committee for Banking Supervision has seen more evidence on the accuracy of these models, the regulatory capital will be also determined using these tools. At the present time, data limitations in the form of sparse financial loan information pose too big of a problem. We have also seen that CreditRisk+ model suits small portfolios of loans to homogeneous borrowers, especially the

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Izgurskii 19 ones not publicly traded. On the other side, the KMVs Credit Portfolio has a monopoly on managing portfolios of highly liquid credit instruments with large exposures. Almost continuous monitoring of default probabilities and credit-Value-at-Risk is possible due to seamless integration with the equity price data. The CreditMetrics model is a second-best alternative to KMV, often producing similar results in terms of credit-VaR. CreditPortfolioView on the other hand is discontinued by McKinsey consultancy either because its developer, Tom C. Wilson left the company or simply for the reasons that it produced unsatisfactory results. Strangely, the academia seems to hold on to this model by citing it in the comparisons with other models. This paper followed suit, but only in order to give a full description of the spectrum of possible CRMs. The availability of information on the model gives the impression that it is nowadays just an archive-filler.

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Works cited

An Examination of the Banking Crises of the 1980s and Early 1990s. Federal Deposit Insurance Corporation. 18 June 2008 . CreditRisk+: A credit risk management framework. Credit Suisse First Boston 1997.

General description of the credit-rating process. Standard and Poors 26 June 2007. Moodys corporation to acquire KMV. Moodys KMV. 11 February 2002. 13 June 2008 . Standard and Poors About Us. Standard and Poors. 18th June 2008 < http://www2.standardandpoors.com/portal/site/sp/en/us/page.topic/ratings_au/2,1,1,1,0,0,0 ,0,0,0,0,0,0,0,0,0.html>. Altman, Edward I. Bankruptcy, Credit Risk, and High Yield Junk Bonds. Malden: Blackwell Publishers Inc., 2002.

Basel Committee on Banking Supervision. Credit Risk Modelling: Current Practices and Applications. Bank for International Settlements April 1999.

Basel Committee on Banking Supervision. The New Basel Capital Accord Consultative Document. Bank for International Settlements 31 May 2001. Crouhy, Michel, Dan Galai and Robert Mark. A comparative analysis of current credit risk models. Journal of Banking and Finance 24 (2000) : 59-117. Deutsche Bundesbank. Concentration risk in credit portfolios. Monthly Report June 2006: 3555. Federal Reserve. Credit Risk Rating at Large U.S. Banks. Federal Reserve Bulletin November 1998: 898-921.

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Moodys KMV. Moodys Corporation to Acquire KMV. Press releases: 2002 11 February 2002. 13 June 2008 . Riskglossary. Contingency Analysis. 18 June 2008 . Saunders, Anthony, and Marcia Millon Cornett. Financial Institutions Management: A Risk Management Approach. New York: McGraw-Hill/Irwin, 2006. Smithson, Charles, Stuart Brannan, David Mengle and Mark Zmiewski. Results from the 2002 Survey of Credit Portfolio Management Practices. International Swaps and Derivatives Association. 19 June 2008 . Wolf, Robert C. and Dennis Vogel. An Overview of Portfolio Credit-Risk Models. Commercial Lending Review 18, 6 (2003) : 13-17. York, Jonathan. Bank Concentration Risk. The Risk Management Association Journal Sep. 2007: 52-57.

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