Toward Credit Portfolio Management

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Toward Credit Portfolio Management

  1. 1. Toward Credit Portfolio Management Part I A Rudimentary Guide to Credit Portfolio Modeling: Theory Introduction Model Development Applications Draft Edition Eric Kuo
  2. 2. Toward Credit Portfolio Management Part I A Rudimentary Guide to Credit Portfolio Modeling: Theory Introduction Model Development Applications Draft Edition Eric Kuo
  3. 3. ii Copyright @ Eric Kuo 2008 All rights reserved No part of this document may be reproduced in any form, by Photostat, microfilm, xerography or any other means, or incorporated into any information retrieval system, electronic or mechanical, without the written permission of the copyright owner.
  4. 4. iii To Liwen, for her patience and support To Tiffany, with joy and pride
  5. 5. iv Preface Banks may fail for a lot of reasons. It may fail to compete with peers and gradually lose the market share. Or it may adopt wrong strategies and target at riskier segments. Or it may fail to manage the market risk and incur massive trading losses. Or it may underestimate the interest rate risk, liquidity risk and unable to manage the funding gap. Of all the possible reasons of failure, the most threatening risk, in my opinion, may be the credit risk. The massive credit losses arise from the credit risk that wipe out bank capital and cause bank failure. In my opinion, these credit losses sometimes are a result of concentration risk, such as single name concentration that one or few obligors account for significant portion of total portfolio. It also may be a result of industry concentration, product concentration or segment concentration, that several losses appear simultaneous during the economic malaise. Moreover, sometimes the credit losses may be the consequence of the problem of miss-pricing that the credit revenue cannot cover the credit losses. Although bankers conceited themselves as credit risk professionals, the banking industry in general doesn’t generate any profit to the shareholders, simply counting the credit losses occurred in the past decade. All theses lead us to conclude that the banking industry is a highly vulnerable, highly competitive and highly regulated business. The business that banks do is risk-taking; however, the amount of potential credit risk is almost unknown – both of the investors and bankers themselves. As banks have moved in the direction of new Basel Accord, the credit risk has become more important and will be more transparent to the investors. However, the measurement of credit risk parameters (such as probability of default, loss given default and exposure at default) is only just the first step toward the credit risk management. The estimation of the credit portfolio risk further allows bankers to understand the unexpected loss. Banks can apply the economic capital into many management applications, such as capital allocation, performance management and business strategic planning. This document is an overture of credit portfolio management. Part 1: Credit portfolio modeling – measuring the unexpected loss of portfolio. (Discussed in this document) Part 2: Credit correlation modeling- estimating the asset correlation among obligors.
  6. 6. v Part 3: Credit portfolio analysis- diagnosing the performance of portfolio – assessing whether if risk and return is balanced. Part 4: Credit concentration risk management- managing the credit concentration risk through setting the limit boundary. This document provides a simple credit portfolio model for readers to estimate the credit portfolio unexpected loss. One important message that I’d like to deliver is that if you cannot measure risk, then you should not expect to manage the risk. This document is not aimed at technicians or quants. There are already many excellent books explore the technique of portfolio modeling. Instead, this document focuses on the application of the credit portfolio risk. How can bank leverage the simple model provided in this document to better understand the unexpected loss of bank’s credit portfolio. In my opinion, the efforts of risk measurement are vanity without promoting the measurement into management. In summary, sound credit risk management must be transparent and well perceived. Only when the board, CEO, rating agencies, equity analysts and the investors are well-informed and are confident at the bank’s risk management- they will not expect bankers perform miracles and they won’t be surprised by the losses in a economic recession. After all, banking business is a cyclical business with frequent expected loss and threatening unexpected losses. I could point out that the most opaque black box in many financial institutions is the quality of credit asset. The figures that bank provided in the annual report only depicts the past and have no value regarding the future asset quality. The disclosure of economic capital will give outsiders a clue. Also is an action of risk governance that will distinguish bank from her peers. Any error and unintentional deviation from the best practices remain my own responsibility. Eric Kuo, Sep, 2008
  7. 7. Table of content Section 1: Foreword and Introduction .......................................................................... 1 Section 2: Why banks need capital .............................................................................. 3 The IRB capital equation...................................................................................... 4 Differences between AIRB capital and Economic Capital .................................... 9 Section 3: Theory & vendor models introduction ....................................................... 17 Portfolio Models Introduction.............................................................................. 18 KMV’s Portfolio manager ................................................................................... 19 Creditmetrics ...................................................................................................... 24 CreditRisk+ ........................................................................................................ 31 Creditportfolioview.............................................................................................. 32 Section 4: Methodology of simple portfolio model development ................................ 37 Unconditional and conditional PD ...................................................................... 37 Loss based or value based ................................................................................ 39 Correlation Model............................................................................................... 40 Model Design Methodology................................................................................ 42 Section 5: Model manual instruction .......................................................................... 47 Data requirement ............................................................................................... 47 Model screenshot............................................................................................... 47 Example ............................................................................................................. 48 Joint default observation .................................................................................... 51 Charts................................................................................................................. 52 Section 6: Applications of in-house credit portfolio model.......................................... 54 Effect of correlation ............................................................................................ 54 Effect of concentration ....................................................................................... 59 Effect of PD ........................................................................................................ 60 Effect of LGD...................................................................................................... 61 Section 7: Future improvements ................................................................................ 64 Correlation.......................................................................................................... 64 Risk contribution................................................................................................. 65 Section 8: Economic capital as management applications ........................................ 67 Risk governance ................................................................................................ 67 External communication..................................................................................... 69 Internal management ......................................................................................... 72
  8. 8. Performance metrics .................................................................................. 72 Capital allocation ........................................................................................ 75 Limit setting ................................................................................................ 76 Section 9: Beyond economic capital .......................................................................... 77 Revisit the commercial banking business model ............................................... 77 Credit portfolio management as a business model ............................................ 79 Section 10: Helping the CEO’s sleep quality.............................................................. 82 Reference .................................................................................................................. 83 Appendix .................................................................................................................... 85 Interpreting the IRB capital equation.................................................................. 85 1. The Vasicek formula............................................................................... 86 2. Correlation estimation: R........................................................................ 88 3. The expected loss .................................................................................. 91 4. Maturity adjustment: ............................................................................... 91 VBA code ........................................................................................................... 93
  9. 9. 1 Section 1: Foreword and Introduction Credit portfolio modeling is one of the most important topics in risk management and finance theory today. The last decade has seen the development of models to compute portfolio credit losses for bonds and loan portfolios. The important output from the credit portfolio model is so called economic capital which is used to gauge how many amount of potential unexpected loss a bank is exposed to given the current credit portfolio constitution. Banks hold ‘Economic Capital’ (or “Risk” Capital) to protect against “Unexpected Loss”. It is opposed to the Basel 1 and is different from the AIRB approach under Basel 2. Although, the Basle 2 has taken the first steps to amend the capital requirement and to promote banks to implement the internal credit risk models for better estimating the unexpected loss (regulatory capital). In the BIS regulatory model, the potential exposures are given by an add-on factor multiplying the notional of each transaction. It is simple to implement, but the model has been widely criticized because it does not accurately capture the diversification effect and concentration risk of portfolio. By contrast, credit portfolio models measure credit economic capital and are specifically designed to capture the portfolio effects, specifically obligor correlations. These models include the pioneers: KMV’s Portfolio Manager (1993), CreditMetrics (JP Morgan 1997), CreditRisk+ (Credit Suisse Financial Products 1997) and Credit Portfolio View (Mckinsey, Wilson 1997a and 1997b). Although superficially they appear quite different—the models differ in their distributional assumptions, restrictions, calibration and solution1. The major limitations, in my point of view, are: the vendor models are expensive and complexity. Expensive means the subscriber needs to pay for the software expense each year, unless bank has a big commitment on the use of economic capital. Most of the model comprises sophisticated mathematic modeling and are difficult to explain in a simple spreadsheet. For the user who is less trained in math will have an impression of ‘Black box’. Both of the above are the motivation of this document. In addition, it is vital for banks to estimate the unexpected loss of their credit portfolio to better understand the uncertainty. 1 Gordy (1998) and Koyluoglu and Hickman (1998) show an underlying mathematical equivalence among these models.
  10. 10. 2 This document will begin at revisit the role of bank capital; why is it essential to the bank management- it is definitely not only to meet the regulatory compliance. Then, review the portfolio theory and introduce several vendors’ portfolio models. In the following, this document will explain the method that grounded on this simple credit portfolio model. There is one section elaborates how to leverage the model provided in this document to simulate the economic capital and gauge the sensitivity of portfolio loss based on bank’s internal risk parameters. The limitation of this model and directions of future improvement are also discussed. I also briefly introduce the management applications and the concept of active credit portfolio management in this document as well.
  11. 11. 3 Section 2: Why banks need capital Banks as chartered financial intermediary institutions require taking many responsibilities and needs to meet many regulations. To prevent from the insolvency and result in financial crisis, banks need to reserve a certain amount of capital to protect from unexpected loss except for the provision reserve. Therefore, the estimation of bank capital is essential for the regulator to gauge the riskiness of bank’s asset and is important for bank itself to do business. In principle, the maximum amount of the credit loss a bank might face is the ‘Credit Exposure’ multiplying by the ‘Loss Given Default’. Maximum Loss = Exposure at Default * Loss Given Default Take a portfolio contains 500 billions of exposure and has an average 40 % of LGD as an example. The maximum loss is equal to 500 Bn*40% = 200 Bn. If the regulator takes a conservative stance in the regulatory capital policy, then bank needs to hold 200 billion for this 500 billion of loan portfolio. However, the occurrence of this maximum loss is close to zero. The event implies that all obligors are going to be insolvent in the same time. The essence of credit portfolio management is to establish portfolio balance with adequate diversification2. This mitigates the consequences of the portfolio's volatility of value (sometimes termed unexpected losses) to a level where an institution can survive such losses given its reserves and capital. The Basel committee, therefore, investigated the existed credit portfolio models and assistance from the best practices3. Finally, Basel committee decided to apply the Merton’s concept and come up with equation4 to estimate the risk weight for bank’s credit asset. 2 Usually comes from the correlation which is to estimate the default event relationship among the obligors. 3 Such as, J.P Morgan, CSFB, Bank of America and other pioneers in credit portfolio management. 4 Basel Committee on Banking Supervision,2004.An Explanatory Note on the Basel II IRB Risk Weight Functions. Page 5, page 6.
  12. 12. 4 The IRB capital equation5 The calculation of AIRB capital requires a bank to utilize the past historical loss information to estimate the PD, LGD and EAD - the same concept as developing a credit scoring card or utilizing the data mining skills to find the customer behaviors. Restricted Bank capital is reserved as a cushion to absorb unexpected loss. Conceptual Generate risk parameters (PD,LGD,EAD) Bank capital (risk or economic capital) from historical loss data. is prepared as cushion to absorb the The expected loss estimation is the cost unexpected credit losses. of doing loan business. Target 1. Basel Capital is used to rating cover these Credit loss generates a Credit Loss extraordinary loss general form of Risk Appetite formula to A proxy the Bank’s actual loss ‘unexpected Risk Unexpec- experience Capital loss’ and as ted loss Average capital credit loss requirement. 2. It might over or EL under estimated the Time Probability risk. Note : Expected Loss = PD*LGD *EAD EL doesn’t necessary equal to the historical loss experience, due to the portfolio component may change. 2008 Eric Confidential 1 The EL is a concept of average credit losses based on the past experience and should be able to cover the credit losses in the most of the time6. The capital requirement is reserved for the losses that exceed the expected loss. Ideally, the capital requirement estimation should link to bank’s desire rating grade. The Basel committee generates a general form of formula to proxy the ‘unexpected loss’ and as capital requirement. It might over or under estimated the risk. For the corporate exposure, the Basel suggests the following formula: 5 Please refer to the appendix ‘Interpreting the IRB capital formula’ for more detail mathematics deduction. 6 The historical expected loss usually doesn’t equal to the current expected loss of the portfolio, for the following reasons : 1. The portfolio mix is different from the past portfolio : The PD and LGD of a portfolio may change over time. If the PD becomes better than the past, the expected loss ratio might be lower and visa’ versa. 2. The exposure may be different: for example the average credit loss is 100 out of 1,000 of exposure, while as the exposure may be expand to 2,000. To compare the absolute amount of expected loss may not be appropriate.
  13. 13. 5 Restricted Basel committee generates a general form of unexpected loss formula for banks to calculate the capital. –”a simplified version of EC”. Basel estimates A General formula Inverse of the Factors in Basel2 For banks standard normal Standard normal distribution distribution (G) (N) applied to threshold and applied to PD to 1 Year PD is considered, conservative value of PD derive default systematic factor instead of cumulative PD threshold Subtract EL based Correlation K= provision Based on historical data LGD ⎡ ⎤ ⎡ ⎤ 0.5 ⎛R⎞ ⎢LGD× N ⎢(1 − R) × G(PD) + ⎜ ⎟ × G(0.999)⎥ − PD × LGD⎥ −0.5 ⎝1− R ⎠ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎢ ⎥ ⎣ Inverse of the ⎦ standard normal Current status of EAD EAD distribution (G) × (1 − 1.5 × b ) × [1 + (M − 2.5) × b ] −1 applied to confidence level to derive Tenor adjustment conservative value of systematic factor [0.11852 − 0.05478 × ln(PD)]2 Tenor RWA = K * 12.50 * EAD B= R= ⎡1 − e (−50× PD ) ⎤ ⎡ ⎛ 1 − e ( −50× PD ) ⎞ ⎤ Asset Capital = RWA * BIS Ratio ⎥ + 0.24 ⎢1 − ⎜ ⎟⎥ 0 .12 × ⎢ ⎜ ⎟ 1 − e (− 50 ) ⎦ − 50 ⎣ ⎝ 1− e Correlation ⎣ ⎠⎦ 2008 Eric Confidential 1 Restricted Basel 2 Capital estimation is a simplified version of EC (or Credit VaR) Basel set at 99.9% of confidence Subtract EL based Correlation provision ⎡ ⎤ ⎡ ⎤ 0.5 ⎛R⎞ ⎢ LGD× N ⎢(1 − R) × G(PD) + ⎜ ⎟ × G(0.999)⎥ − PD × LGD⎥ × (1 − 1.5 × b )−1 × [1 + (M − 2.5) × b ] −0.5 K= ⎝1− R ⎠ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎢ ⎥ ⎣ ⎦ Tenor adjustment 2008 Eric Confidential Source : An Explanatory Note on the Basel II IRB Risk Weight Functions, Basel 2 1 Higher the target BIS ratio, larger the capital required to reserve. The Basel 2 AIRB capital is a simplified version of VaR model 7 . From Basel committee’s perspectives, the confidence 7 An Explanatory Note on the Basel II IRB Risk Weight Functions, Basel 2.
  14. 14. 6 interval for protecting the risk of insolvency is set at 99.9%. This implies that there is only 0.1% of possibility that the loss will exceed ‘expected loss + unexpected loss’ within 1 year. The major difference between wholesale and retail bank’s capital computation can be further explained by the below chart: Restricted The major difference in Basel 2 capital estimation between Corporate and Retail Banking is ‘Correlation’. Retail example Corporate example Frequency Frequency Credit Loss Credit Loss 1. UL more important than EL (small number 1. EL more important than UL (large number of of relatively good quality loans) loans minimises Impact of fluctuations) 2. High correlation 2. Low correlation 3. Significant capital requirements 3. Capital required is relatively low: Constant correlation = 15% for Mortgage Correlation = = 4% for Revolving Correlation = 23.8% for obligor with 0.03% (AA-)of PD K= K= RWA= K * 12.5*EAD 2008 Eric Confidential 1 As illustrated in the chart, the Basel committee considered the retail products have a lower asset correlation than wholesales banking. Based on the equation; the asset correlation for the AA grade8 is around 23.82%. By contrary, the correlation for the B- grade is less than half of the 1st grade – 12%. We can find that the asset correlation function is built of two boundaries: correlations of 12% and 24% for very high and very low PDs. Correlations between these boundaries are modeled by an exponential weighting function that displays the dependency on PD. The exponential function decreases rather fast; its pace is determined by the risk weight equation; the so-called “k-factor”. The upper and lower bounds for the correlations and the functions are based on the empirical studies. On the other hand, the mortgage asset has a 15% of constant correlation; while as the revolving product has a 4% of correlation. Both of the above retail products’ correlations are lower than most of the corporate rating’s. The reason that the retail products have lower 8 PD of AA grade is 0.03%. PD of B- grade is 12.61%.
  15. 15. 7 correlations is that the retail products are viewed as more diversified portfolio compare to corporate obligors. Several studies also confirmed the same result9. On the other hand, the mortgage has higher dependency with the real estate industry and is deeply influenced by the economy; therefore, the mortgage has higher asset correlation compare with other retail products10. Restricted Better grade has higher asset correlation under Basel committee’s assumption. ORR_Grade PD Correlation AA 0.03% 23.82% 25% 23.82% A+~A- 0.10% 23.41% BBB+ 0.16% 23.08% 20% BBB 0.26% 22.54% Mortgage BBB- 0.42% 21.73% 15% BBB- Negative 0.61% 20.85% Asset 12% Correlation perspective 10% BB+ 0.90% 19.65% Resolving Product BB 1.35% 18.11% 5% BB- 2.04% 16.33% 11 BB-Negative 3.15% 14.48% perspective 0% 1 2 3 4 5 6 7 8 9 10 11 12 13 B+ 4.93% 13.02% B 7.82% 12.24% CTCB Rating Grates B- 0.1261 12.02% 2008 Eric Confidential 1 The Basel deployed the correlation effect on the rating grade instead of on the country, industry. The difficulty that the Basel committee faces is that it’d be challenge to estimate average correlation for different country and different industry. Therefore, they turn to implement the correlation into the probability of default. The rational is that better rating obligor usually has larger asset size; larger asset usually has a higher dependency with the state of economy11. For example, the Honhai company has conducted many business across the world and is a major export contributor to Taiwan’s GNP. Therefore, if the economic declines, the Honhai company will be easier influenced by the economic downturn than SMEs or retail products may have. 9 Asset correlation of mortgage is range from 7% ~ 10% and 2%~5% for the retailing products, based on MKMV’s survey, Technical note. ‘Including non-corporate credit risk’, 2007. 10 Paul Calem and James Follain also found the 15% of correlation is reasonable and is supported by their empirical test. 11 Lopez,2002. The empirical relationship between average asset correlation,firm probability of default and asset size.
  16. 16. 8 We can use the following example to illustrate the effect of correlation on the capital estimation. Restricted Same lending amount, different capital charge are result from correlation. Both have the same EL = PD * LGD * EAD Mortgage Corporate Clients = 1.35% * 45% * 100 Mn = 0.61 Million 1.35% 1.35% PD While as mortgage has Corporate has higher lower ‘K’ , due to lower ‘K’ correlation 45% K = 0.082 K = 0.0549 45% LGD RWA = K * 12.50 * EAD RWA = K * 12.50 * EAD NTD 100 Million NTD 100 Million EAD = 0.082 * 12.5* 100 Mn = 0.0549 * 12.5* 100 Mn = 102 Million = 68.7 Million 2.5 Years 2.5 Years Tenor Capital = RWA * BIS Ratio Capital = RWA * BIS Ratio =102 Mn * 10% =68.7 Mn * 10% 15 % 18.11% Correlation =10.2 Million =6.87 Million 2008 Eric Confidential 1 In this example, the PD, LGD, EAD and loan maturity are the same for both of the corporate loan and retail mortgage. As a result, the EL is the same for both exposures.12. Given the correlation formula, the corporate client has an 18.11% of asset correlation and result in a capital charge of 10.2 million higher than the 6.87 million of mortgage’s. Even though, the correlation difference between this corporate client and mortgage is merely 3.11% but this tiny variation result in a 3.15 million of capital divergence. 12 EL = PD * LGD* EAD
  17. 17. 9 Restricted It also implies that Mortgage will faces longer tail risk of uncertainty. Probability of loss 98.65% Mortgage Corporate Case Case Best effort estimation if default 1.35% 1.35% Loss Most likely loss If default = Max loss =100million EAD * LGD =100mn*45% =45 Million Expected loss Unexpected loss Tail Risk Corporate 0.61 89.19 Million 10.2 Million Case Million Expected loss Tail Risk Unexpected loss Mortgage 0.61 92.52 Million Case 6.87 Million Million Total lending amount = 100 Million 2008 Eric Confidential 1 We can further depict the loss assumption under the Basel by using the above chart. The maximum amount of loss is the total principle, in our case it is 100 million. The most likely loss in the event of default is the EAD* LGD, in this case is 45 million. If the loan is still performing, the bank needs to reserve 0.61 million of EL as provision and requires to charge 10.2 million of capital13 for the unexpected loss in this corporate lending example. In oppose to the corporate loan, the mortgage also needs to reserve the same provision, but the capital is far lower. The amount that is not covered by the EL and UL is so called tail risk. The tail risk is a risk that rarely happens but once it does, it will cost you an arm and a leg. We can easy observe that the mortgage asset retains a longer tail than corporate client’s. The recent sub-prime credit lesson is a perfect example to demonstrate the importance of tail risk management. Differences between AIRB capital and Economic Capital There are five major differences between economic capital and regulatory capital, in my point of views: 1. The linkage to bank’s target rating: the AIRB capital is large depends on the BIS ratio, however, the BIS ratio doesn’t links to bank’s desire rating. The determination of economic capital requires bank to identify the confidence interval which direct links to bank’s target rating. 13 Assume BIS =10%
  18. 18. 10 Restricted The amount of EC held by a bank reflects the risk appetite of a bank. Illustrative EC links to bank‘s target Probability of rating loss ‘A’ rating ‘AA’ rating Loss Distribution :Confidence of :Confidence of =99.9% =99.97% Better rating requires increased capital holding and Y demonostrates the appetite of a bank X Credit Losses 0 Loss Tail Risk Expected Unexpected loss loss = Economic Capital Regulator Capital is also used to cover unexpected loss.The Basel Comittee uses a general form of formula to proxy the UL 2008 Eric Confidential 1 In the above chart illustrates that determination of economic capital links to the bank’s target rating. The X axis represents for the amount of credit losses. On the other hand, the Y axis stands for the occurrences of the corresponding credit losses. If bank is aiming at ‘A’ rating grade bank, given the riskiness of the current credit portfolio, this bank requires X amount of economic capital. If this bank shooting for a better rating, say ‘AA’, then needs Y amount of economic capital. Better rating grade means bank need to hold more capital for protecting unexpected loss. The economic capital represents for risk governance of a bank. As shown in the chart below: the Winterthur illustrates that their risk exposure in line with risk taking capacity to a confidence of 99.97% over 1 year period. The 99.97% implies that the possibility of not be able to cover the losses is 0.03%. The 0.03% equal to the default probability of AA rating grade’s. This indicates the ‘Risk Appetite’ of Winterthur.
  19. 19. 11 Restricted Risk appetite makes explicit how much risk the institution is willing to take. Winterthur The bank’s current available Link to its target rating capital is sufficient to cover 99.7% is equal to ‘AA’ 99.97% ‘s potential unexpected loss. The possibility of loss amount exceeds the current available capital is 0.03% Sources: Credit Suisse analyst day presentation 2006 2008 Eric Confidential 1 2. The consideration of diversification effect, which usually refers to the estimation of customized asset correlation, instead of using the constant correlation suggested by the Basel. Restricted Higher the correlation will have high relationship with the global economics, result in a higher impact to obligor’s business. Higher the correlation higher the UL, therefore, bank needs to reserve higher capital requirement Low correlation High correlation Basel Committee generates the asset correlation through ‘Reverse Engineering’ – Empirical experimental through several banks’ EC. 2008 Eric Confidential Source : An Explanatory Note on the Basel II IRB Risk Weight Functions, Basel 2 1
  20. 20. 12 Higher the asset correlation of a portfolio, usually result in a higher unexpected loss; vice versa14. Use a constant correlation (or formula to estimate) doesn’t really capture Restricted the correlation nature. Different types of loan assets have different asset correlation. 2008 Eric Confidential 1 Conceptually, as shown in the above, that the large corporations have higher asset correlation than SME and retail banking products. Higher correlation usually results in a higher economic capital requirement under everything being equal. The reason behind this is that: large corporations generally have better rating and usually have larger amount of financing needs. Once default, the credit losses may result in a catastrophe. For example, a bank has a 400 billion on loan exposure- 200 billion lends to one corporate client and a 200 billion credit card portfolio; and with 100 billion capital reserve. Assuming both has 50% of LGD. Once the corporate client defaults the bank capital will be wiped out. Credit loss = 200 billion * 50% =100 billion =total bank capital Even under economic downturn, the credit card portfolio encounters all card holders claim insolvency event is rare. This may explain that the retailing products are considered a more diversified and enjoy a lower correlation. 14 An Explanatory Note on the Basel II IRB Risk Weight Functions, Basel 2 working paper.
  21. 21. 13 3. Estimation of concentration risk : concentration risk refer to a bank’s credit portfolio that concentrated on certain country, industry, rating grade, single name or collaterals. Once the above encounter systematic risk that will cause banks significant losses. In the worse situation, bank may not be able to raise capital and turn out to be insolvent. Credit concentration risk is the largest source of risk to the solvency of a bank. This can occur in the form of the default of a large customer, and causes the simultaneous default of a few sizeable customers, or a downturn in the industry the bank is exposed to. Credit expected loss risk is something that can be priced for in most circumstances, whereas concentration risk is simply too expensive to price and need to be covered by the bank capital. Paradoxically, banks tend to have concentrated exposure to their best customers, and hence underwriting standards alone would not be sufficient to control this form of credit risk. Below chart illustrates that obligor ‘Y’ has larger exposure with low PD. In the event of default, bank will suffer large credit loss from obligor ‘Y’ that may jeopardize bank’s operation. Obligor ‘X’ has higher risk but lower exposure, even bank faces the insolvency of obligor ‘X’, the loss will be covered with the bank’s provision. Restricted Paradoxically, banks tend to have concentrated exposure to their best customers or certain industries that might result in an extreme losses when Illustrative economic downturn. Our view Illustrative – Impact of concentration on portfolio loss distribution • Credit concentration risk is the largest source of risk to the solvency of a bank, and this can occur in the form of the Default probability default of a large customer, the Company X simultaneous default a few sizeable but Or industry weak customers, or a downturn in the High risk and high industry the bank is exposed to exposure • Credit expected loss risk is something that can be priced for in most Name level circumstances, whereas concentration concentration risk is simply too expensive to price for Or Industry in most cases Solvency concentration • Paradoxically, banks tend to have Company Y concentrated exposure to their best Low risk and very high customers, and hence underwriting exposure standards alone would not be sufficient to control this form of credit risk Provision Capital 2008 Eric Confidential 1 A good demonstration is Enron event occurred in 2002. J.P Morgan lost a total of perhaps $0.5 billion in the course of Enron meltdown. Yet, as events unfolded, shareholders lost confidence
  22. 22. 14 and share price plummeted to all time low. JPMC’s share price fell from about $40-$15 dollars, destroying about $50 billion of market cap. This gives us a good example that the concentration risk will not only cause bank large credit loss but also result in: Stock price drops Market capitalization decline even more than the credit loss Downgrade by rating agency The recent sub-prime credit crunch is an example 15 . If banks’ revenue relies on certain products, industries or obligors in the recession, the concentration risk will penalize banks a lag and an arm sooner or later. In the worst case, bank may not be able to raise capital from the capital market, due to investors lose confidence on banks’ future. Restricted Usually the low possibility of ‘Large unexpected loses’ not only wiped out the profits but also results in significant market cap decline… – In addition to putting in danger bank’s target credit rating, large losses can erode shareholder confidence – Implications for • JPM Bank lost a total of market perhaps $0.5 billion in the capitalization course of Enron meltdown. Yet, can far exceed as events unfolded, actual losses shareholders lost confidence and share price plummeted to all time low • XX Bank’s share price fell from about $40-$15 dollars, destroying about $50 billion of market cap 2008 Eric Confidential 1 4. The estimation of economic capital requires bank to utilize the simulation skill to simulate the occurrences of loss and its corresponding credit loss amount based on the internal rating system (PD, LGD,EAD). The simulation will simulate different state of economy, under which the obligor may defaults or even results in a joint default event. The simulation result will form the loss distribution of a portfolio. 15 Several American and British banks have claim insolvent. This event also demonstrates these banks have over concentrated on the sub-prime segments.
  23. 23. 15 5. Objective is different: The last but not least, the major objective of regulator capital is to assess the capital sufficiency. On the other hand, the regulatory capital is for the measure of capital sufficiency. The regulator needs to have easier way to estimate the capital requirement to supervise the banks and to measure whether if banks have sufficient cushion to sustain against unexpected loss. The economic capital is a better management tool for bank to demonstrate the capital efficiency to their shareholder. For example, under the AIRB capital estimation, bank may need to reserve 30 dollars of capital, after considering the diversification and concentration effect, the economic capital is only 27 dollars; as illustrate in the blow. Restricted The objective of economic capital is to measure the ‘Capital Efficiency’. While as the objective of regulatory capital is ‘Capital sufficiency’. Illustrative Total = 30 Total = 27 5 2 Credit Regulatory Capital Diversification Concentration - Economic Regulatory Bank’s current Effect- Benefit Punishment , due Capital Capital available Requirement from correlation to concentrated on capital certain name , industry… EC is the maximum amount of unexpected losses Regulatory capital is the minimum amount of capital to potentially arising from all sources that could be Definition meet regulator’s request. absorbed while remaining solvent, with a given level of confidence over a given time horizon. Capital efficiency : Shareholder’s interest, measures if Capital sufficiency : regulator’s Objective main concern. capital is utilized efficient. For example, given 100 dollar of exposure, A portfolio consumes 10 dollar of capital while as B only consumes 5 dollar. 2008 Eric Confidential 1 The regulator capital is what we need to comply with. By contrast, the economic capital exhibits the real risk capital given the current portfolio mix and we have enough capital to prevent against unexpected loss – we are a fine bank with high disciplined in risk management. We can further use one example to illustrate the capital efficiency: assuming there are 2 portfolios, each has 100 dollar of exposure but the portfolio components are different16 which result in ‘A’ portfolio has 10 dollar EC while as ‘B’ only consumes 5 dollar of EC. Therefore, we 16 The weights of exposures are different, such as industries, countries, ratings or collaterals.
  24. 24. 16 17 find that portfolio ‘A’ has a 10% of capital ratio and portfolio ‘B’ has 5% of capital ratio. We, then, can conclude that portfolio ‘B’ is more efficient than portfolio ‘A’ in terms of use of bank’s capital.18 17 Estimated by divided EC with exposure. 18 We can also measure the capital efficiency by using the regulatory capital, such as AIRB approach. Using economic capital is more accurate in terms of the risk estimation.
  25. 25. 17 Section 3: Theory & vendor models introduction In the past decade, four important credit portfolio models have been introduced to measure the credit portfolio risk: 1. KMV’s portfolio manager is the first model introduced in 1993 2. J.P Morgan’s Credit metrics in 1997 3. Credit Suisse First Boston introduced CreditRisk+ in 1997 4. Also in 1997, McKinsey brought out portfolioview in different approach There are other vendors and consulting firms provide solutions in this field. Some banks also developed their in-house models. According to the survey conducted by the IACPM 19 (International Association of Credit Portfolio Managers), 44% of the IACPM members have in-house models 20 . In terms of vendor model, the KMV’s portfolio manager is widely subscribed. Restricted Understand your MODEL and what is the ASSUMPTION before further implementation. Findings from credit portfolio management Comments study in 2004 1. Different models may have different results. Which models are used? • Each vendor model has his own In-house features. developed CSFB Credit Risk+ 6% 44 % • Understand what Credit Metric 6% are you doing when using vender’s Vendor model model. MKMV 42% 66% Banks need to understand Macro Model 2% what methods are you using in estimating EC and gain confidence internally before communicating with regulator and rating agency. 2008 Eric Confidential Source: IACPM -Survey of CPM practices 2004 1 This section provides brief introductions of the vendor models. 19 Source: IACPM -Survey of CPM practices 2004. Wedsite: www.iacpm.org 20 Some banks even maintain 2 models-vendor model and in-house model.
  26. 26. 18 Portfolio Models Introduction In the last decade, a whole range of modeling techniques has been developed to analyze portfolio credit risk. Broadly viewed, there are three groups of portfolio credit risk models. The first group is ’structural’ and based on Merton’s21 model of firm capital structure: individual firms default when their assets’ value fall below the value of their liabilities. Examples of such a microeconomic causal model are CreditMetrics and KMV’s PortfolioManager. The second group consists of econometric factor risk models, like McKinsey’s CreditPortfolioView 22 . McKinsey’s model is basically a logistic model where default risk in ’homogeneous’ subgroups that determined by a macroeconomic index and a number of idiosyncratic factors. These two model types apply similar Monte Carlo simulations to calculate portfolio risk, as both are ’bottom-up’ models that compute default rates at either the individual firm level or at sub-portfolio level. Both thus require a similar kind of aggregation. The third group contains actuarial models, like Credit Suisse’s CreditRisk+23, that make no assumptions with regard to causality. The credit portfolio models usually construct the portfolio loss density in two stages. First, one has to derive the credit risk on the level of individual asset. Second, these risks have to be aggregated to the portfolio level. The first stage needs to have obligor’s PD and rating transition metrics to capture default and migration risk. In the event of default, model estimates the credit loss by applying the LGD. If obligor upgrades or downgrades due to the rating migration instead of insolvent, then estimate the value of loan correspondingly.24 The second stage requires take the correlation into consideration. Usually leverage the factor model to capture the default dependency and estimate the joint probability for all obligors. Most models employ the Monte Carlo simulation technique to derive the portfolio loss. 21 Merton, Robert, (1974), On the pricing of corporate debt: the risk structure of interest rates, Journal of Finance, Vol 29, pp. 449-470. 22 Wilson, Thomas, (1997), Portfolio credit risk (I), Risk,Vol. 10, No. 9. 23 CreditRisk+ - a credit risk management framework,1997. 24 Similar to the bond valuation. When bond being upgraded, the price goes up and visa’ versa. Models apply the Net Present Value and risk neutral methodology to evaluate the value of loan. These models also called ‘Value’ based model.
  27. 27. 19 KMV’s Portfolio manager Portfoliomanager is the most comprehensive tool to accomplish a measurement of three objectives 25 : diversification, optimization and valuation, though it is complex in terms of methodology. The estimation of economic capital require user to input the PD, LGD, EAD, tenor, credit spread26 and obligor’s information: weighting of country, industry as minimum requirements.27 In the first step, KMV’s model applies Merton’s concept that debt behaves like a short put option on the value of firm’s asset. In Merton’s world, default occurs when the value of the firm’s asset falls below default point – determined by the structure of the individual firm and its asset volatility. KMV modifies the Motern’s model and assumes that asset values follow a log-normal process with a specific growth rate to calculate the distance to default of obligor. Combing the simulation, KMV then simulate a credit quality transition table (KMV’s used the term : Distance to Default Dynamic) of each obligor instead of leveraging the rating transition metrics that provided by the rating agency. The loan’s value depends on the financial condition of each facility, such as credit spread, upfront fee, tenure and payment type. The individual loan or facility can have a range of possible values at future dates depends on the obligor’s change of default probability. The following chart provides the logic behind the generation of such value distribution in portfolio manager.28 KMV assumes that, at some time in the future or the horizon, the value of firm’s asset will follow a lognormal distribution. Furthermore, individual value for the firm’s assets at the horizon will correspond to values the facilities (loans or bonds). In other words, if the firm’s asset value increased, there is a high chance that the firm’s rating will be upgraded and result in a higher value of the facilities. If the value of the firm’s assets falls below the default point, then the firm will default and the value of the facilities will be the recovery value. 25 Brian Ranson, Credit risk management,2005. page 10-22. Printed by Sheshunoff. 26 The user can choose to use KMV’s EDF as a measure of PD, or use internal rating system. Credit spread is used for loan valuation. 27 The more detail can be found from the PM’s preprocess documentation. 28 More detail can be found in the ‘Modeling Portfolio Risk’ and ‘Credit portfolio management’, Charles Smithson.
  28. 28. 20 In the step 1 of the below chart demonstrates how the KMV simulates the firm’s future value and proxies the firm’s credit quality. Based on the credit quality and the credit related spread, the KMV estimates the value of the loan (the step 2). Final step is to map the loan value with probability – the value distribution of a firm’s facilities29. Restricted Log( Asset Value) Log( Asset Value) Step 1 Step 2 Step 3 Probability Value distribution 2008 Eric Confidential 1 To estimate the portfolio value distribution requires to take asset correlation into consideration. KMV decomposes asset returns into systematic and idiosyncratic factor. The asset return is derived from equity prices30 and incorporated into the firm’s liability. The correlation model (so called GCorr ) incorporates 120 factors to capture the macro factor, country factor and industry factor. This model estimates asset correlation among obligors and can translate into default correlation and joint probability of default. Please refer to the following chart. As we can see in the next chart that KMV’s GCorr decomposes the firm’s asset return into country’s, industry’s, sector’s, globe’s and firm’s specific risk. Moreover, user can easy to see the asset and default correlation. It is well known that if higher portion of systematic risk, the easier to be influenced by the macroeconomic fluctuation. The source of the diversification comes from the firm’s specific risk. The GCorr also contains a feature that can estimate 29 An obligor may have multiple credit lines (facilities) in a bank in the same time for different purpose and bank charges different rate for the risk taking activities. 30 KMV collects the stock index around the world to calculate the market value of firm, by adding the liability of firms, KMV can estimate the asset value of firms. Therefore, KMV can utilize these information and to re-contracture a benchmark index and to estimate the asset return of firms.
  29. 29. 21 correlation in matrix. Restricted Bank can extend the one factor model into multiple factors model to estimate the correlation. Systematic Risk Country Risk Industry Risk US Electronic UK Manufacturing Taiwan Service Korea Real estate . . • Bank can extend the on factor into multiple factors model Common Firm Specific Countries Industries Risk 14 45 61 rk = ∑ βkf rf + ∑βkcεc +∑βkiεi + εk f =1 c=1 i=1 2008 Eric Confidential 1 Restricted Higher the asset correlation easier to be influenced by the state of the economy. Asset correlation between obligor and the state of the economy Asset correlation between 2 obligors Joint default probability of 2 obligors Default correlation between 2 obligors Systematic Risk Can be Further Diversified Through Firm Specific Add more risk obligors 2008 Eric Confidential 1
  30. 30. 22 Restricted 2008 Prepared by Eric — CTCB Confidential 1 The portfolio value distribution is calculated simply by summing up all the facility values31. Then, the loss distribution is obtained by using the risk-free rate to calculate the future value of the portfolio at the horizon and subtracting the simulated value of the portfolio at the horizon: Portfolio Loss at Horizon = Expected Future Value of Current Portfolio– Simulated Value of the Portfolio at Horizon The portfolio value distribution and the loss distribution are mirror images of each other. The below chart32 in the next page shows how the two distributions that are related graphically. The value-distribution highlights several reference points and depict the boundary of the portfolio: VMax—Maximum possible value of the portfolio at the horizon (assuming there are no defaults and every obligor upgrades to AAA). VTS—Realized value of the portfolio if there are no defaults and all borrowers migrate to their forward EDF (maintain at the same credit rating grade). VES—Realized value when the portfolio has losses equal to the expected loss (or earns the 31 Considering the correlation effect in this step. For example, all obligors maintain solvency, then A obligor defaults and causes B obligor defaults and so on. Then evaluate the recovery value of the loan. 32 Source, ‘Modeling Portfolio Risk’ and ‘Credit portfolio management’, Charles Smithson. Page 117.
  31. 31. 23 expected spread over the risk-free rate)—expected value of the portfolio. VRF—Realized value when credit losses wipe out all the spread income—zero spread value of the portfolio. VBBB—Realized value when the losses would consume the entire portfolio’s capital if it were capitalized to achieve a BBB rating (equivalent to approximately a 15 bps EDF). Restricted Portfolio value distribution and the loss distribution are mirror images of each other. Expected value Value Distribution VES VBBB VRF VTS VMax Expected loss Loss Distribution 2008 Eric Confidential 1 KMV defines two loss distributions. One is based on the expected spread for the portfolio, so the loss is that in excess of the expected loss. The other is based on the total spread to the portfolio, so it is the loss in excess of total spread. Expected loss is expressed as a fraction of the current portfolio value. The economic capital estimation requires user to pre-define the target rating before running the simulation. EC is the difference between unexpected loss and expected loss. This capital value is calculated at each iteration, and is binned and portrayed graphically as the tail of the loss distribution. It answers the question: “Given the risk of the portfolio, what losses should we be prepared to endure?”33 33 KMV also provide portfolio optimization and trade optimization and can provide information which obligor should reduce or increase exposure. We won’t spend time to introduce these functions here.
  32. 32. 24 Creditmetrics In April 1997, J.P. Morgan introduced CreditMetrics, a model that first developed by the banking practitioner and sponsored by the KMV and other financial institutions. Like KMV’s model is based on Merton’s concept - debt behaves like a short put on the value of the firm’s assets, the stochastic variable in CreditManager is the value of the firm’s assets. 2 4 1 3 5 Inputs The approach can be explained as following34: First, calculate the different exposure profiles and dynamics for each exposure type with the consideration of the volatility of value due to credit quality migration for each individual exposure.35 The below chart explains the rating change within 1 year. That the BBB grade has an 86.93% will remain at the same grade. 6% of possibility will be upgraded and 0.18% of possibility may be insolvent within 1 year. 34 We summarized the steps into 2 steps to keep it simple and consistent in this paper, although Credit manager has many, many steps. Please refer to the ‘Introduction of CreditMetrics,1997’ for more details. 35 Source, Creditmertics’s technical note.
  33. 33. 25 1 Creditmetrics then estimates the value of the loan corresponding to credit quality of the obligor – as shown in the below charts. 1
  34. 34. 26 2 3 Second, calculate the volatility of value due to credit quality migration across the entire portfolio and different approaches. The estimation of correlations of credit quality migrations plays the core. Consequently, portfolio effects – the benefits of diversification and costs of concentrations – can be properly quantified36. 36 Refer to the ‘4’, ‘5’.
  35. 35. 27 4 Similar to KMV’s correlation approach, the major differences are illustrated below: Moody’s–KMV Model CreditMetrics Group’s Model 37 Asset value driven Equity index proxy Default correlation derives Systematic risk based on Default correlation derives Default correlation derives from asset correlation from correlation in the proxy (equity returns) Assuming obligor ‘s return is related to 2 systematic factors described as below : rA= uA+wA1f1+wA2f2+εA where : f1 ~ N(0,σ21) , f2 ~ N(0,σ22), εA ~ N(0,σ2A) σ1 ,σ2 is the standard deviation of factor 1 ,2 and σA is the firm-specific risk standard deviation. The correlation between two obligors A and B’s returns are given by: 37 Equity correlation would be a perfect proxy if the value of the debt remained fixed. The RiskMetrics Group argues that the approximation is good as long as the firm’s volatility is primarily driven by equity fluctuations, and the volatility of the debt level is relatively small in comparison to the equity fluctuations.
  36. 36. 28 w A1 wB1σ 12 + w A2 wB 2σ 2 + ( w A1 wB 2 + w A 2 wB1 )σ 1σ 2 ρ ( f1 , f 2 ) 2 ρ (rA , rB ) = σr σr A B Where σrA=(wA12σ21+ wA22σ22+σ2A)1/2 and similarly for obligor B. What is left is to determine the relationship between the correlation of the returns and the default event correlation for two obligors. We see that correlation depends both on the weights on the factors and on the correlation between the factors38. 4 Utilized the correlation model, Creditmetrics measures the joint migration probability based on the asset correlation, as exhibited above. Next step is to apply the Merton’s model to estimate the firm’s credit rating based on the joint migration. 4 38 General assumption is the correlation between the factors is zero.
  37. 37. 29 The process reiterates many times and then can generate the value distribution of the portfolio. 5
  38. 38. 30 The differences between the Creditmetrics and KMV are as follows: 1. Rating migration : User of KMV can choose to use the Distant to Default Dynamic or applies the rating agency’s rating transition matrix, whiles as the credit metrics only provide rating agency’s rating transition matrix to measure the rating migration likelihood. 2. Correlation : KMV constructs index by their own and estimate the asset return. The creditmetrics utilize the equity index39 to estimate the asset correlation. A core assumption of both of the KMV and CreditMetrics models is the multivariate normality of the latent variables. The asset return correlations are calibrated by assuming that asset returns follow a factor model, where the underlying factors are interpreted as a set of macro-economic variables40, such as country, industry etc. At each simulation, the return will determine if the obligor’s credit quality (credit migration) and then estimate the loan value of the obligor. The result is a value distribution of the portfolio. Restricted KMV and Creditmatrics run numerous simulations to generate a ‘Value Distribution’ and then translate it into loss distribution. For Each Simulation Draw Calculate Recover Correlat individual Sum Calculate y Rate in ed asset Obligor’s asset across Save the Obligor’s Simulati the case value value return, r, obligors to result new rating on of returns given index get (loss given asset #3436 default for each returns and portfolio #3436) return and index ∆I idiosyncratic losses calculate component loss Portfolio Value Distribution Tabulated Simulation Results ∆Portfolio Simulation # Company A Company B Value 1 Default; loss = 100 No Default 100 2 No default No Default 0 3 Default, loss = 60 Default, loss = 50 110 . . . . . . . . . . . . . . . . 2008 Eric Confidential 1 39 MSCI global index or local equity index. User of creditmetrics needs to estimate the correlation in the implementation stage, while as KMV embedded the GCorr into the Portfoliomanager already. 40 For further reading see papers by Koyluoglu and Hickman (1998), Gordy (2000) and Crouhy, Galai, and Mark (2000).
  39. 39. 31 CreditRisk+ Creditrisk+ is an actuarial model also called a reduced form model. Economic causality is ignored—there is no “story” to explain default. Consequently, specific asset values and leverage details for specific firms are irrelevant. Actuarial models specify a distribution for the default rate and apply statistics to obtain a closed form expression for the joint distribution of loss events. By extension the expected severity can be incorporated to arrive at a distribution of losses. An attractive feature of Credit Risk+ is that it requires only limited data. There are three required inputs: 1. PD of the obligor. 2. Volatility of default rate for the obligor—the model is very sensitive to this parameter; and this parameter is difficult to accurately measure and seldom can be provided by the user. 3. Facility exposure (amount at risk net of recovery)—Credit Risk+ takes the loss given default as fixed. The user inputs a net figure taking into account usage at default (for committed lines) and the amount of recovery. Unlike the Moody’s–KMV model and the RiskMetrics Group’s model, there is no simulation of how much is actually lost when default occurs for the recovery rate. Given the data input, it doesn’t require the calculation of individual default risk, and neither does it look at changes in market value in the even of upgrade or downgrade- as oppose to the KMV and creditmetrics. In this model, correlation is handled through the aggregation of like assets sorted by industry and country or the termed sector. Sectors allow users to influence the degree of default correlation between obligors: Specific risk sector—Placing some of an obligor’s risk in the specific risk sector means that that risk can be fully diversified away. Systematic sectors (maximum nine)—Within each sector, the default rates of each obligor are correlated. Across the sectors, the default rates are independent. For the loss aggregation, Credit Risk+ assumes that the default rate may vary, thus introducing the concept of “default rate volatility” for each obligor. Because this implies an underlying distribution for the average default rate, the developers made the assumption that the mean
  40. 40. 32 default rate (for each sector) is governed by a gamma distribution. Though there is no upper bound for the gamma distribution, this is permissible because the default rate for a sector can be greater than one, as opposed to a default probability. The actuarial approach has the appearance of precision because results are calculated via mathematical model rather than a simulation; however, just the opposite is true. Actuarial models are closed form approximations to the true distribution of defaults. However, Credit Risk+ is subject to at least two criticizes: 1. It is possible for a credit to default more than once. 2. The approximation used to calculate the portfolio distribution from the individual loss distributions relies on default rates being small. This means, for example, that noninvestment grade credits of longer. Creditportfolioview The first widely discussed macrofactor model was introduced by McKinsey & Company and was called CreditPortfolioView.41 The model starts not with the individual obligors’ information but rather with the view about the situation of the economy. The major difference between is the structured model ( KMV, CreditMetrics) estimates risk parameters (for example, PD and migration probabilities) as un-conditional, the Creditportfolioview’s approach focuses on conditional modeling conditional on the state of economy. The model requires the country risk of the economy, the industry risk within the economy and the rating of the obligor in order to predict default. To gauge the diversification, this model segments the portfolio based on the number of firms in the segment index. The systematic (non-diversifiable) risk – risk of economy – has a large predictable impact on credit migration and on default probabilities. That implies that we should use conditional rather than unconditional models! As an example Wilson42 presents the following table, in which he has found a linear regression model forecasting defaults and having the highest explaining power and only one explanatory variable. 41 Designed by the Thomas Wilson 42 Wilson, T. (1997a) Measuring and Managing Credit Portfolio Risk: Part I: Modelling Systematic Default Risk. The Journal of Lending and Credit Risk Management, July, 61 – 72. Wilson, T. (1997b) Measuring and Managing Credit Portfolio Risk: Part II: Portfolio Loss Distributions. The Journal of Lending and Credit Risk Management, August , 67 – 78.

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