"Credit Risk-Probabilities Of Default"


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Credit risk refers to the risk that a borrower will default on any type of debt by failing to make payments which it is obligated to do. The risk is primarily that of the lender and includes lost principal and interest, disruption to cash flows, and increased collection costs. The loss may be complete or partial and can arise in a number of circumstances. For example:
• A consumer may fail to make a payment due on a mortgage loan, credit card, line of credit, or other loan
• A company is unable to repay amounts secured by a fixed or floating charge over the assets of the company
• A business or consumer does not pay a trade invoice when due
• A business does not pay an employee's earned wages when due
• A business or government bond issuer does not make a payment on a coupon or principal payment when due
• An insolvent insurance company does not pay a policy obligation
• An insolvent bank won't return funds to a depositor
• A government grants bankruptcy protection to an insolvent consumer or business.

To reduce the lender's credit risk, the lender may perform a credit check on the prospective borrower, may require the borrower to take out appropriate insurance, such as mortgage insurance or seek security or guarantees of third parties, besides other possible strategies. In general, the higher the risk, the higher will be the interest rate that the debtor will be asked to pay on the debt.

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"Credit Risk-Probabilities Of Default"

  1. 1. - Arun Singh, (M.Sc Financial Mathematics)
  2. 2.  Financial risk is an umbrella term for multiple types of risk associatedwith financing, including financial transactions that include company loans in riskof default. Risk is a term often used to imply downside risk, meaning theuncertainty of a return and the potential for financial loss.Or The possibility that shareholders/investors will lose money when they invest in acompany that has debt, if the companys cash flow proves inadequate to meetits financial obligations. When a company uses debt financing, its creditors willbe repaid before its shareholders if the company becomes insolvent. Financial risk also refers to the possibility of a corporation or governmentdefaulting on its bonds, which would cause those bondholders to lose money.2
  3. 3. Credit riskForeigninvestmentriskLiquidityriskAsset-backed riskExchangerate riskMarket riskOperationalrisk3
  4. 4.  Credit risk refers to the risk that a borrower will default on any type ofdebt by failing to make payments which it is obligated to do. The risk isprimarily that of the lender and includes lost principal and interest,disruption to cash flows, and increased collection costs. The loss may becomplete or partial and can arise in a number of circumstances. Forexample:- A consumer may fail to make a payment due on a mortgage loan, creditcard, line of credit, or other loan. A company is unable to repay amounts secured by a fixed or floatingcharge over the assets of the company. A business or consumer does not pay a trade invoice when due. A business does not pay an employees earned wages when due.4
  5. 5. 5 A business or government bond issuer does not make a payment ona coupon or principal payment when due. An insolvent insurance company does not pay a policy obligation. An insolvent bank wont return funds to a depositor. A government grants bankruptcy protection to an insolvent consumeror business. To reduce the lenders credit risk, the lender may perform a creditcheck on the prospective borrower, may require the borrower to takeout appropriate insurance, such as mortgage insurance orseek security or guarantees of third parties, besides other possiblestrategies. In general, the higher the risk, the higher will be theinterest rate that the debtor will be asked to pay on the debt.
  6. 6. Credit RiskCredit Default RiskConcentration RiskCountry RiskCredit Spread Risk6
  7. 7. Credit risk can be classified in the following way:- Credit default risk - The risk of loss arising from a debtor being unlikelyto pay its loan obligations in full or the debtor is more than 90 days past dueon any material credit obligation; default risk may impact all credit-sensitivetransactions, including loans, securities and derivatives. Concentration risk - The risk associated with any single exposure orgroup of exposures with the potential to produce large enough losses tothreaten a banks core operations. It may arise in the form of single nameconcentration or industry concentration.7
  8. 8.  Country risk -The risk of loss arising from a sovereign state freezingforeign currency payment (transfer/conversion risk) or when it defaults onits obligations (sovereign risk). Credit spread risk - The risk occurring due to volatility in the differencebetween investments’ interest rates and the risk free return rate.8
  9. 9. 9
  10. 10.  Xylem (XYL) is a leading global water technology provider, enablingcustomers to transport, treat, test and efficiently use water for public utility,residential and commercial building services, industrial and agriculturalsettings. The company does business in more than 150 countries through anumber of market-leading product brands, and its people bring broadapplications expertise with a strong focus on finding local solutions to theworlds most challenging water and wastewater problems. Launched in 2011 from the spinoff of the water-related businesses of ITTCorporation, Xylem is headquartered in White Plains, N.Y., with 2011revenues of $3.8 billion and 12,500 employees worldwide. In 2012, Xylemwas named to the Dow Jones Sustainability World Index for advancingsustainable business practices and solutions worldwide.10
  11. 11.  Structural approach: Assumptions are made about the dynamics of afirm’s assets, its capital structure, and its debt and share holders. A firmdefaults if the assets are insufficient according to some measure. A liabilityis characterized as an option on the firm’s assets. Reduced form approach: No assumptions are made concerning why adefault occurs. Rather, the dynamics of default are exogenously given bythe default rate (or intensity). Prices of credit sensitive securities can becalculated as if they were default free using the risk free rate adjusted bythe level of intensity. Incomplete information approach: Combines the structural andreduced form approaches.11
  12. 12. The Structural Approach can further be classified into:- The Black Scholes- Merton Model (1973-1974) Altman Z-Score model The KMV-Merton Model12
  13. 13. The KMV-Merton model estimates the market value of debt by applying theMerton (1974) bond pricing model. The Merton model makes anassumptions that the total value of a firm is assumed to follow geometricBrownian motion,Where, V is the total value of the firm.µ the expected continuously compounded return on V,is the volatility of firm value andis a standard Weiner process.13
  14. 14.  Merton extended the work of Black & Scholes on option pricing theory in thedefault prediction of the firm, along with certain strong assumptions. In late1980’s, the application of Merton’s model to forecast default of the firm wasdeveloped by KMV Corporation, and we call this application the KMV-MertonModel. In 1989 Stephen Kealhofer, John McQuown and Oldrich Vasicekfounded company KMV. In 2002 the three entrepreneurs sold thecompany to Moodys. In 2007, Moodys KMV was renamed to MoodysAnalytics.14
  15. 15.  Merton’s assumption regards that the firm’s assets are tradable is violated byKMV. KMV is aware of this point. Instead of this point, KMV only uses the Black-Scholes and Merton setups as motivated to calculate an immediate phasecalled “distance-to-default” (DD) before computing the probability of default. The default event happens when the value of firm’s assets is below the defaultpoint. The face value of the debt is regarded as the default point in Merton’sModel. By using the volatility of the firm’s assets to measure, we can calculatethe Distance-to-default. The larger the number is in the Distance-to-default, theless the chance the company will default.15
  16. 16. The Distance-to-default or EDF (expected default frequency) isexpressed as:- Where, V = Market value of the assets.F = Market value of the debt/liability.µ = is an estimate of the expected annual return of the firm’s assets.= Standard deviation.T = Time.16
  17. 17. The Standard deviation can be calculated usingthe formula:- Where, x is the sample mean, average (number1, number2…) andn is the sample size.17
  18. 18. The corresponding probability of default, sometimes called the expecteddefault frequency (or EDF) is given by,In this model:- Credit risk increases as the volatility of the assets ( ) increases. Credit risk increases as T, the time to the repayment of the debt, goes up. Credit risk increases as µ, the return on assets, goes down.18
  19. 19. We can compute the “default probabilities" of the firm’s that are listedor traded in various exchange by using the historical data, as doneby various Credit Rating Agency, but what about the small firm’sthat are registered (i.e. Pvt. Ltd. Company) but are not listedanywhere?Solution!We can use the “KMV-Merton Model” with some modification to findthe “default Probabilities” of the these firm’s using their Financialreports/data.19
  20. 20.  Total Current Assets:- Total current asset is an asset which can eitherbe converted to cash or used to pay current liabilities within 12 months. It’ssum of a companys total cash, accounts receivable, inventory, depositspaid, and prepaid expenses. Total Current Liabilities:- Total current liabilities are often understoodas all liabilities of the business that are to be settled in cash within the fiscalyear or the operating cycle of a given firm. Working Capital:- Working capital measures how much in liquidassets a company has available to build its business. The number canbe positive or negative, depending on how much debt the company iscarrying.“Working Capital= Current Assets – Current Liabilities”20
  21. 21.  Total Assets:- The sum of current and long-term assets owned bya person, company, or other entity. Total Liabilities:- The aggregate of all debts an individual or company isliable for. Total liabilities can be easily calculated by summing all of onesshort-term and long-term liabilities Cash & Cash Equivalence:- Cash & cash equivalents are assets thatare readily convertible into cash, such as money market holdings, short-term government bonds or Treasury bills, marketablesecurities and commercial paper. Inventory:- The raw materials, work-in-process goods and completelyfinished goods that are considered to be the portion of a businesss assetsthat are ready or will be ready for sale.21
  22. 22.  Net worth:- The amount by which assets exceed liabilities.“Net Worth= Total Assets – Total Liabilities” Default Discount:- It is the discount given to the customers/clients by thecompany/firm. Period Discount:- The discount period is the time period during which acompany offers its customers a discount on the purchases that companymakes. The term is associated with the accounts receivable credit policy ofthe business firm.22
  23. 23.  Cash Ratio:- Cash ratio is the ratio of cash and cash equivalents of acompany to its current liabilities. It is an extreme liquidity ratio since only cashand cash equivalents are compared with the current liabilities. It measures theability of a business to repay its current liabilities by only using its cash and cashequivalents and nothing else.Cash Ratio = Cash + Cash EquivalentsCurrent Liabilities Current Ratio:- A liquidity ratio that measures a companys ability to payshort-term obligations.Current Ratio = Current AssetsCurrent Liabilities23
  24. 24.  Net Income:- In business, what remains after subtracting allthe costs (namely, business, depreciation, interest, and taxes) froma companys revenues. Net income is sometimes called the bottom line. Itis also called earnings or net profit. Return on Assets (µ):- It measures the amount of profit the companygenerates as a percentage of the value of its total assets. Acompanys return on assets (ROA) is calculated as the ratio of its netincome in a given period to the total value of its assets. Volatility (σ) :- It is the standard deviation of the return on assets. Alsoknown as the Volatility. Time:- Horizon of liability/debt.24
  25. 25.  The KMV EDF (expected default frequency) reactsquickly to changes in economic prospects of a firm,whereas agencies are often slow to adjust ratings. EDFs tend to reflect the current macroeconomicenvironment and tend to be better predictors of defaultsover short time horizons.25
  26. 26.  It is difficult to construct the theoretical EDF curves without theassumption of normality of asset returns. Private firm EDFs can only be constructed by using accounting dataand other observable characteristics of the borrower. The KMV approach does not distinguish between different types ofdebt (bonds that vary by seniority, collateral, covenants,convertibility, etc.) The KMV model is static - - once the debt is in place the firm doesnot change it. The default behavior of firms that manage theirleverage positions is not captured.
  27. 27.  We this methodology, we can find the “Probabilities of Default” usingthe Financial data/accounting data of the firms. However the resultcan further be improved if we have an access to last 8-10 yearsdatas. This method can also be useful for Private or PSU bank’s or NBFC’s,which often give loans to small firms on the basis of their Businessplans, Past Business Tax Returns, A Statement of Personal FinancialStatus etc..There is always a chance of improvement and I would really appreciateif you have any suggestion!27
  28. 28.  Credit risk-T. Bielecki, M. Jeanblanc and M. Rutkowski Forecasting Default with the KMV-Merton Model- Sreedhar T Bharath and TylerShumway(University of Michigan) Distance-to-Default (According to KMV model)- Tetereva Anastasija (NumericalIntroductory Course School of Business and Economics, Humboldt-Universität zu Berlin,http://www.wiwi.hu-berlin.de) How good is Merton model at assessing credit risk? Evidence from India- AmitKulkarni, Alok Kumar Mishra, Jigisha Thakker Quantitative Risk Management-Rüdiger Frey (Universität Leipzig,Universität Leipzig) A Default Probability Estimation Model: An Application to Japanese Companies (MasatoshiMiyake1Department of Industrial Administration, Tokyo University of Science, ) Search engines line Google, Investopedia, Risk Prep, etc..28
  29. 29. Thank for giving your valuable timeand sharing your expertise.29