Credit Risk- Probabilities of default

- Arun Singh, (M.Sc Financial Mathematics)

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Financial risk  is an umbrella term for multiple types of risk associated

with financing, including financial transactions that include company loans in risk

of default. Risk is a term often used to imply downside risk, meaning the

uncertainty of a return and the potential for financial loss.

Or

The possibility that shareholders/investors will lose money when they invest in a

company that has debt, if the company's cash flow proves inadequate to meet its

financial obligations. When a company uses debt financing, its creditors will be

repaid before its shareholders if the company becomes insolvent. 

Financial risk also refers to the possibility of a corporation or government defaulting

on its bonds, which would cause those bondholders to lose money.

Introduction

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Credit risk

Foreign investment risk

Liquidity risk

Asset-backed riskExchange rate risk

Market risk

Operational risk

Types of Financial Risk

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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.

What is Credit Risk?

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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.

What is Credit Risk?

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Credit Risk

Credit Default Risk

Concentration Risk

Country Risk

Credit Spread Risk

Types Of Credit Risk

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Credit risk can be classified in the following way:-

Credit default risk - The risk of loss arising from a debtor being unlikely to pay its loan obligations in full or the debtor is more than 90 days past due on any material credit obligation; default risk may impact all credit-sensitive transactions, including loans, securities and derivatives.

Concentration risk - The risk associated with any single exposure or group of exposures with the potential to produce large enough losses to threaten a bank's core operations. It may arise in the form of single name concentration or industry concentration.

Types of credit risk

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Country risk  -The risk of loss arising from a sovereign state freezing

foreign currency payment (transfer/conversion risk) or when it defaults on its

obligations (sovereign risk).

Credit spread risk - The risk occurring due to volatility in the difference

between investments’ interest rates and the risk free return rate.

Types of credit risk

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About Xylem Inc.

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Structural approach: Assumptions are made about the dynamics of a firm’s assets, its capital structure, and its debt and share holders. A firm defaults if the assets are insufficient according to some measure. A liability is characterized as an option on the firm’s assets.

Reduced form approach: No assumptions are made concerning why a default occurs. Rather, the dynamics of default are exogenously given by the default rate (or intensity). Prices of credit sensitive securities can be calculated as if they were default free using the risk free rate adjusted by the level of intensity.

Incomplete information approach: Combines the structural and reduced form approaches.

Three main approaches to modeling credit risk in the Finance literature

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The Structural Approach can further be classified into:-

The Black Scholes- Merton Model (1973-1974)

Altman Z-Score model

The KMV-Merton Model

Credit Risk Models

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The KMV-Merton model estimates the market value of debt by applying the

Merton (1974) bond pricing model. The Merton model makes an

assumptions that the total value of a firm is assumed to follow geometric

Brownian motion,

Where, V is the total value of the firm.

µ the expected continuously compounded return on V,

is the volatility of firm value and

is a standard Wiener process.

The KMV-Merton approach for measuring -Probabilities of default

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Merton extended the work of Black & Scholes on option pricing theory in the

default prediction of the firm, along with certain strong assumptions. In late

1980’s, the application of Merton’s model to forecast default of the firm was

developed by KMV Corporation, and we call this application the KMV-Merton

Model.

In 1989 Stephen Kealhofer, John McQuown and Oldrich Vasicek

founded company KMV. In 2002 the three entrepreneurs sold the

company to Moody's. In 2007, Moody's KMV was renamed to Moody's

Analytics.

The KMV-Merton Model

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Merton’s assumption regards that the firm’s assets are tradable is violated by

KMV. 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 phase

called “distance-to-default” (DD) before computing the probability of default.

The default event happens when the value of firm’s assets is below the default

point. The face value of the debt is regarded as the default point in Merton’s

Model. By using the volatility of the firm’s assets to measure, we can calculate

the Distance-to-default. The larger the number is in the Distance-to-default, the

less the chance the company will default.

Calculation of Distance-to-default (DD)

The Distance-to-default or EDF (expected default frequency) is

expressed 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

Distance-to-Default (DD)

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The Standard deviation can be calculated using the formula:-

Where, x is the sample mean, average (number1, number2…) and n is the sample size.

Standard deviation

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The corresponding probability of default, sometimes called the expected default 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.

Probability of default (PD)

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We can compute the “default probabilities" of the firm’s that are listed

or traded in various exchange by using the historical data, as done

by various Credit Rating Agency, but what about the small firm’s that

are registered (i.e. Pvt. Ltd. Company) but are not listed anywhere?

Solution! We can use the “KMV-Merton Model” with some modification to find

the “default Probabilities” of the these firm’s using their Financial

reports/data.

Problem?

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Total Current Assets:- Total current asset is an asset which can either be converted to cash or used to pay current liabilities within 12 months. It’s sum of a company's total cash, accounts receivable, inventory, deposits paid, and prepaid expenses.

Total Current Liabilities:- Total current liabilities are often understood as all liabilities of the business that are to be settled in cash within the fiscal year or the operating cycle of a given firm.

Working Capital:- Working capital measures how much in liquid assets a company has available to build its business. The number can be positive or negative, depending on how much debt the company is carrying.

“Working Capital= Current Assets – Current Liabilities”

Parameters required for Credit Limit

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Total Assets:- The sum of current and long-term assets owned by a person, company, or other entity.

Total Liabilities:- The aggregate of all debts an individual or company is liable for. Total liabilities can be easily calculated by summing all of one's short-term and long-term liabilities

Cash & Cash Equivalence:- Cash & cash equivalents are assets that are readily convertible into cash, such as money market holdings, short-term government bonds or Treasury bills, marketable securities and commercial paper.

Inventory:- The raw materials, work-in-process goods and completely finished goods that are considered to be the portion of a business's assets that are ready or will be ready for sale.

Parameters

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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 the company/firm.

Period Discount:- The discount period is the time period during which a company offers its customers a discount on the purchases that company makes. The term is associated with the accounts receivable credit policy of the business firm.

Parameters

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Cash Ratio:- Cash ratio is the ratio of cash and cash equivalents of a company to its current liabilities. It is an extreme liquidity ratio since only cash and cash equivalents are compared with the current liabilities. It measures the ability of a business to repay its current liabilities by only using its cash and cash equivalents and nothing else.

Cash Ratio = Cash + Cash Equivalents

Current Liabilities

Current Ratio:- A liquidity ratio that measures a company's ability to pay short-term obligations.

Current Ratio = Current Assets

Current Liabilities

Parameters

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Net Income:- In business, what remains after subtracting all the costs (namely, business, depreciation, interest, and taxes) from a company's revenues. Net income is sometimes called the bottom line. It is also called earnings or net profit.

Return on Assets (µ):- It measures the amount of profit the company generates as a percentage of the value of its total assets. A company's return on assets (ROA) is calculated as the ratio of its net income in a given period to the total value of its assets.

Volatility (σ) :- It is the standard deviation of the return on assets. Also known as the Volatility.

Time:- Horizon of liability/debt.

Parameters for default Probabilities:-

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The KMV EDF (expected default frequency) reacts

quickly to changes in economic prospects of a firm,

whereas agencies are often slow to adjust ratings.

EDFs tend to reflect the current macroeconomic

environment and tend to be better predictors of defaults

over short time horizons.

Advantages of KMV Approach

It is difficult to construct the theoretical EDF curves without the assumption of normality of asset returns.

Private firm EDFs can only be constructed by using accounting data and other observable characteristics of the borrower.

The KMV approach does not distinguish between different types of debt (bonds that vary by seniority, collateral, covenants, convertibility, etc.)

The KMV model is static - - once the debt is in place the firm does not change it. The default behavior of firms that manage their leverage positions is not captured.

Critique of the KMV Model

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We this methodology, we can find the “Probabilities of Default” using

the Financial data/accounting data of the firms. However the result

can further be improved if we have an access to last 8-10 years

data's.

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 Business

plans, Past Business Tax Returns, A Statement of Personal Financial

Status etc..

There is always a chance of improvement and I would really appreciate

if you have any suggestion!

Conclusion

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Credit risk-T. Bielecki, M. Jeanblanc and M. Rutkowski

Forecasting Default with the KMV-Merton Model- Sreedhar T Bharath and Tyler

Shumway(University of Michigan)

Distance-to-Default (According to KMV model)- Tetereva Anastasija (Numerical Introductory

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- Amit Kulkarni, Alok

Kumar Mishra, Jigisha Thakker

Quantitative Risk Management-Rüdiger Frey (Universität Leipzig,Universität Leipzig)

A Default Probability Estimation Model: An Application to Japanese Companies (Masatoshi

Miyake1Department of Industrial Administration, Tokyo University of Science, )

Search engines line Google, Investopedia, Risk Prep, etc..

Reference

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Thank for giving your valuable time and sharing your expertise.

Acknowledgement