"Credit Risk-Probabilities Of Default"

- Arun Singh, (M.Sc Financial Mathematics)

 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.
2

Credit risk
Foreign
investment
risk
Liquidity
risk
Asset-
backed risk
Exchange
rate risk
Market risk
Operational
risk
3

 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.
4

5
 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.

Credit Risk
Credit Default Risk
Concentration Risk
Country Risk
Credit Spread Risk
6

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.
7

 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.
8

 Xylem (XYL) is a leading global water technology provider, enabling
customers to transport, treat, test and efficiently use water for public utility,
residential and commercial building services, industrial and agricultural
settings. The company does business in more than 150 countries through a
number of market-leading product brands, and its people bring broad
applications expertise with a strong focus on finding local solutions to the
world's most challenging water and wastewater problems.
 Launched in 2011 from the spinoff of the water-related businesses of ITT
Corporation, Xylem is headquartered in White Plains, N.Y., with 2011
revenues of $3.8 billion and 12,500 employees worldwide. In 2012, Xylem
was named to the Dow Jones Sustainability World Index for advancing
sustainable business practices and solutions worldwide.
10

 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.
11

The Structural Approach can further be classified into:-
 The Black Scholes- Merton Model (1973-1974)
 Altman Z-Score model
 The KMV-Merton Model
12

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 Weiner process.
13

 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.
14

 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.
15

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

The Standard deviation can be calculated using
the formula:-
 Where, x is the sample mean, average (number1, number2…) and
n is the sample size.
17

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.
18

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.
19

 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”
20

 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.
21

 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.
22

 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
23

 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.
24

 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.
25

 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.

 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!
27

 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..
28

Thank for giving your valuable time
and sharing your expertise.
29

"Credit Risk-Probabilities Of Default"

More Related Content

What's hot (20)

Viewers also liked (20)

Similar to "Credit Risk-Probabilities Of Default" (20)

Recently uploaded (20)

"Credit Risk-Probabilities Of Default"