# Classification

## Default Model and Value-based Valuations

A borrower’s default constitutes default risk. On the other hand, in case of default, the amount recovered is usually than the amount lent. The risk associated with this is referred to as recovery risk.

Compared to the current exposure, in case of a possibility of exposure rising at the default time, exposure risk is present. All these risks are taken into account by a default-mode valuation or loss-based valuation.

In a similar manner, if assets exposed to credit risk are sold, it is important to consider the fact that the quality of credit could change over time, leading to a change in market value. A rating migration depicts the change in credit quality hence the name migration risk.

A new risk source will come up by including in the trading books and valuing at market prices positions that are exposed to credit risk. Moreover, in case the market becomes less liquid leading to the sell-off of credit exposures, asset liquidity risk will be associated hence lower than expected values will be accepted.

## Default Risk

No credit management approach that is modern can be pursued without measuring the counterparty credit quality. The following alternatives enable the determination of this probability:

- Studying a borrower’s homogeneous classes’ historical default frequencies. Default rates and assigned ratings are recorded in an almost secular manner by rating agencies observing per rating class ex-post.
- With respect to databases, applying mathematical and statistical tools by credit portfolios of banks having lots of portfolios.
- The application of approaches that is both judgmental and mechanical in nature with automatic classification being generated by structures that are either statistical or numerical.
- The implicit default likelihood attached to prices in the market can be extracted by a completely different approach applicable specifically to public listed counterparties on the securities and equities markets.

The likelihood of default within the given period, often a year, measures default risk but cumulative likelihoods can be assessed should exposure be more than a year.

## Recovery Risk

Several elements influence the net position proceeds should there be a default. Based on the involved credit contracts types, a difference in the procedure of recovery might be necessary. General conditions of the economy might also determine the rate of recovery.

Business sectors belonging to defaulted borrowers are also crucial due to the difference in volatilities is various sectors. Covenants between lenders and borrowers are also of the utmost importance as they increase a borrower’s actions limits.

Collecting the data of recovery rate is not an easy task. The reference of recoveries to original contracts, collaterals and guarantees is often lost since they are managed worldwide.

Comprehensive models are not easily created however sophisticated the model is, hence the adoption of simpler models through top-down procedures summarizing the average LGD rates.

## Exposure Risk

In case of default, the amount of risk can be referred to as exposure risk. Using a plan of reimbursement that is contractual, then it is simple to determine this amount. The specification of a model such as the one shown below can compute the amount at default that is due.

$$ Exposure\quad at\quad default=drawn+\left( limit-drawn \right) \times LEQ $$

Where the amount currently used is called drawn, the available limit’s rate of usage that is beyond the ordinary usage is \(LEQ\), and the maximum amount a bank lends an obligor is called limit.

In instances like the financing of account receivables, the origin of additional complexities is due to the ability to alter the amounts owed by the buyer to the bank.

# Key Concepts

## Expected Losses

In the long run, the average loss generated by a group of credit facilities is referred to as the expected loss and is written as a default exposure percentage.

In case the method applied to get the expected loss is financial, we identify the loss by declining market values due to any credit risk. If the method is actuarial, we fail to consider some risks and recognizing only losses from default events.

In banks, the expected loss is viewed as an industrial cost faced by lenders in one way or another. On a provided period to compute the expected loss, we have to get the product of the following factors: the likelihood of default, loss severity, and exposure at default.

## Unexpected Losses, VaR and Concentration Risk

In credit decisions and bank businesses, expected loss will be embedded since it is expected in the long run. Because of credit cycles and other events, a strong deviation in expected losses is likely to be witnessed in short periods of time.

When adequate equity capital is held by banks for absorbing losses recorded in the income statements during hard times, unexpected losses are faced by banks.

To deal with all risks, banks are supposed to have enough capital on hold. Capital should be computed by models of risk that are robust and analytical in nature.

To accurately measure variability, \(VaR\) is applied when dealing with credit risk. \(VaR\) is the value obtained by subtracting the maximum rate of loss at a particular confidence level from the expected rate of loss from a specific period of time.

Naturally, probability distributions are highly asymmetric based on credit risk. Identifying the probability of default is crucial for the computation of economic capital. Adopting a parametric closed-form distribution and using numerical simulations and discrete probability solutions is possible when constructing a loss distribution and \(VaR\) measure computation.

Rather than accounting for risk deriving from portfolio concentration, risk summary measures that are important are given by expected losses and measures of \(VaR\). For a large number of counterparties, the willingness and capacity to honor outstanding obligations are affected by risk factors.

Analytic quantification of marginal risk attributable to different credit exposure is impossible if a model of credit portfolio is lacking. Estimation of concentration risk can be achieved with the availability of a portfolio model.

Default co-dependencies (the likelihood of more counterparties defaulting jointly hence worsening their ratings) can be modeled by firstly asset value correlation and the framework provided by Merton. The likelihood of the asset values of two obligors getting lower than their respective outstanding debt is associated to joint default.

Secondly, in homogeneous groups of obligors’ historical correlations, the default correlation’s direct measure models co-dependencies. The risk of a portfolio is equal to the sum of risks by individual obligors if the correlation coefficient is one. Banks will deal in financial timeframes that are different in cases of default events not being positively correlated in a perfect manner.

A crucial measure is ways in which individual exposures contribute to concentration and overall portfolio risk and the economic capital of the portfolio.

Marginal contribution can be expressed as:

$$ { ULC }_{ i }=\frac { \partial U{ L }_{ portfolio } }{ { \partial }_{ { w }_{ i } } } { w }_{ i } $$

By traditional variance/covariance approaches as:

$$ { ULC }_{ i }={ \rho }_{ i;portfolio }{ w }_{ i }U{ L }_{ portfolio } $$

The \({ i }^{ th }\) loan beta providing a meaningful measure which compares the \({ i }^{ th }\) loan risk to the average portfolio risk level is defined as:

$$ { \beta }_{ i }=\frac { { { ULC }_{ i } }/{ { w }_{ i } } }{ { UL }_{ portfolio } } $$

Where:

- \({ { UL }_{ portfolio } }\) is the unexpected loss in a portfolio;
- \({ w }_{ i }\) is the \({ i }^{ th }\) loan weight on the overall portfolio \({ \rho }_{ i;portfolio }\) as the default correlation between \({ i }^{ th }\) loan and overall portfolio; and
- \({ ULC }_{ i }\) is the marginal contribution of the \({ i }^{ th }\) loan portfolio unexpected loss.

\(A\) larger than 1 \(\beta \) values implies a larger addition by the marginal risk as compared to the portfolio’s average risk and vice versa.

To establish a risk driver measure that is quantitative, a correlation coefficients \({ \rho }_{ i;portfolio }\) and \({ \beta }_{ i }\) are computed at portfolio levels that are distinct.

## Risk-Adjusted Pricing

Due to the expectations of shareholders on the return on investment, capital can be very costly. The appetite for economic capital that is high can be exemplified by increased \(VaR\)s suggesting the need for higher profits. A lending cost has to be included in credit spreads or assumed to be costs during the computation of risk-adjusted performance measures.

When information is provided, the setting of credit strategy can be substantially innovated. Theoretically, prices are exogenous to banks acting as price takers, assessing a deal’s expected return and actual return by measures of risk-adjusted performance.

But markets are practically segmented since they are made up of various segments. The implication is that prices may be a credit policy tool as well as a criterion for shaping portfolio risk profile by finding rules for combining individual loans’ risks and returns. Pricing policies that are risk-based at the level of the bank will:

- Ensure that the active portfolio risk management’s basis is well structured;
- Facilitate the market and operational risk’s integration to credit risks for an effective economic budgeting support; and
- At business unit levels, ensure the formulation of management objectives with respect to the profitability of economic capital.

When supporting pricing models, most banks will apply performance measures that are credit adjusted. The finance theory provides the criterion for the applications assuming that different business’ lines values are dependent on the capacity to provide higher returns as compared to those needed when rewarding market risk premium.

Credit risk spread and market risk premium have to be proportional considering comparable investment’s risk premium.

The target return of a bank’s credit risk-taking activities can be fixed beyond the capital cost threshold by establishing target levels that can be used as assets assigned to that division. Therefore, the following condition is a value creation transaction.

$$ RARORAC>{ ROE }_{ target } $$

Note: \(RARORAC\), the risk-adjusted return on risk-adjusted capital, combines \(RAROC\) with \(RORAC\) to adjust both the return and the capital based on the risks being taken.

In the form of economic value added (\(EVA\)), the relationship becomes:

$$ EVA=\left( RARORAC-{ K }_{ e } \right) \times Economic\quad Capital $$

Where \({ K }_{ e }\) is the cost of shareholder’s capital.

A management approach that is value-based having fundamental variables has to be incorporated in risk-based pricing as shareholders may require. By computation of minimum interest rate making shareholders value to rise, the process of credit is affected by economic capital.

Therefore:

$$ RARORAC=\frac { Spread+Fees-Expected\quad loss-Capital\quad cost-Operations\quad cost }{ Economic\quad capital } $$

To override decisions regarding prices, the product and the internal rules governing the credit process have to be taken into account. In general, for strict monitoring of these exceptions, a requirement that the decisions be taken by higher management level is a must.

For the process to be considered complete, feedback on the final result of the decision taken should be given to management. An analysis of client profitability gives a complete view of all client generated costs, revenues, and risks.

The task of implementing this analysis through the identification of unprofitable or marginally profitable clients can be realized if clients are divided into ranges of per unit of risk return. Areas to intervene during overseeing of profitability of customer are provided by this methodology in a straightforward manner.

The following reasons are responsible for the adoption of models the models:

- The complexity of investors exhibited when maximizing the value of shareholders by promoting the adoption of distinct tools; and
- The organization of banking groups by specific profit centers due to their growth in size and sophistication.

The implication is that the usefulness and importance of rating as a measure of a borrower’s creditworthiness is crucial. Otherwise, lenders could not:

- Operate all capital markets;
- Ensure important factors of value creation are managed; and
- Establish a comparison between business units, economic performance, and their actions coordination.

# Practice Questions

1) Almanac Glasses submitted to BCA Bank the following data from their financial statement to be used to assess its capacity.

Almanac net income for the year ended on \(December \quad { 31 }^{ st }, \quad 2017\) was $154,000, with costs of goods sold amounting to $1,250,000. On the same date, Almanac reported total assets of $670,000 and total liabilities of $125,000.

As a credit analyst for BCA Bank, calculate Almanac’s return on equity.

- 1.23
- 0.23
- 2.01
- 0.28

The correct answer is **D**.

The first step is computing the equity of the stockholder by establishing the difference between the total assets and total liabilities.

$$ \Rightarrow Stockholders\quad equity=$670,000-$125,000=$545,000 $$

The net income is then expressed as a ratio of the equity of the stockholder as shown below:

$$ \Rightarrow ROE={ Net\quad income }/{ Total\quad equity }={ $154,000 }/{ $545,000= }0.28 $$