Basel Modeling and Validation

General-

Pillar 1- describes the guidelines for calculating the bank’s risk profile and capital requirements.

·         Internal risk management;

·         Risk modeling and quantitative measurement;

·         Calculation of minimum capital requirements according to Basel II.

Pillar 2- Related to sound capital assessment process and outlines the role of the supervisor and responsibilities of the bank’s board and senior management.

Interest Rate and country risk is treated under this pillar.

Pillar 3- describes the disclosure requirements towards stakeholders. By this stakeholders are enabled to evaluate the bank’s financial stability in a better way.

Major Changes in Basel 111-

 (a) Capital Conservation Buffer:    Banks will be required to hold a capital conservation buffer of 2.5%.  The aim of asking to build conservation buffer is to ensure that banks maintain a cushion of capital that can be used to absorb losses during periods of financial and economic stress.

(b) Countercyclical Buffer:  Basically to increase capital requirements in good times and decrease the same in bad times.  The buffer will slow banking activity when it overheats and will encourage lending when times are tough i.e. in bad times.  The buffer will range from 0% to 2.5%, consisting of common equity or other fully loss-absorbing capital.

 (c) Minimum Common Equity and Tier 1 Capital Requirements :   The minimum requirement for common equity has been raised under Basel III from  2% to 4.5% of total risk-weighted assets.  The overall Tier 1 capital requirement, consisting of not only common equity but also other qualifying financial instruments, will also increase from the current minimum of 4% to 6%.   Although the minimum total capital requirement will remain at the current 8% level, but will increase to 10.5% when combined with the conservation buffer.

 (d) Leverage Ratio A leverage ratio is the relative amount of capital to total assets (not risk-weighted).   This aims to put a cap on swelling of leverage in the banking sector on a global basis.   3% leverage ratio of Tier 1 will be tested before a mandatory leverage ratio is introduced in January 2018.

Comparison of Capital Requirements under Basel II and Basel III :

Requirements	Under Basel II	Under Basel III
Minimum Ratio of Total Capital To RWAs	8%	10.50%
Minimum Ratio of Common Equity to RWAs	2%	4.50% to 7.00%
Tier I capital to RWAs	4%	6.00%
Core Tier I capital to RWAs	2%	5.00%
Capital Conservation Buffers to RWAs	None	2.50%
Leverage Ratio	None	3.00%
Countercyclical Buffer	None	0% to 2.50%
Minimum Liquidity Coverage Ratio	None	100%(2015)
Minimum Net Stable Funding Ratio	None	100%(2018)
Systemically important Financial Institutions Charge	None	TBD (2011)

Credit Risk-

The difference between the approaches is how the parameters PD, LGD and EAD is calculated in the formula for calculating the required regulatory capital-

Total risk-weighted assets= 12.5 *(Capital Requirement (Market Risk + Operational Risk)) + sum of risk-weighted assets for credit risk.

Scaling factor is applied to the risk-weighted asset amounts for credit risk assessed under the IRB approach. The current estimate of the scaling factor is 1.06.

The risk weight formulas represent only unexpected loss (UL) and do not include expected loss (EL). EL is the average loss that the bank expects from an exposure over a fixed time period.

If EL exceeds the total eligible provisions then banks must deduct the difference – 50% of the difference is deducted from Tier 1 and 50% is deducted from Tier 2 capital.

If EL is less than the provisions, then banks may adjust the difference in Tier 2 capital subject to the 0.6% limit of credit risk weighted assets.

Banks generally cover their ELs on a continuous basis through provisions and write off. Banks are required to keep capital for UL.

Under the IRB approach, banks are required to categorize their banking book exposures into the following asset classes-

·        Corporate

·        Sovereign

·        Bank

·        Retail

·        Equity

The IRB foundation approach uses internal models and estimates of the PD parameter to calculate the regulatory capital required for credit risk.

The IRB advanced approach uses internal models and own estimation of all parameters.

Types of Exposures-

a.    Exposures to central governments and central banks.

b.    Exposures to institutions.

c.    Exposures to corporate.

d.    Retail exposures.

e.    Equity exposures.

f.     Securitization positions.

g.    Other non-credit-obligation assets, including the residual value of leased real estate, which do not apply to another class.

·       EAD ( Exposure at Default)-

A total value that a bank is exposed to at the time of default.EAD must not be lower than the book value of balance sheet receivables and has to be calculated without considering provisions.

Calculation of EAD according to the product type can be divided into two sections:

1-   Lines of credit:  Some types of “lines of credit‟ are demand loan, term loan, revolving credit, and overdraft protection.

The methods used to estimate the EAD for lines of credit and off-balance sheet items is- Credit Conversion Factor (CCF) Method

2-     Derivatives- over-the-counter (OTC) instruments (interest rate swap, caps, floors, swaptions, cross currency swaps, equity swaps, and commodity swaps).

EAD estimation methods for derivative products can be done by the below methods:

1-     - Current Exposure Method (CEM)

2-     - Standardized Method (SM)

3-     - Internal Model Method (IMM)

Under the internal ratings-based approach, calculation of EAD is further divided into the following two sections:

Foundation Approach (F-IRB): In this approach, EAD associated with „lines of credit‟ and „off-balance sheet transactions‟ are to be calculated using the CCF method, where the CCFs are provided in the Basel guidelines; collaterals, guarantees or security are not taken into consideration while estimating EAD. To estimate EAD of derivatives, any of the abovementioned methods under the derivatives section can be chosen.

Advanced Approach (A-IRB): Banks are allowed to use their own models, and they have the flexibility in choosing their models. For the CCF method, the CCFs are not provided by the regulatory guidelines and have to be calculated.

1-   CCF Method-

-      Fixed exposure: Exposures for which the bank has not made any future commitments to provide credit in the future and the on-balance sheet value gives the value of exposure. The value of the exposure is given by the following formula:

EAD = Drawn Credit Line

EAD for the fixed exposures will equal to the current amount outstanding on the balance sheet.

-      Variable exposure- the exposure will contain both on- and off-balance sheet values. The value of exposure  is given by the following formula:

EAD = Drawn Credit Line + Credit Conversion Factor * Undrawn Credit Line   

Where,

Drawn Credit Line = Current outstanding amount

Credit Conversion Factor = Expected future drawdown as a proportion of undrawn amount

Undrawn Credit Line = Total amount committed - drawn credit line

Credit Conversion Factor (CCF) Modeling-

CCF is calculated for the default exposures which are used to estimate the CCF for the non-default exposures.

CCF lies between 0 and 1.

-      CCF Estimation for Defaulted Exposures-

·        Fixed-horizon method - assumes that all the exposures that are in non-default state will default at the same time over the time horizon chosen for the estimation. The CCF is calculated with respect to the time horizon that is always fixed.

Where,

-      EAD: Exposure at the time default occurred

-      On_balance (fixed horizon): Exposure of the bank at fixed time horizon (one year) prior to default

-      Limit (fixed horizon): Maximum exposure that the bank can have with the counterparty at the fixed horizon.

Cohort Method for CCF- The observed time horizon is divided into different short time windows.

The amount that will be drawn at maturity is related to the drawn/undrawn amount at the beginning of the different time horizons.

EAD: Exposure at the time default occurred

On_balance (start of window): Exposure of the bank at the start window period prior to default

Limit (start of window): Maximum exposure that the bank can have with the counterparty at the start of the time window

-      CCF Estimation for Non-Defaulted Exposures-

Regression analysis can be used to estimate the non-default exposure CCFs. Once the CCFs for default exposures are calculated, the EADRDs (Exposure at Default Risk Drivers) can be grouped as independent variables and the CCFs calculated as dependent variable.

2-   Current Exposure Method-

EAD = (CE+ PFE) - Collateral

CE = Current Exposure, PFE = Potential Future Exposure.

Potential Future Exposure- is the maximum amount of exposure expected to occur on a future date with a high degree of statistical confidence.

The PFE is calculated by multiplying the notional values of the contracts with a fixed percentage which is the Credit Conversion Factor (CCF) as shown below:

3-   Internal Model Method-

EAD = α * Effective EPE (Expected Positive Exposure)

α: multiplier set by regulators to 1.4

EPE is the average of Expected Exposure (EE) for certain time interval at a future date.

LGD (Loss Given Default)

LGD is defined as the percentage loss rate on EAD or share of an asset that is lost when a borrower defaults.

Under the IRB Foundation approach the LGD is determined by the regulator.

However the bank can use the CRM (Credit Risk Mitigation) Framework to determine the value of collateral by using internal.

A.    When Collateral is there and there is chance of double default or counterparty credit risk-

LGD = LGD * E▪/E, Where E▪ = max (0, [EAD*(1+ He) – C * (1-Hc – Hfx)]

H_e = Haircut Appropriate for exposure.

H_c = Haircut Appropriate for Collateral.

H_fx = Haircut Appropriate for Foreign exchange.

Haircut is defined as %age by which asset value, margin, collateral or currency market value is devalued.

B.     LGD =

Economic Loss / Exposure at Default

= [Exposure at Default – PV*(Recoveries or collateral) + PV*(Costs)] / Exposure at Default.

PV is a function of Discount rate = Estimating discount rates as

o   Weighted average cost of capital- WACC = Wd*(Kd)*(1-t) + Wpfd*(Kpfd) + (We)*(Ke). (Kpfd = Dividend / Share Price).

C.     LGD =

1- Recovery Rate.

Recovery Rate –

1.     By Beta Distribution-

Alpha- tells us center,

And Beta tells us shape

Alpha = {(LGD Mean) ^2 * (1 - LGD Mean) / Variance LGD)} – Mean LGD.

Beta- Tells us shape-

 = Alpha * [(1/Mean LGD) – 1]

Recovery Rate = alpha / (Alpha + Beta).

LGD averages and standard deviations are estimated by a historical analysis of recovery history.

2.    Instantaneous Recovery Rate Models

·        For bonds, it is possible to determine market recovery rates, which can be calculated as the ratio of the actual market price and the nominal value

 Identify stress points based on historical default rates and/or macroeconomic indicators, estimate default rates during these stressed conditions and calculate their averages. Plug these default rates into a stressed LGD model.

Compute weighted average LGD across these stress points and compare them with average LGD over the cycle. Use the higher of the two for capital calculation purposes. Scaling factor of 1.06 for BASEL AND 1.25 for CAD (EU) to reflect downturn risk.

The BCBS Basel III minimum requirements impose a downturn LGD floor of 10 per cent for Residential mortgage portfolio and 15% for High Volatile Commercial Real Estate.

PD (Probability of Default)-

Estimation of PD depends on two broad categories of information:

1.     Macroeconomic – unemployment, GDP growth rate, interest rate

2.     Obligor specific – financial ratios/growth (corporate), demographic information (retail).

Any of the following four modeling techniques can be used to estimate PD:

1.     Pooling– estimated empirically using historical default data of a large universe of obligors.

2.     Statistical– estimated using statistical techniques through macro and obligor-specific data.

3.     Reduced-form– estimated from the observable prices of CDSs, bonds, and equity options.

4.     Structural– estimated using company level information.

1- Statistical Approach-

-         Common variable sources used to estimate the PD of a corporate are financial statements, owner’s data, type of loan, size of loan, and industry of the company.

-         Retail obligors, variable sources could be customer demographics, income statistics, age of loan, and the number of late payments.

Requirements to have effective model-

-         Arranging data and cleaning them to filling for missing data –

·        Removal of data which are obviously erroneous or irrelevant. This should be done with caution: outliers or data which are anomalous.

·        Normalizing or reducing your data means that you eliminate the influence of some well known but uninteresting factor. For example, you may remove the effect of inflation by dividing all the prices with the price index of the date of the purchase.

·        Delta factor is taken instead of the given factor.  This difference models are called ARIMA models.

·         Multicollinearity-

Detection- variance inflation factor (VIF) for Multicollinearity:

where   is the coefficient of determination of a regression of explanator j on all the other explanatory. A tolerance of less than 0.20 or 0.10 and/or a VIF of 5 or 10 and above indicates a Multicollinearity problem.

By removing variable or can be reduced by increasing the sample size of your study. You can also reduce Multicollinearity by centering the variables. You can center variables by computing the mean of each independent variable, and then replacing each value with the difference between it and the mean.

·        Factor Analysis-  Independent variables in regression with high correlation (Multicollinearity).

-         Mathematical transformations on the variables to improve the model fitment -

·        Sq. root transformations moved skewed distributions closer to normality.

·       Transformations such as logarithms can help to stabilize the variance of a time series. Differencing can help stabilize the mean of a time series by removing changes in the level of a time series, and so eliminating trend and seasonality.

·         

 Furthermore, validating the model with out-of-sample data is an important step to have effective model.

The PD for each wholesale obligor or retail segment may not be less than 3 %.

Method – 1

·         By logistic regression to calculate PD and incorporated macroeconomic variables-

Dependent Variable-
 Taking two Non default companies assigning Dependent variable as zero and by taking two default companies data assigning 1 to them.

Default companies, Among nonbanks-
only one institution initially rated 'AAA' has ever defaulted--
- Ally Financial, formerly known as GMAC Financial, a subsidiary of General Motors Corp. S&P downgraded Ally to 'SD' from 'CC'
Among Banks-

The largest banks to be acquired have been the presumed
 Merrill Lynch acquisition by Bank of America,
the Bear Stearns and Washington Mutual acquisitions by JPMorgan Chase, and
the Countrywide Financial acquisition also by Bank of America.

Independent Variables- Historical Data-

·        Profitability ratios- Operating Profit Margin, Interest Coverage Ratio, Return on Equity.

·        Leverage Ratio- Debt/ Equity, Debt Ratio – (Debt / Total Assets),

·        Activity ratio - Accounts Receivable Ratio, Payable Ratio.

·        Liquidity Ratio- Quick- Ratio, Operating Cash Flow Ratio (OCF / Total Debt.

·        Coverage Ratio:-  Debt to Service coverage , Interest service coverage ratio.

Ratios with high correlation with default rates and linear relation should be selected.

·        Macroeconomic variables like (GDP growth, Interest Rates, CPI, and HPI etc.) of current economic conditions.

The time series of an economic factor is not stationary, in other words, it has a varying mean and variance over time. Delta factor is taken instead of the given factor.  This difference models are called ARIMA models.

·        Than after getting Logit for variables mentioned above in different time horizons.

·        Financial ratios that have the highest correlation coefficients (r) with the individual possibility of default were selected.
Used equation = e*L/(1 + e*L) to get PD. PDs from averages of historical default rates
Assigned ratings (0,.5) - Reliable
(.5, 1)- Non Reliable companies.

-         Then, the rating is subsequently mapped to a master scale to derive PDs.

-          For stress testing historical values were taken as in recessionary or mild recession period).

The highest (Max), the least (Min) values and the median (Me) of financial ratios and the individual possibility of default (p) were found. The intervals of values were divided into two parts: from Min to Me and from Me to Max. Every of these two parts were divided into 4 equal intervals. The scores (0-7) were attributed to these 8 intervals. The higher scores indicate the stronger financial condition of companies. So the highest scores were attributed to companies which were characterized by low debt ratio (IK1) and low individual possibility of default (p).

1- Altman Model for Ratings-

= 1.2 * (WC/TA) + 1.4 * (RE/TA) + 3.3 * (EBIT/TA) + 0.6 * (MC/Debt) + Sales/ Total Assets.

Score > 3.1 “Good”

1.8 > Score > 3.1 “Grey Period”.

Score < 1.8 “Bankruptcy”

Analysis of Logistic Regression Output’s-

-         Multiple R - The correlation coefficient between the observed and predicted values. It ranges in value from 0 to 1. A small value indicates that there is little or no linear relationship between the dependent variable and the independent variables.

-         R- Square- of Correlation i.e. square of multiple R.  It ranges from zero to one, with zero indicating that the proposed model does not improve prediction over the mean model and one indicating perfect prediction.

-         Adjusted R- Square - Adjusted R2 is used to compensate for the addition of variables to the model. Adjusted R-squared will decrease as predictors are added if the increase in model fit does not make up for the loss of degrees of freedom. Likewise, it will increase as predictors are added if the increase in model fit is worthwhile.

-         Significance F – Tells us that output is not by chance. Smaller the value greater the probability that output is not by chance. Significance F tells us the probability about the output is a good fit.

-         P-Value - Smaller the value greater the probability that output is not by chance.

-         F – Regression Mean Square / Residual Mean Square.

-         Sum of Squares due to Regression-  is a quantity used in describe how well a regression model, represents the data being modeled. In particular, the explained sum of squares measures how much variation there is in the modeled values and this is compared to the total sum of squares, which Used for t-test and f-test calculations.

-         Residuals- are the difference between the observed values and those predicted by the regression equation.

-         Residual sum of squares- measures how much variation there is in the observed data, and to the, which measures the variation in the modeling errors. A smaller residual sum of squares is ideal.

-         Mean Square – Sum of Square / Degrees of Freedom.

-         Residual Mean Square - . A smaller residual sum of squares is ideal.

2- Structural Approach- Structural models are used to calculate the probability of default for a corporate based on the value of its assets and liabilities.

The most widely used versions are:

-         Merton Model

-         KMV Model (a variant of the Merton’s model)

1-     Merton Model- the basic set-Consider zero coupon bond with notional value L and maturing at T. So, there will be no payments until T, at which point the default decision is taken. Therefore, the PD is the probability that the value of the assets is below the value of liabilities, at time T.

Value of firm- calculated as Present value of operating cash flows (cash generated by operation)-

Cash Flow from Operating Activities = EBIT + Depreciation - Taxes

Discounting Factor- WACC 

Or growth rate (RR * ROE)

d₁= Distance to default,

 K (Default Point) = Liabilities,

 S = Value of firm,

 r = mean of assets (Last five years)

s² = Variance of assets,

 Implied Volatility- value of the volatility of the underlying instrument which, when input in an option pricing model (such as Black–Scholes) will return a theoretical value equal to the current market price of the option

Market value of assets and its volatility needs to be done. This is accomplished through the Black-Scholes option pricing formula, using an iterative approach.

t= time under consideration.

Now as distribution is standard normal, we can calculate probability (in excel – normsdist (-d1))

Market Risk Capital Requirements

Market risk- is defined as the risk of losses in on and off-balance sheet positions arising from movements in market prices.

The risks subject to this requirement are the risks pertaining to interest rate related instruments and equity securities in the trading book and foreign exchange risk and commodities risk throughout the bank on a worldwide net consolidated basis irrespective of where the instruments are booked.

Value at Risk- VaR is defined as a threshold loss value, such that the probability that the loss on the portfolio over the given time horizon exceeds this value.

1.     The Existing Value at Risk based Capital Requirement.

Maximum of -

·        VaR (99.9% of one tailed confidence interval at 10 days VaR).

·        Average of these metrics over the previous 60 business days.

Maximum value is then multiplied by multiplier m.

VaR Calculated as –

Inputs - Portfolio Value, Volatility in currency (from Historical record), Confidence Interval (99.9 %).

Calculating –

Student t distribution – TINV (1 – CI) ^2, Degree of Freedom = Say is x.

Multiplier “m” depends on exceptions (If the quarterly back testing shows that the bank's daily net trading loss exceeded its corresponding daily VaR-based measure, a back testing exception has occurred) while validating the model-

¨     Green Zone :          0-4 exceptions

¨     Yellow zone :          5-9 exceptions

¨     Red zone       :          10 or more exceptions

Minimum of 3- Than addition to this should be between (0, 1). Means maximum of 4.

4 or fewer exceptions = 3.

5 exceptions                 = 3.4

6 exceptions                 = 3.5

VaR = max (VaR of Last 10 days, multiplier * Average VaR of Last 60 Days)

2.     A Stressed Long Term Capital Requirement.

Same as VaR of Basel 11 except-

10-day, 99th %ile, one-tailed confidence interval value-at-risk   measure of the current portfolio, with model inputs calibrated to historical data from a continuous 12-month period of significant financial stress relevant to the bank’s portfolio.

The stressed VaR should be calculated at least weekly.

3.     A Long Term Incremental Risk Charge.

The Long‐Term Incremental Risk Charge (LTIRC) for a bank’s portfolio under the IMA requires estimates of future credit losses arising from specific risks (default and migration) over one‐year capital horizon under the entire range of potential risk factor vector and yield curve sample paths.

·        An one‐year capital horizon at a 99.9% confidence level.

·        In liquidity horizon (  the time to liquidate or hedge a given exposure) be less than the smaller of three months or the contractual maturity of the position is to be that which would prevail in stressed market conditions and cannot

4.     A Comprehensive Risk Capital Requirement.

The Comprehensive Risk Capital Requirement represents an estimate of all price risks of the bank’s portfolio of correlation trading positions over a one‐year time horizon at the 99.9% confidence level, again assuming maintenance of a constant level of risk over the one‐year capital horizon.

 Correlation positions include:

·        A securitization position for which all or substantially all of the value of each of the   underlying exposures is based on the credit quality of a single actively traded company, or

·        A non‐securitization position that hedges a securitization position described above.

Calculation by detailed analysis of the default adjusted performance of each underlying exposure, with special attention to the degree of co‐variation in such performance.

5.     A Specific Risk Charge.

Specific risk is the risk of losses of market risk exposures caused by factors other than broad market movements, including event risk and idiosyncratic risk (assets with zero or no correlation with market). E.x. News that is specific to either one stock or a group of companies, such as the loss of a patent or a major natural disaster, labor problems, management records to adapt changes.

	Maturity	Coupon	Value
A	45 days	12.5%	25
B	9 months	9	-15 (short)

.3% for time band 0- 6 months.

1.125% for 6 – 24 months.

1.8% for 24 or more

- Based on maturity charge on A = .3% of 25

And on B is = 1.125% of -15.

6.     General market risk or Systematic Risk- is defined as changes in the market value of positions resulting from broad market movements, such as changes in the general level of interest rates, equity prices, foreign exchange rates, or commodity prices.

Based on market movements.

Net Open position + vertical Disallowance + Horizontal Disallowance.

Net Open Position – Is calculated on net open position (Long + Short (Short has –ve value) positions) of the zone. As, for 1 to 3 months and for 3 to 6 months and 9 to 12 months.

Modified duration multiply by exposure (Value) of each position than adding all.

Vertical Allowance – Applicable when positions are offset (smallest of mode of amount in time band) with in time bracket.

Because of Basis Risk. Calculated on offset amount.

Value * Modified Duration * 5%.

Vertical disallowance is applicable under 3-6 month time band and 7.3- 9.3 year time band.

Horizontal Allowance –Netting of long short position across time bands. Est Than smallest of mode of amount across time bands.  When positions are offset in time bracket.  Because of imperfect correlation of prices across different maturities. Yield curve risk.

·        Total risk Charge for bonds – Specific Charge + General risk charge.

·        Total Capital Charge for Equity Position – 11.25% (Specific Risk Charge) of Gross Equity Position + 9% (General Risk Charge) of Gross Equity Position.

·        Total Capital Charge for Foreign Exchange & Gold Portfolio – 9% (Specific Risk Charge) of Net Position + 9% (General Risk Charge) of Net Position.

·        There is No specific risk charge on Derivatives Position- General Risk Charge is applied in same manner as for equities, Bonds and Foreign Exchange & gold Portfolios.

Capital Adequacy Directive (Market Risk same as in Basel) is based on the European Union version of Basel. Scaling Factor 1.25 is used in calculation instead of 1.06 as in Basel.

Asset Correlation-

Joint Behavior of asset values of borrowers. Decreasing function of PD but increasing function of Asset size.

Calculated as-

1-    Wholesale (Corporate, Banks and Sovereigns) Asset Correlation-

S = Firm size measured as annual sales and 5m £ S £ 50m

2-    Retail Asset Correlation-

-         Residential Mortgages: Asset Correlation (R) = 0.15

-         Qualifying Revolving Retail Exposures: Asset Correlation (R) = 0.04

-         Other Retail Exposures: 

1.     Estimates of asset correlations were developed through a two-step process.

-          First, economic capital allocations for single-family mortgages were generated using these models of mortgage credit risk calibrated with industry data.

-         Second, an asset-correlation parameter was “reverse engineered” to match as closely as possible the capital charges implied by the Basel II formula with the economic capital allocations derived.

2.     Can be calculated by Regression Analysis-

a)    Put X range and Y range

b)    In the result adjusted R- Square is the correlation.

Stress Testing –

Stress testing is fairly developed in the area of market risk.

Same as VaR of Basel 11 except-

10-day, 99.9th %ile, one-tailed confidence interval value-at-risk   measure of the current portfolio, with model inputs calibrated to historical data from a continuous 12-month period of significant financial stress relevant to the bank’s portfolio

Banks do that

Sensitivity Analysis for Stress Testing-

Discovering which risk factors have the biggest impact on the portfolio risk in terms of the VaR or whatever is used for the evaluation of unexpected losses, is the target and the benefit of sensitivity analysis.

Ø Unexpected loss = VaR – Expected Loss (PD*EAD*LGD).

Ø Unexpected Loss = EAD * {PD * σ^2(LGD) + (LGD) ^2* σ^2(PD)} ^.5

o   σ^2(PD) = PD * (1-PD)

           

Usually done by modeling risk parameters as a function of stressed macroeconomic variables (e.g., GDP, interest rate risk, foreign exchange

Risk, equity price risk, and commodity price risk, unemployment rate, Inflation, CPI, HPI etc.) Corresponding  to different downturn conditions (e.g., mild recession,  severe recession, etc.) e.x.

·        Oil crisis 1973/1974

·        Stock market crash (Black Monday 1987, global bond price crash 1994, Asia 1998).

·        Terrorist attacks (New York 9/11 2001, Madrid 2004) or wars (Gulf war 1990/1991, Iraq war 2003)

·        Currency crisis (Asian 1997, European Exchange Rate Mechanism crisis 1992, Mexican Peso crisis 1994).

·        Emerging market crisis.

·        Failure of LTCM5 and/or Russian default (1998)

 And compare the capital requirements against their current capital level.

Calculate the unexpected loss as the difference between VaR for a confidence level of 99.99% and expected loss.

Other model, the projected figures for the main macroeconomic variables are used to estimate the future income statement and balance sheet of each company and on this basis to calculate individual probabilities of default

(PDs).  Data are then aggregated to estimate the banking sectors

Total loan loss.

Data Validation

Back-testing procedure consists of calculating the number of times that the operational losses fall outside the VaR estimates, these are called exceptions.

Banks have to validate their models on an ongoing basis.

Model should be validated in every 10 days. Is used to calculate multiplication factor.

If the quarterly back testing shows that the bank's daily net trading loss exceeded its corresponding daily VaR-based measure, a back testing exception has occurred.

Model for Data Validation-

1)    Binomial test- Model is accepted if the number of historical defaults k in particular rating category is less than or equal to a critical value c-

2)     Hosmer and Lemeshow or Chi- Square.

Five groups were formed. For every group the average estimated default Probability is calculated and used to derive the expected number of defaults per group. Next, this number is compared with the amount of realized defaults in the respective group. Then, test statistic of groups is used for the estimation sample is chi-square distributed in turn calculating p-value for the rating model.

Calculated as =

P-Value – The closer the p-value is to zero, the worse the estimation is.

o k =  (number of rating classes), n_i = number of companies in rating class i, D_i is the number of defaulted obligors in class i, p_i is the forecasted probability of default for rating class i

o Compare with p-value.

o No critical value of p that could be used to determine whether the estimated PD’s are correct or not

o The closer the p-value is to zero the worse the estimation is .

o First –all else equal, the greater the chi square number, the stronger the relationship between the dependent and independent variable.

o Second –the lower the probability associated with a chi-square statistic, the stronger the relationship between the dependent and independent variable.

o Third –If your probability is .05 or less, then you can generalize from a random sample to a population, and claim the two variables are associated in the population.

Operational Risk –

Operational Risk- Risk of losses due to failed or inadequate process, include legal risk but exclude reputational risk.Approaches-

Business Lines-

1-   Retail brokerage

2-      Corporate finance

3-      Trading & sales

4-   Retail Banking

5-   Commercial Banking

6-   Payment & Settlement

7-   Agency and services

8-   Asset Management

Basic Indicator Approach- Average of total income of last 3 years * Alpha (Currently 15%)

Definitions

Numerator covers tier 1, tier 2, tier and

·        The sum of tier 2 and tier 3 capital allocated for market risk may not exceed 250 % of tier 1 capital. As a result tier 1 capital must equal at least 28.6 % of the measure for market risk.

·        The sum of tier 2 (both allocated and excess) and allocated tier 3 capital may not exceed 100 % of tier 1 capital (both allocated and excess).

·        Term subordinated debt and intermediate-term preferred stock and related surplus included in tier 2 capitals (both allocated and excess) may not exceed 50 % of tier 1 capital (both allocated and excess).

·        Tier 3 capital is subordinated debt that is unsecured, is fully paid up, has an original maturity of at least two years, is not redeemable before maturity.

Ø Capital Adequacy Directive III (CAD III) increased capital requirements for the trading book and complex securitization positions and introduced stressed value-at-risk capital requirements and higher capital requirements for re-securitizations for both in the banking and trading book.

Ø Liquidity coverage ratio- The liquidity coverage ratio (LCR) will require banks to have sufficient high quality liquid assets to withstand a 30-day stressed funding scenario that is specified by supervisors. Will, be introduced in 2015.

(Stock of High Quality Liquid Assets / Net Cash Outflow for 30 days) >=100%.

Ø Net Stable Funding - ratio measures the amount of available longer-term stable sources of funding over the required amount under a one year stress scenario. Will, be introduced in 2018.

(Available Stable Funding / Required Stable Funding) >=100%.

Ø Covered Positions are defined as all on- and off-balance sheet positions in the

Bank’s trading account. Covered positions exclude all positions in the trading account that, in form or substance, act as liquidity facilities that provide liquidity support to asset-backed commercial paper.

Ø  Maturity Mismatch- occurs when the residual maturity of a credit risk mitigant is less than that of the hedged exposure(s). 3 months.

Ø Leverage Ratio –  (Tier 1 / Balance sheet and other off Balance Sheet      Exposures) >= 3%

Ø Free Cash Flow- A measure of financial performance calculated as operating cash flow minus capital expenditures.

Macroeconomic variables

·        Interest Rate at a Particular Tenor on a Specified Yield Curve Denominated in a Given Currency.

·         Underlying Risk Factor for a Dynamic Yield Curve Model for a Specified Yield Curve in a Given Currency.

·        Spot FX Rate Between a Base Currency Denomination and Another Currency Denomination.

·        Equity Market Index with a Specified Market Symbol in a Given Currency Denomination.

·        Black Scholes Implied Volatility for an Option Contract on an Underlying Asset, Rate Index, or Spot FX Rate.

·        The economic value of securitization tranche instruments (securitized assets and synthetic CDOs) as the expected present value of projected future tranche cash flows by applying Monte Carlo pricing methods. The present value of future tranche cash flows is calculated using discount rates obtained from the pricing yield curve applicable to the securitization tranche instrument.

·        Interest Rate Spread on a Specified Category of Bonds in a Specified Currency Denomination.

·        Interest Rate Spread on Bonds with a Specified Credit Rating

·        Macroeconomic Risk Factors such as GDP Indices, CPI, Purchasing Power parity ,Industrial Production index,  Inflation Rates, or Housing Price Indices

·        Performance Risk Factors for Industries, Asset Classes, or Other Market Segments

·        Credit Risk Factors such as Obligor Default Intensity and Recovery Rate

·        Counterparty‐Specific Risk Factors Representing Idiosyncratic Risk.

Financial Statements Screening

·        For each of the key expense components on the income statement, calculate it as a %age of sales for each year.

·        Look for non-recurring or non-operating items.  These are "unusual" expenses not directly related to ongoing operations.

·        Determine whether the company’s dividend policies are supporting their strategies.

·        Examine the cash flow statement, which gives information about the cash inflows and outflows from operations, financing, and investing.

·        Whether fixed assets grown rapidly in one or two years, due to acquisitions or new facilities?  Has the proportion of debt grown rapidly, to reflect a new financing strategy?  

Forecasting Attributes- Cumulative Accuracy Profile

It plots the empirical cumulative distribution of the defaulting debtors ^ CD against the empirical cumulative distribution of all debtors ^ CT. For a given rating category Ri, the %age of all debtors with a rating of Ri or worse is determined. Next, the %age of defaulted debtors with a rating score worse than or equal to Ri. This determines the point A in Fig. 13.1. Completing this exercise for all rating categories of a rating system determines the CAP curve. Therefore, every CAP curve must start in the point (0, 0) and end in the point (1, 1).

Accuracy Ratio = aR / aP,

aR is the area between the CAP curve of the rating model and CAP curve of the random model.

aP is the area between the CAP curve of the perfect forecaster and the CAP curve of the random model.

 


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