P2.T7. Operational & Integrated Management

John Hull, and Financial Institutions

Basel I, II, and Solvency II

Bionic Turtle FRM Video Tutorials

By David Harper, CFA FRM I, II, and Solvency II

• Explain the motivations for introducing the Basel regulations, including key risk exposures addressed and explain the reasons for revisions to Basel regulations over time. • Explain the calculation of risk-weighted assets and the per the original guidelines. • Describe and contrast the major elements—including a description of the covered—of the two options available for the calculation of : Standardized Measurement Method & Internal Models Approach • Calculate VaR and the capital charge using the internal models approach, and explain the guidelines for backtesting VaR. • Describe and contrast the major elements of the three options available for the calculation of : Standardized Approach, Foundation IRB Approach & Advanced IRB Approach

- Continued on next slide -

Page 2 Basel I, II, and Solvency II

• Describe and contract the major elements of the three options available for the calculation of : , standardized approach, and the Advanced Measurement Approach. • Describe the key elements of the three pillars of Basel II: minimum capital requirements, supervisory review, and market discipline. • Define in the context of Basel II and calculate where appropriate: Probability of (PD), (LGD), (EAD) & Worst- case • Differentiate between solvency capital requirements (SCR) and minimum capital requirements (MCR) in the Solvency II framework, and describe the repercussions to an insurance company for breaching the SCR and MCR. • Compare the standardized approach and the internal models approach for calculating the SCR in Solvency II.

Page 3 Explain the motivations for introducing the Basel regulations, including key risk exposures addressed and explain the reasons for revisions to Basel regulations over time.

The primary motivation for regulation is to ensure that a bank holds enough capital for the risks it assumes. It is impossible to eliminate the possibility of a bank failure, but governments want to maximize confidence in the banking system by minimizing the default probability of .

Deposit Insurance: Governments provide deposit insurance programs to protect depositors. Without deposit insurance, banks who take excessive risks relative to their capital base would find it difficult to attract deposits. Governments do not want to create a deposit insurance program that results in banks taking more risks. So, deposit insurance is accompanied by regulation concerned with capital requirements.

Page 4 Explain the motivations for introducing the Basel regulations, including key risk exposures addressed and explain the reasons for revisions to Basel regulations over time (continued)

Systemic risk is the risk that a failure by a large bank will lead to failures by other large banks and a collapse of the financial system.

When a bank or other large financial institution experiences financial difficulties, governments have a dilemma. • If they allow the institution to fail, they create a • But if they “bail out” the institution, they March 2008: Fed begins engender moral Sep 2008: Lehman Brothers

During the 2007-08 crisis, many large financial institutions were bailed out, rather than being allowed to fail, because governments were concerned about systemic risk. But the U.S. government allowed Lehman Brothers to fail in September 2008 to make it clear to the market that bailouts for large financial institutions were not automatic. Hull notes this decision to let Lehman Brothers fail arguably made the credit crisis worse.

Page 5 Explain the motivations for introducing the Basel regulations, including key risk exposures addressed and explain the reasons for revisions to Basel regulations over time (continued)

The Basel Committee formed in 1974 met regularly in Basel, , under the patronage of the Bank for International Settlements. The first major result of these meetings was a document titled “International Convergence of Capital Measurement and Capital Standards”, and referred to as the 1988 BIS Accord; aka, “Basel I.”

Before the formation of Basel I guidelines, banks maintained a pre-set minimum ratio of capital to their total assets, but there was lack of standardization in defining the capital as well as the banks’ assets. Each country had its own definitions for deriving the capital-assets ratio which gave undue advantages to the banks belonging to the countries with liberal guidelines on the ratio. The situation worsened with the increase in international exposure of the banks.

Page 6 Explain the motivations for introducing the Basel regulations, including key risk exposures addressed and explain the reasons for revisions to Basel regulations over time (continued)

Huge exposures created by loans from international banks to less developed countries (LDCs), and the accounting games used to cover those exposures including debt rescheduling raised questions about the adequacy of capital levels.

• Banks started booking various unregulated (over-the-counter) derivative deals such as interest rate swaps, currency swaps, and foreign exchange options giving rise to complexity in bank transactions and exposing them to substantial credit risk.

• Banks started booking over-the-counter derivatives as “off-balance sheet” transactions which lessened the pressure on banks’ balance sheet as the assets in their balance sheet remained unaffected due to the derivative contracts. As a result, banks required to keep lesser capital vis-à-vis their assets while ignoring the off-balance sheet transactions.

Page 7 Explain the motivations for introducing the Basel regulations, including key risk exposures addressed and explain the reasons for revisions to Basel regulations over time (continued)

In June 1999, the Basel Committee proposed new rules that have become known as Basel II which were revised in January 2001 and April 2003. A final set of rules agreed to by all members of the Basel Committee was published in June 2004. This was updated in November 2005. Implementation of the rules began in 2007 after a Quantitative Impact Studies (QIS).

Page 8 Explain the calculation of risk-weighted assets and the capital requirement per the original Basel I guidelines.

The Basel I Accord

This accord was the first outcome of the efforts of Basel committee to design uniform banking risk management standards to ensure capital adequacy in banks. The accord was readily accepted for implementation by all 12 members.

The accord put forth 2 mandatory conditions that banks had to necessarily fulfill: • Banks to keep capital equal to at least 8.0% of the risk-weighted assets. • Cooke Ratio as a primary regulatory requirement.

Page 9 Explain the calculation of risk-weighted assets and the capital requirement per the original Basel I guidelines (continued)

Cooke Ratio (= 8.0%)

The Cooke ratio was used to compute minimum capital that a bank was required to keep vis-à-vis the risk associated to its on and off-balance sheet assets called risk- weighted assets (RWA), a measure of the bank’s total credit exposure. Let us understand the derivation of risk-weighted assets of a bank in detail on the next slide.

Page 10 Explain the calculation of risk-weighted assets and the capital requirement per the original Basel I guidelines (continued)

Risk Weighted Assets for On-Balance Sheet Items

In Basel I accord, for each type of on-balance sheet asset, a specific risk-weight was assigned signifying the risk associated with the asset type. The table below shows a snapshot of such assignment from the accord:

Risk Weights for On-Balance-Sheet Items

Risk Weight (%) Asset Category 0 Cash, gold bullion, claims on OECD governments such as Treasury bonds or insured residential mortgages 20 Claims on (loans to) OECD banks and OECD public sector entities such as securities issued by U.S. government agencies or claims on municipalities 50 Uninsured residential mortgage loans 100 All other claims such as corporate bonds and less- developed country debt, claims on non-OECD banks

Page 11 Explain the calculation of risk-weighted assets and the capital requirement per the original Basel I guidelines (continued)

The total risk weight for a bank’s on-balance sheet assets portfolio is simply the sum of risk-weighted assets, as shown in the formula below:

Total on-balance sheet RWA = ∑

th where is the principal amount of the item and is the corresponding risk weight.

Example: The assets of a bank consist of $100.0 million of corporate loans, $10.0 million of OECD government bonds, and $50.0 million of residential mortgages. Compute the total risk-weighted assets.

Total RWA = 100% x 100 + 0% x 10 + 50% x 50 = 125 or $125 million.

Page 12 Explain the calculation of risk-weighted assets and the capital requirement per the original Basel I guidelines (continued)

Risk Weighted Assets for Off-balance Sheet Items

The off-balance sheet items include bankers’ acceptances, guarantees, and loan commitments. For deriving RWA they are converted into their credit equivalent amount. Conversion into credit equivalent amount leads to derivation of a loan principal amount having same credit risk.

For non-derivative items such as trade financing products, note issuance facilities etc., a specific was defined for each category. The factor is denoted in terms of percentage capped at 100% or 1. The credit equivalent amount could be derived by multiplying the off-balance sheet asset amount with the conversion factor, i.e.

Credit equivalent (non-derivative) = Off-balance sheet asset × Conversion Factor (%)

Page 13 Explain the calculation of risk-weighted assets and the capital requirement per the original Basel I guidelines (continued)

For over-the-counter derivative such as swaps, options or forward contracts, the credit equivalent amount is calculated as:

Credit equivalent (derivatives) = , + where is the current value of the derivative to the bank, is an add-on factor, and is the principal amount of the derivative contract.

Page 14 Explain the calculation of risk-weighted assets and the capital requirement per the original Basel I guidelines (continued)

The factor , 0 signifies the current exposure of the bank. If the contract remains profitable for the bank, then will carry some positive value and the bank is set to lose if the counterparty defaults. If the contract is profitable for the counterparty then will be negative for the bank and bank will not lose anything in the event of default, in which case it would be a ‘no profit no loss’ situation for the bank.

The add-on amount, , is used to capture future or potential exposure. The add-on factor, depends upon the remaining maturity & type of contract, as shown below in terms of percentage (%) of principal.

Page 15 Explain the calculation of risk-weighted assets and the capital requirement per the original Basel I guidelines (continued)

Add-On Factors as a Percent of Principal for Derivatives

Remaining Foreign Precious Maturity Interest Exchange Metals Other (yr) Rate rate & Gold Equity (except Gold) Commodities <1 0.0 1.0 6.0 7.0 10.0 1 to 5 0.5 5.0 8.0 7.0 12.0 <5 1.5 7.5 10.0 8.0 15.0

Example: A bank has entered in to a $100.0 million interest rate swap with a remaining life of four years. The current value of the swap is $2.0 million. Compute the credit equivalent amount of the swap contract and the RWA if: a) the counterparty is a corporation, b) the counterparty is an OECD bank. In this case, we use an add-on factor of 0.5% for the Interest Rate swap contract with remaining maturity (of 4 years) falling in the 1-5 years’ bucket. Now the credit equivalent amount can be computed as: CE: 0.5% × 100 + 2.0 = 0.5 + 2.0 = $2.5 million.

Page 16 Explain the calculation of risk-weighted assets and the capital requirement per the original Basel I guidelines (continued)

Corporation: The risk weights are similar to those in table “Risk Weights for On- Balance-Sheet Items”, except the risk weight for a corporation is 0.50 rather than 1.0. The RWA for a corporation is: 50% x 2.5 = $1.25 Million

OECD Bank: Referring to the same table again, the RWA when the counterparty is an OECD bank will be: 20% x 2.5 = $0.5 Million

Now, the total (credit) risk-weighted assets for a bank with N on-balance-sheet items and M off-balance-sheet items is ∗ Total (Credit) RWA = ∑ + ∑ ∗ where, and respectively are the risk weight of the counterparty and credit equivalent amount of jth off-balance-sheet item.

Page 17 Explain the calculation of risk-weighted assets and the capital requirement per the original Basel I guidelines (continued)

Minimum Capital Requirement The Basel I accord also defined and standardized the capital structure of the bank where a bank’s capital was divided into Tier 1 & . Basel I also prescribed the minimum capital to be kept by banks as 8% of its total risk-weighted assets.

Tier 1 Capital: Consists of bank’s equity and non-cumulative perpetual preferred stock. The goodwill of bank is deducted from its equity. • Noncumulative perpetual preferred stock is preferred stock lasting forever where there is a predetermined dividend rate. Unpaid dividends do not cumulate.

Tier 2 Capital: Also called supplementary capital, the main constituents of Tier 2 capital are cumulative perpetual preferred stock, certain types of 99-year debenture issues, and subordinated debt with an original life of more than five years. • In cumulative preferred stock, unpaid dividends cumulate. Any backlog of dividends must be paid before dividends are paid on the common stock.

Page 18 Explain the calculation of risk-weighted assets and the capital requirement per the original Basel I guidelines (continued)

The equity capital absorbs losses incurred by the bank.

• If equity capital is greater than losses, a bank can continue as a going concern.

• If equity capital is less than losses, the bank is insolvent. In this latter case, Tier 2 or other capital items are expected to help banks in meeting their liabilities to the depositors in the event of bank fall down. • If a bank is wound up after its Tier I capital has been used up, losses should be borne first by the Tier 2 capital and, only if that is insufficient, by depositors.

Since is the high-quality capital when compared with Tier 2 capital, the Basel I accord prescribes that minimum 50% of the total capital of the bank (i.e. 4% of total risk- weighted assets) should comprise of Tier 1 capital. The accord restricts the minimum common equity as 2% of the total risk-weighted assets to be included in capital structure.

Page 19 Describe and contrast the major elements—including a description of the risks covered—of the two options available for the calculation of market risk: Standardised Measurement Method & Internal Models Approach

In 1996, there were a few amendments made in the Basel accord commonly known as 1996 Amendments. The amendments were implemented in the banks by 1998, and are referred to as “BIS 98”. The amendment involves keeping capital for the market risks associated with trading activities.

The committee realized the requirement to be able to compute risk for the trading book of the banks which comprises of • debt and equity traded securities and • positions in commodities and foreign exchange.

Page 20 Describe and contrast the major elements—including a description of the risks covered—of the two options available for the calculation of market risk: Standardised Measurement Method & Internal Models Approach (continued)

The 1996 amendment prescribed two methods for calculating market risk of a bank:

1. Standardized Approach: The standardized approach assigned capital separately to each of debt securities, equity securities, , commodities risk, and options. The approach does not consider the correlation between the above-mentioned market instruments.

Page 21 Describe and contrast the major elements—including a description of the risks covered—of the two options available for the calculation of market risk: Standardised Measurement Method & Internal Models Approach (continued)

2. Internal Models Approach: The internal models approach is a more sophisticated method of measuring market risk. The banks can use their own models to compute market risk capital charge. The process involves computation of value-at-risk for a given portfolio to eventually arrive at capital requirement by using the formula provided in 1996 amendment. The VaR model calculates the losses expected to be incurred by the bank over a horizon of 10-days with 99% confidence level. The market risk capital charge is derived as:

, × +

where is a multiplicative factor SRC is a specific risk charge

is the previous day’s

is the average value-at-risk over the last 60 days.

The minimum value for as given in the amendment is 3. However, regulators can generally or specifically for a certain bank prescribe value higher than 3.

Page 22 Describe and contrast the major elements—including a description of the risks covered—of the two options available for the calculation of market risk: Standardised Measurement Method & Internal Models Approach (continued)

Diversification Benefits: Standardized approach does not provide any benefit of diversification for a bank because it computes market risk charge for each instrument separately. Most large banks preferred to use the internal model-based approach because it better reflected the benefits of diversification and led to lower capital requirements.

Specific Risk Charge (SRC): VaR model calculates the impact of macroeconomic factors such as interest rates, exchange rates, stock indices, and commodity prices. It does not include the factors ‘specific’ to the instrument/counterparty.

Page 23 Describe and contrast the major elements—including a description of the risks covered—of the two options available for the calculation of market risk: Standardised Measurement Method & Internal Models Approach (continued)

Consider a corporate issued by a company, which offers two associates risks:

1. , as rise in prevailing interest rates can have negative impact of bond’s yield (value of bond will fall down) 2. Credit risk, risk that the bond issuer will not be able to fulfill its liability to the bond buyers.

In this case, interest rate risk is estimated with the help of VaR model whereas the credit risk is computed as specific Risk.

The 1996 amendment provides standardized & internal models approach to compute SRC. In SRC internal model, the value-at-risk for specific risks is computed at 99% confidence level for a 10-day horizon, along with the minimum value of 4 for (multiplicative factor) to arrive at specific risk charge. In order to deter banks from taking advantage by using internal models, as per the 1996 amendment, the resultant capital (SRC) must be at least 50% of the capital given by the standardized approach.

Page 24 Calculate VaR and the capital charge using the internal models approach, and explain the guidelines for backtesting VaR.

Computation of Market Risk Capital Charge using Internal Models (VaR)

Consider a market risk exposure with the following values: =400, = 350 10-day, 99% VaR for SRC = $150. The market risk capital charge for the exposure at =3 will be:

, × + = , × + = $,

The market risk capital charge when multiplied by 12.5 (1/8%) gives market RWA. Hence, the total capital requirement for banks as per 1996 amendment is:

= % × ( + )

Page 25 Calculate VaR and the capital charge using the internal models approach, and explain the guidelines for backtesting VaR (continued)

Back-Testing VaR Models Most of the banks following internal-models approach calculate one-day 99% VaR and scale it to 10 day 99% VaR by 10. The BIS Amendment requires banks to back-test their VaR models over the previous 250 day’s observations.

Back-testing is performed by using the bank’s current procedure for estimating VaR for each of the most recent 250 days. If the actual loss that occurred on a day is greater than the VaR level calculated for the day, an “exception” is recorded. Calculations are typically carried out: a. including changes that were made to the portfolio on the day being considered and b. assuming that no changes were made to the portfolio on the day being considered. (Regulators pay most attention to the first set of calculations.)

Page 26 Calculate VaR and the capital charge using the internal models approach, and explain the guidelines for backtesting VaR (continued)

Based on the number of exceptions observed during the previous 250 days, the value of is derived, refer the table below:

Number of Exceptions Value of Less than 5 3.00 5 3.40 6 3.50 7 3.65 8 3.75 9 3.85 ≥ 4.00

The 1996 amendment reserves the right to apply higher multipliers with the supervisors if the reason for the exceptions is identified as a deficiency in the VaR model being used. If changes in the bank’s positions during the day result in exceptions, the higher multiplier should be considered, but does not have to be used. When the only reason that is identified is bad luck, no guidance is provided for the supervisor.

Page 27 Describe and contrast the major elements of the three options available for the calculation of credit risk: Standardised Approach, Foundation IRB Approach & Advanced IRB Approach

In Basel II Accord, there are 3 approaches prescribed for banks to compute their credit risk:

1. Standardized Approach – Banks that are not sophisticated and do not have the technical expertise and resources to build their own models adopt the standardized approach. There are many similarities between Basel II standardized approach & Basel I approach for computing bank’s credit risk. However, Basel II comprises of several new rules as well. In Basel II standardized approach, the types of customer for assigning risk weight, underwent changes as shown in the table below:

Rating A+ BBB+ BB+ B+ Customer Type AAA to to to to to AA- A- BBB- BB- B- Below B- Unrated Country* 0 20 50 100 100 150 100

Banks** 20 50 50 100 100 150 50

Corporations 20 50 100 100 150 150 100

Page 28 Describe and contrast the major elements of the three options available for the calculation of credit risk: Standardised Approach, Foundation IRB Approach & Advanced IRB Approach (continued)

Apart from the risk weights covered in the table above, there are more provisions defined in the Basel II standardized approach for assigning risk weight to Banks. • As an alternative to the above risk weighting, supervisory banks can assign risk weight on the basis of the rating of the country of incorporation of the bank  Risk weight assigned to the bank will be 20% if the country of incorporation has a rating between AAA and AA–, 50% if it is between A+ and A–, 100% if it is between BBB+ and B–, 150% if it is below B–, and 100% if it is unrated.

• While assigning risk weights to bank customers as per the table above, banks can select lower risk weight for the claims with an original maturity less than three months such that the risk weights are 20% if the rating is between AAA+ and BBB– , 50% if it is between BB+ and B–, 150% if it is below B–, and 20% if it is unrated. • For exposures to individual customers i.e. in retail banking a general risk weight of 75% is applied. However, if the loan is secured either by residential mortgage or by commercial real estate, a fixed risk weight of 35 & 100% is applied, respectively.

Page 29 Describe and contrast the major elements of the three options available for the calculation of credit risk: Standardised Approach, Foundation IRB Approach & Advanced IRB Approach (continued)

Example: Consider the assets of a bank consist of $100.0 million of loans to corporations rated A, $10.0 million of government bonds rated AAA, and $50.0 million of residential mortgages. Calculate the total risk-weighted assets under Basel II standardized approach.

Solution: Assigning risk weight to each exposure, for example, if customer type is Corporation and rating is A, risk weight is 50% or 0.5. Similarly, risk weight to government bonds and residential mortgage loan will be 0 and 35%.

= . ∗ + . ∗ + . ∗ = . $.

This compares with $125 million under Basel I.

Page 30 Describe and contrast the major elements of the three options available for the calculation of credit risk: Standardised Approach, Foundation IRB Approach & Advanced IRB Approach (continued)

Adjustments for collateral

Collateral is a financial or non-financial asset pledged by the borrower against the loan which can be used by the bank for mitigating the risk arising in the event of default.

The bank can reduce or nullify its losses with the proceeds of the collateral. A few of the Basel eligible collaterals are – Cash, Gold, Equity, Bonds and Mutual Funds. Pledging a collateral helps the customer borrow from bank at a lower interest rate and the bank is benefitted with lower RWA computation which reduces the regulatory capital requirement.

Page 31 Describe and contrast the major elements of the three options available for the calculation of credit risk: Standardised Approach, Foundation IRB Approach & Advanced IRB Approach (continued)

There are two ways banks can adjust risk weights for collateral. The first is termed the simple approach and is similar to an approach used in Basel I.

• Under the simple approach, the risk weight of the counterparty is replaced by the risk weight of the collateral for the part of the exposure covered by the collateral. (The exposure is calculated after netting.) • For any exposure not covered by the collateral, the risk weight of the counterparty is used. The minimum level for the risk weight applied to the collateral is 20%. • A requirement is that the collateral must be revalued at least every six months and must be pledged for at least the life of the exposure.

Page 32 Describe and contrast the major elements of the three options available for the calculation of credit risk: Standardised Approach, Foundation IRB Approach & Advanced IRB Approach (continued)

Basel II covers another approach for risk mitigation called comprehensive approach. • Banks adjust the size of their exposure upward to allow for possible increases in the exposure and adjust the value of the collateral downward to allow for possible decreases in the value of the collateral. Thus, the revaluation formula in its simple terms for exposure can be written as:

= × + = × −

• A new exposure equal to the excess of the adjusted exposure over the adjusted value of the collateral is calculated and the counterparty’s risk weight is applied to this exposure. • The adjustments applied to the exposure and the collateral can be calculated using rules specified in Basel II or, with regulatory approval, using a bank’s internal models. • Where netting arrangements apply, exposures and collateral are separately netted and the adjustments made are weighted averages.

Page 33 Describe and contrast the major elements of the three options available for the calculation of credit risk: Standardised Approach, Foundation IRB Approach & Advanced IRB Approach (continued) Example: Suppose that an $80.0 million exposure to a particular counterparty is secured by collateral worth $70.0 million. The collateral consists of bonds issued by an A-rated company. The counterparty has a rating of B+. The risk weight for the counterparty is 150% and the risk weight for the collateral is 50%. Calculate the risk-weighted assets applicable to the exposure using the simple and comprehensive approach.

Page 34 Describe and contrast the major elements of the three options available for the calculation of credit risk: Standardised Approach, Foundation IRB Approach & Advanced IRB Approach (continued) Simple approach: Exposure amount to which counterparty risk weight will be applied is exposure amount less collateral amount i.e. 80-70 = $10 Million. • Risk weight to be applied to the balance exposure amount ($10 M) = 150% • Risk weight to be applied to the collateral amount ($70 M) = 50% Hence, = . × + . × = $

Note the effect of collateral in reducing a bank’s risk: Had there been no collateral pledged, the entire exposure amount would have been risk weighted at 150%, leading to the risk- weighted amount as 1.5 x 80 = $120 Million. Thus, collateral helps in substantially bringing down the risk as well as capital requirement (which is 8% of the RWA) of the bank.

Page 35 Describe and contrast the major elements of the three options available for the calculation of credit risk: Standardised Approach, Foundation IRB Approach & Advanced IRB Approach (continued) Comprehensive approach: Assume the adjustment to exposure to allow for possible future increases in the exposure is +10% and the adjustment to the collateral to allow for possible future decreases in its value is –15%. Calculate the new exposure as per comprehensive approach and RWA if the risk-weight to be applied to the exposure is 150%. = × + . = , = × − . = . = − . = $.

A risk weight of 150% is applied to this exposure to give risk adjusted assets:

= . × . = $.

Page 36 Describe and contrast the major elements of the three options available for the calculation of credit risk: Standardised Approach, Foundation IRB Approach & Advanced IRB Approach (continued)

Internal Ratings Basel (IRB) Approach Let us first understand the underlying model upon which the IRB approach is defined. The figure below illustrates the loss probability density function. The vertical axis represents probability of losses whereas the horizontal axis represents the magnitude of losses.

Loss Probability Density Function and the Capital Required by a Financial Institution

The capital requirement is derived on the basis of Value-at-Risk(VaR) calculated using the one-year time horizon at a 99.9% confidence level as shown in the Figure. The VaR computed comprises of expected and unexpected losses.

Page 37 Describe and contrast the major elements of the three options available for the calculation of credit risk: Standardised Approach, Foundation IRB Approach & Advanced IRB Approach (continued)

• The expected losses are usually covered by the way a financial institution prices its products. For example, the interest charged on a loan is designed to recover expected loan losses. • The unexpected losses cannot be predicted, which compels regulators to prescribe banks to keep minimum regulatory capital for covering these losses. • The capital required by the bank is VaR minus expected losses. The Value at Risk is computed using one-factor Gaussian copula model of time to default.

Page 38 Describe and contrast the major elements of the three options available for the calculation of credit risk: Standardised Approach, Foundation IRB Approach & Advanced IRB Approach (continued)

Worst Case Probability of Default

Suppose one of the customers of bank has one-year probability of default as PDi and the copula correlation between each pair of the (obligors) customers is . Note that is denoted as R in Basel II accord. Then the formula for Worst Case Probability of

Default, WCDRi is:

+ (. ) = −

The formula derives worst case probability of default at 99.9% confidence level over a horizon of one year of the customer i. When the correlation is zero, WCDR = PD because there is no default correlation and the percentage of loans defaulting can be expected to be the same in all years. As increases, WCDR increases.

Page 39 Describe and contrast the major elements of the three options available for the calculation of credit risk: Standardised Approach, Foundation IRB Approach & Advanced IRB Approach (continued)

For a large portfolio with multiple types of exposures and similar correlation, the 1 year, 99.9% VaR is computed as:

× × where and , are respectively Exposure at Default and Loss Given Default for the customer i.

Exposure at Default, is the amount owed by the customer at the time of default and is inclusive of interest amount as well.

Page 40 Describe and contrast the major elements of the three options available for the calculation of credit risk: Standardised Approach, Foundation IRB Approach & Advanced IRB Approach (continued)

Loss Given Default, is the percentage of EAD that will be lost in the event of default. For example, an LGD of 30% signifies that the bank is set to lose 30% of the EAD amount, should the obligor default.

Formula for computing expected losses from default against each customer:

= × ×

The total expected loss for the bank will be a linear summation for all the exposures i.e.

× ×

Finally, the capital required is derived as the excess of 99.9% worst- case loss over the expected loss; i.e.,

× × ( − )

Page 41 Describe and contrast the major elements of the three options available for the calculation of credit risk: Standardised Approach, Foundation IRB Approach & Advanced IRB Approach (continued)

Let us understand the methodology of computing RWAs before laying down the definitions of the two approaches under IRB: Foundation IRB and Advanced IRB.

RWA computation for claims on Corporate, Sovereign & Bank Exposures

For exposures against corporate, sovereign & banks, Basel II guidelines define the linkage between PD & correlation as shown below:

− (− × ) − (− × ) = . + . − − (−) − (−)

Page 42 Describe and contrast the major elements of the three options available for the calculation of credit risk: Standardised Approach, Foundation IRB Approach & Advanced IRB Approach (continued)

Since −50 is a negligibly small amount, the above formula in its simpler and shorter form can be re-written as:

= . ( + ×)

PD is inversely proportional to hence the correlation decreases with increase in PD which is evident from the fact that, when a company becomes less creditworthy its probability of default increases, irrespective of the prevailing market conditions.

Page 43 Describe and contrast the major elements of the three options available for the calculation of credit risk: Standardised Approach, Foundation IRB Approach & Advanced IRB Approach (continued)

Now, for the aforementioned customers, the capital requirement is computed as:

× × ( − ) × where MA is the maturity adjustment factor and is derived as:

+ ( − . ) × = − (. × ) where = 0.11852 − 0.05478 × ln () , M is the remaining maturity of the exposure.

Page 44 Describe and contrast the major elements of the three options available for the calculation of credit risk: Standardised Approach, Foundation IRB Approach & Advanced IRB Approach (continued)

Finally, to compute RWA under IRB approach, the expression for capital requirement calculation is multiplied by 12.5 (inverse of 8%), i.e.

= . × × × ( − ) ×

Example: Suppose that the assets of a bank consist of $100.0 million of loans to A-rated corporations. The PD for the corporations is estimated as 0.1% and the LGD is 60%. The average maturity is 2.5 years for the corporate loans. Compute RWA for the loan if WCDR is 3.4%.

Page 45 Describe and contrast the major elements of the three options available for the calculation of credit risk: Standardised Approach, Foundation IRB Approach & Advanced IRB Approach (continued)

In the problem statement EAD is given as $100M and residual maturity, M is 2.5 year. Let us first calculate Maturity Adjustment, starting with derivation of b:

= . − . × (. ) = .

+ . − . × . = = . − . × .

= . × × . × . − . × . = . $.

The RWA computation expressions are similar for both foundation and advanced IRB approach. Therefore, understand the differences between both the approaches.

Page 46 Describe and contrast the major elements of the three options available for the calculation of credit risk: Standardised Approach, Foundation IRB Approach & Advanced IRB Approach (continued)

Foundation Internal Ratings Based Approach (FIRB) In FIRB approach, banks rely upon the BASEL prescribed guidelines for using/estimating LGD, EAD & M but, can have their own models to derive PD. • Under FIRB, the estimated value of PD cannot be allowed to fall below 0.03% i.e. even if the internally derived PD is lesser than 0.03%, banks will have to use 0.03% value for RWA computation. • The floor for PD value is applicable for banks & corporate customers (retail as well) only and no such flooring is required in case of claims on sovereigns. • For senior claims, banks can use LGD value of 45% and for subordinated claims an LGD of 75% is applied. A senior claim is the claim in which bank has first right on the assets on the obligor in case of default whereas a subordinated claim is settled only after all the senior claims are fulfilled.

Page 47 Describe and contrast the major elements of the three options available for the calculation of credit risk: Standardised Approach, Foundation IRB Approach & Advanced IRB Approach (continued)

Foundation Internal Ratings Based Approach (FIRB) (continued) • For credit risk mitigation, instead of reducing exposure amount by the value of collateral as done in standardized approach, the value of LGD is adjusted (reduced) to discount for the effect of collateral. The LGD is reduced by the ratio of the adjusted value of the collateral to the adjusted value of the exposure by using the comprehensive approach as prescribed in standardized approach for credit risk.

• The calculation of EAD is similar to standardized approach and the value of M is standardized at 2.5. For conversion of off balance sheet assets into their credit equivalent, banks can use the same credit conversion factors as used in standardized approach.

Page 48 Describe and contrast the major elements of the three options available for the calculation of credit risk: Standardised Approach, Foundation IRB Approach & Advanced IRB Approach (continued)

Advanced Internal Ratings Based Approach (AIRB) Under AIRB approach, banks can build their own internal models to estimate all the risk parameters i.e. PD, LGD, EAD and M for corporate, sovereign & bank exposures. • Similar to FIRB, the flooring of PD value at 0.03% for banks & corporate exposures is applicable under AIRB as well.

• While estimating the LGD from internal models, the two main factors that dictate its severity are seniority of the claim and the existence & coverage of collateral.

• While adopting AIRB, banks can also estimate their own credit conversion factors to compute EAD for off balance sheet assets. • Note that only AIRB approach can be used for RWA computation of retail exposure with a slightly tweaked expression of computing the value of correlation, . The rest of the formulas for RWA computation are similar to those for other customer types.

Page 49 Describe and contrast the major elements of the three options available for the calculation of credit risk: Standardised Approach, Foundation IRB Approach & Advanced IRB Approach (continued)

RWA computation for claims on Retail Exposures The model underlying the calculation of capital for retail exposures is similar to that underlying the calculation of corporate, sovereign, and banking exposures. However, the Foundation IRB and Advanced IRB approaches are merged and all banks using the IRB approach provide their own estimates of PD, EAD, and LGD. There is no maturity adjustment, MA.

Page 50 Describe and contrast the major elements of the three options available for the calculation of credit risk: Standardised Approach, Foundation IRB Approach & Advanced IRB Approach (continued)

RWA computation for claims on Retail Exposures (continued)

• The capital requirement is therefore × × ( − )

• The risk-weighted assets are 12.5 × × × ( − )

• WCDR is calculated the same way shown earlier. For residential mortgages, is set equal to 0.15. For qualifying revolving exposures, is set equal to 0.04. For all other retail exposures, a relationship between and PD is specified for the calculation of WCDR as:

1 − exp (−35 × ) 1 − exp (−35 × ) = 0.03 + 0.24 1 − 1 − exp (−35) 1 − exp (−35)

• Since exp −35 is a very small number, this formula reduces to:

= 0.03 + 0.13×

Page 51 Describe and contrast the major elements of the three options available for the calculation of credit risk: Standardised Approach, Foundation IRB Approach & Advanced IRB Approach (continued)

Example Consider that the assets of a bank consist of $50 million of residential mortgages where the PD is 0.005 and the LGD is 20%.

In this case, i.e., for residential mortgages, ρ=0.15

. + . . = = . − .

The risk-weighted assets are 12.5 × 50 × 0.2 × (0.067−0.005) = 7.8 or $7.8 million. This compares with $25 million under Basel I and $17.5 million under the Standardized Approach of Basel II.

Page 52 Describe and contract the major elements of the three options available for the calculation of operational risk: basic indicator approach, standardized approach, and the Advanced Measurement Approach.

Basel II defines operational risk as, “the risk of direct or indirect loss resulting from inadequate or failed internal processes, people and systems or from external events”.

On one hand Basel II helps banks in (reducing) easing their credit risk capital requirement whereas on the other hand, it brings up the total capital requirement at the same levels of Basel I by mandating banks to keep regulatory capital against operational risk as well.

Page 53 Describe and contract the major elements of the three options available for the calculation of operational risk: basic indicator approach, standardized approach, and the Advanced Measurement Approach (continued)

Basic Indicator Approach (BIA) – This is the simplest approach for computing operational risk capital requirement. It is computed by multiplying a constant factor of 0.15 with the bank’s average annual gross income over the last three years, as shown in the formula below:

∑ − = . ×

Here denotes gross income of bank. Gross income is defined as net interest income plus noninterest income where net interest income is the excess of income earned on loans over interest paid on deposits and other instruments that are used to fund the loans.

Page 54 Describe and contract the major elements of the three options available for the calculation of operational risk: basic indicator approach, standardized approach, and the Advanced Measurement Approach (continued)

Standardized Approach – This approach is similar to the BIA in the manner of multiplying the gross income with a pre-defined factor. However, instead of considering bank’s gross income, the approach divides a bank’s business into 8 business lines namely, , trading and sales, retail banking, commercial banking, payment and settlement, agency services, , and retail brokerage.

For each business line a Beta Business Line Factor specific value called beta Corporate finance 18.0% factors is prescribed as shown Trading and sales 18.0% in the table here: Retail banking 12.0% Commercial banking 15.0% Payment and settlement 18.0% Agency services 15.0% Asset management 12.0% Retail brokerage 12.0%

Page 55 Describe and contract the major elements of the three options available for the calculation of operational risk: basic indicator approach, standardized approach, and the Advanced Measurement Approach (continued)

The average gross income over the last three years for each business line is multiplied by its corresponding “beta factor” and the resultant values for all 8 business lines are summed to determine the total capital required under standardized approach.

= − × , /

KSA = Capital charge under the Standardized Approach

GI1-8 = Annual gross income in a given year, as defined above in the Basic Indicator Approach, for each of the eight business lines.

Β1-8 = Beta factor for each business line.

In any given year, negative capital charges in any business line may offset positive capital charges in other business lines without limit.

Page 56 Describe and contract the major elements of the three options available for the calculation of operational risk: basic indicator approach, standardized approach, and the Advanced Measurement Approach (continued)

Advanced Measurement Approach (AMA) – Under this approach, the bank uses its own internal models to calculate the operational risk loss that it is 99.9% certain will not be exceeded in one year. Similar to the way credit risk capital is calculated in the IRB approach, operational risk capital is set equal to this loss minus the expected loss.

Page 57 Describe and contract the major elements of the three options available for the calculation of operational risk: basic indicator approach, standardized approach, and the Advanced Measurement Approach (continued)

Calculation of VaR for Operational Risk under AMA: The conditions that should be fulfilled by banks to adopt AMA comprises of the ones mentioned under standardized approach along with the conditions mentioned below.

• The bank must be able to estimate unexpected losses based on an analysis of relevant internal and external data, and scenario analyses.

• The bank’s system must be capable of allocating for operational risk across business lines in a way that creates incentives for the business lines to improve operational risk management.

Page 58 Describe the key elements of the three pillars of Basel II: minimum capital requirements, supervisory review, and market discipline.

Although the 1998 Basel I Accord was a significant step in standardization of regulatory capital computation worldwide, there were multiple areas of improvements identified which led to the formation of Basel II accord in June, 2004. • Basel I accord was unable to differentiate between corporate customers on the basis of their credit rating i.e. corporate with AAA rating and B rating, both were assigned a same risk weight of 100%. • The Basel 1 accord failed in identifying and utilizing the default correlations while computing RWA.

Page 59 Describe the key elements of the three pillars of Basel II: minimum capital requirements, supervisory review, and market discipline.(continued)

The first proposal consisting of new rules was presented by the Basel committee in June 1999 and was called as Basel II. After multiple revisions to the accord in 2001 & 2003, the Basel II accord was agreed by all the committee members leading to publishing of the accord in June 2004. The accord went under further revisions in 2005 and its actual implementation started in 2007 only.

Page 60 Describe the key elements of the three pillars of Basel II: minimum capital requirements, supervisory review, and market discipline.(continued)

Pillar 1- Minimum Capital Requirements: This pillar covers guidelines for banks to compute risk weighted assets & subsequently the minimum required capital.

For computation of credit risk, the magnitude of RWA largely depends upon the credit ratings of counterparties. The market risk computation remained unchanged since 1996 amendments. Operational risk is a new addition in the Basel II accord. The minimum capital requirement at 8% of total risk-weighted assets also remained unchanged, i.e.

= 0.08 × + +

When the capital requirement for a particular risk is calculated directly rather than in a way involving RWAs, it is multiplied by 12.5(1/ 8%) to convert it into an RWA- equivalent.

Page 61 Describe the key elements of the three pillars of Basel II: minimum capital requirements, supervisory review, and market discipline.(continued)

Pillar 2 - Supervisory Review: Pillar 2 aims at defining the guidelines for the regulators (supervisory banks) to carry out supervisory review process.

• The regulators must ensure consistency in the computation approaches followed by the banks. The role of regulators goes beyond just ensuring that the banks are holding the minimum capital required under Basel II. • The regulators are expected to encourage banks to develop and use better risk management techniques and to keep evaluating these techniques on a timely basis to ensure that they remain relevant and accurate in the prevailing conditions. • Pillar 2 evaluates risks that not covered under Pillar 1; e.g., concentration risks.

Page 62 Describe the key elements of the three pillars of Basel II: minimum capital requirements, supervisory review, and market discipline.(continued)

Below are the four key principles of supervisory review as specified in the Pillar II: • Banks should have a process for assessing their overall capital adequacy in relation to their risk profile and a strategy for maintaining their capital levels. • Supervisors should review and evaluate banks’ internal capital adequacy assessments and strategies, as well as their ability to monitor and ensure compliance with regulatory capital ratios. Supervisors should take appropriate supervisory action if they are not satisfied with the result of this process. • Supervisors should expect banks to operate above the minimum regulatory capital and should have the ability to require banks to hold capital in excess of this minimum.

Page 63 Describe the key elements of the three pillars of Basel II: minimum capital requirements, supervisory review, and market discipline.(continued)

• Supervisors should seek to intervene at an early stage to prevent capital from falling below the minimum levels required to support the risk characteristics of a particular bank and should require rapid corrective action if capital is not maintained or restored.

 The Basel Committee suggests that regulators should particularly monitor the interest rate risk in the banking book, credit risk, and operational risk. Key issues in credit risk are stress tests used, default definitions used, credit risk concentration, and the risks associated with the use of collateral, guarantees, and credit derivatives.

 The Basel Committee stresses that there should be transparency and accountability in the procedures used by bank supervisors. This is important when a supervisor exercises discretion in the procedures used or sets capital requirements above the minimum specified in Basel II.

Page 64 Describe the key elements of the three pillars of Basel II: minimum capital requirements, supervisory review, and market discipline.(continued)

Pillar 3 - Market Discipline: The third pillar, market discipline, requires banks to disclose more information about the way that they allocate capital and the risks that they take. Such information is revealed in the form of reports. Regulatory banks can prescribe their own reporting formats as part of market disclosures. The idea here is that banks will be subjected to added pressure to make sound risk management decisions if shareholders and potential shareholders have more information about those decisions.

Page 65 Describe the key elements of the three pillars of Basel II: minimum capital requirements, supervisory review, and market discipline.(continued)

A few of the items that are specifically required to be disclosed by banks worldwide are:

• The entities in the banking group to which Basel II is applied and adjustments made for entities to which it is not applied • The terms and conditions of the main features of all capital instruments

• A list of the instruments constituting Tier 1 capital and the amount of capital provided by each item • The total amount of Tier 2 capital. • Capital requirements for credit, market, and operational risk • Other general information on the risks to which a bank is exposed and the assessment methods used by the bank for different categories of risk. • The structure of the risk management function and how it operates.

Page 66 Differentiate between solvency capital requirements (SCR) and minimum capital requirements (MCR) in the Solvency II framework, and describe the repercussions to an insurance company for breaching the SCR and MCR.

Solvency II, a regulatory framework in the European Union is for insurance companies prescribing minimum capital levels for investment risk, underwriting risk, and operational risk.

• Solvency I only focused upon capital calculation for underwriting risks whereas Solvency II has taken a broader view by including investment risk and operational risk as well for the purpose of computing minimum capital requirement.

• Solvency II is similar to Basel II accord in many ways. It comprises of three pillars, each serving the same purpose as in Basel II.  Pillar 1 covers definitions and computation of minimum capital requirement.  Pillar 2 provides guidelines for supervisory review process.  Pillar 3 concerns market disclosure by the insurance companies.

Page 67 Differentiate between solvency capital requirements (SCR) and minimum capital requirements (MCR) in the Solvency II framework, and describe the repercussions to an insurance company for breaching the SCR and MCR (continued)

Capital Structure under Solvency II: There are three types of capital in Solvency II. 1. Tier 1 capital consists of equity capital, retained earnings, and other equivalent funding sources. 2. Tier 2 capital consists of liabilities that are subordinated to policyholders and satisfy certain criteria concerning their availability in wind-down scenarios. 3. Tier 3 capital consists of liabilities that are subordinated to policyholders and do not satisfy these criteria.

Page 68 Differentiate between solvency capital requirements (SCR) and minimum capital requirements (MCR) in the Solvency II framework, and describe the repercussions to an insurance company for breaching the SCR and MCR (continued)

Solvency II specifies the below two types of capital requirements.

1. Minimum Capital Requirement (MCR): It is the bare minimum capital that an insurance company must keep with itself to carry out its business. If the capital at any point in time falls below the MCR then the supervisor can ask the company to stop engaging in any new business.

Apart from imposing the restrictions on taking new business, a supervisor can liquidate the company or transfer the company’s business (insurance policies) to another organization. The MCR will typically be between 25% and 45% of the SCR. The MCR can be derived in multiple ways, such as setting MCR as a percent of SCR or calculating MCR in the same way as SCR but with a lower confidence level than 99.5% which is used in case of SCR.

Page 69 Differentiate between solvency capital requirements (SCR) and minimum capital requirements (MCR) in the Solvency II framework, and describe the repercussions to an insurance company for breaching the SCR and MCR (continued)

2. Solvency Capital Requirement (SCR): The SCR involves a capital charge for investment risk, underwriting risk, and operational risk. Investment risk is subdivided into market risk and credit risk. Underwriting risk is subdivided into risk arising from life insurance, non-life insurance, and health insurance. Capital should be adequate to deal with large adverse events. If the capital of an insurance company falls below the prescribed SCR level then the company should, at minimum, deliver to the supervisor a plan to restore capital to above the SCR level. The supervisor may require the insurance company to take measures to correct the situation.

Page 70 Compare the standardized approach and the internal models approach for calculating the SCR in Solvency II.

In Solvency II, there are two approaches prescribed for computing the SCR i.e. the Standardized Approach & the Internal Models Approach. • The internal models approach involves a VaR calculation with a one-year time horizon and a 99.5% confidence limit. (The confidence level is therefore less than the 99.9% confidence level used in Pillar 1 of Basel II.) Longer time horizons with lower confidence levels are allowed when the protection provided is considered equivalent.

• The internal models are required to satisfy three tests.  The first is a statistical quality test. This is a test of the soundness of the data and methodology used in calculating VaR.  The second is a calibration test. This is a test of whether risks have been assessed in accordance with a common SCR target criterion.  The third is a use test. This is a test of whether the model is genuinely relevant to and used by risk managers.

Page 71 The End

P2.T7. Operational & Integrated Risk Management

John Hull, Risk Management and Financial Institutions

Basel I, II, and Solvency II