Introduction

• The first “regulations” were the result of  financial firms coming together to share resources in  the event of runs. The Bank of England, for example, was originally a private-sector entity that  would provide support to other banks. In addition, early clearinghouses were partly  arrangements for mutual support. Specifically, clearinghouse members shared financial  statements with each other and had rights of inspection, and so monitoring and enforcement of  solvency was a part of the arrangements. However, this was done privately. Such private  arrangements had several limitations –
  • a) If a panic was big enough, no entity without the power to print money would have enough  resources to support the financial system. As a result, government controlled central banks  gradually replaced clearinghouses and private banks as lenders of last resort.
  • b) Governments learned that financial crises imposed large costs on the economy as a whole  (e.g., crises were often followed by depressions). So they began making attempts to ensure  that financial institutions were solvent and liquid to survive plausible levels of distress.
  • c)Fraud was common, but even when a failure was not associated with fraud, customers  complained of unfairness and of the difficulty in monitoring a financial institution’s safety  and soundness.
  • d) International trade blossomed in the 1960s and 1970s, and as multinational corporations became more numerous, foreign exchange flows and capital flows grew ever larger. Hence,  globalization was another trigger of regulation, and especially of international coordination  of regulation, as it gave rise to the following issues –
    • Large financial firms, especially international banks, became interlinked, so a failure of  one would cause problems in many countries, not just its home country.
    • Second, banks and regulators became concerned about competitive (dis)advantages  flowing from differences in capital requirements across nations.
    • Third, technical arrangements in clearing and settlement proved to be important. For  example, when Herstatt Bank failed in the summer of 1974, differences in the required  delivery times for currencies across countries and time zones caused large amounts of  foreign exchange transactions to fail to clear. In turn, this raised concerns about a  potential collapse of the global financial system.
    • The Basel Committee on Banking Supervision (BCBS) – initially named the Committee on  Banking Regulations and Supervisory Practices – was established by the central bank Governors  of the G10 countries at the end of 1974 after serious disturbances in international currency and banking markets (particularly the failure of Bankhaus Herstatt in West Germany).

The Basel Accord: Basel I Variant

• The Basel Committee met regularly in Basel, Switzerland, under the patronage of the Bank for  International Settlements (BIS). In the late 1980s, the BCBS developed a specification for  capital (solvency) regulation. First published in December 1987, it was formally agreed in July  1988 fully implemented by the end of  1992. This accord, which came to be known as Basel I,  was initially agreed upon by the members of the BCBS (roughly, the G10 nations). By the early  2000s, however, it became a de facto global minimum capital standard. It is important to note  that Basel I has no legal standing in and of itself. Rather, nations haven chosen to incorporate  its standards through domestic law and regulation.

• Two events motivated creation of Basel I –
  • Growth of  cross-border finance continued after Herstatt’s failure the G10 nations had a  common interest in ensuring that banks had enough equity to absorb large losses.
  • Minimum levels of required capital varied significantly across nations, creating a perception  that banks headquartered in countries with low minimums had a competitive advantage. So  members of the BCBS decided to develop a global minimum standard to “level the playing  field” and avoid a race to the bottom. Hence, the Basel Accord was about ensuring safety  and soundness, along with maneuvering for perceived competitive advantage.

Capital and Risk Weighted Assests

• The central elements of Basel I are a risk-based capital ratio, a minimum level of this ratio, and  definitions of the numerator and denominator.

• Given the perception that minimums specified in terms of leverage ratios would disadvantage  banks with low-risk portfolios and advantage those with high-risk portfolios, the BCBS decided  on a risk-based capital ratio (i.e., a ratio of capital to risk-weighted assets (RWA)) instead.  Moreover, these assets included not only assets on the balance sheet according to accounting  conventions (e.g., loans or securities), but also off-balance-sheet exposures (e.g., loan  commitments) and derivative exposures. Though crude by modern standards, these risk-based  ratios represented a major innovation at the time.

• The accord laid down that minimum ratio of bank’s assets to its capital had to be less than 20,  which implied capital to total assets had to be greater than 1/20 or 5%. This was similar to the  requirements in many countries before 1988.

• The key innovation in the 1988 Accord was the Cooke Ratio. It is the ratio of the capital  to risk-adjusted assets. The Cooke Ratio considers credit risk exposures that are both on-balance-sheet and off-balance-sheet. It is based on the bank’s total risk-weighted assets (also  known as risk-weighted amount). This is a measure of the bank’s total credit exposure.
• Basel I required consolidated banking organizations to maintain

and

𝑇𝑜𝑡𝑎𝑙 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 is the sum of  𝑇𝑖𝑒𝑟 1 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 and 𝑇𝑖𝑒𝑟 2 𝐶𝑎𝑝𝑖𝑡𝑎𝑙. By design, Tier 2 capital  may comprise no more than half of total capital. To the extent that Tier 1 capital exceeded 4  percent of risk-weighted assets, the excess could be included with Tier 2 capital to satisfy the  second (8%) requirement.

• Under Basel I, Tier 1 capital consists of common equity and disclosed reserves (i.e., retained  earnings plus some types of minority interest in subsidiaries) minus goodwill. Later frameworks include a limited amount of non-cumulative perpetual preferred stock.

• Tier 2 capital consists of
  • loan loss reserves not already allocated to impairment of particular assets;
  • undisclosed reserves (including some revaluation reserves); and
  • hybrid instruments (i.e., unsecured, subordinated, not redeemable at the investor’s behest,  on which payment default would not precipitate bankruptcy or resolution, and on which  interest or dividend payments could be deferred.)

• Though never expressed by the BCBS, two assumptions were implicit in these definitions.
  • First, preservation of solvency was the job of Tier 1 capital, whereas Tier 2 capital would  provide resources for recapitalization of an entity in resolution and reduce the impact of  failures on depositors.
  • Second, although general loan loss reserves were often viewed as covering losses that are  likely already embedded in the entity’s portfolio but that have not yet occurred, they were  not counted as loss-absorbing capacity that could preserve solvency.
• Credit risk exposures can be divided into three categories:
  • Those arising from on-balance sheet assets (excluding derivatives).
  • Those arising for off-balance sheet items (excluding derivatives).
  • Those arising from over-the-counter derivatives.

1)  Risk Weighted Assets for On-balance sheet Items

In Basel I accord, each on-balance-sheet asset is assigned a risk weight reflecting its credit risk.  To  make  the  ratio  risk-sensitive,  the  on-balance-sheet  amount  of  each  type  of  asset  is multiplied by the percentage weight according to the risk it poses. The 𝑅𝑊𝐴 is the sum of such products

where 𝑤_i is the risk weight and 𝐴_i is the size of the asset.

In the absence of other adjustments, the maximum amount that a position could contribute to 𝑅𝑊𝐴 was the book value of its assets (since the maximum risk weight was 100 percent).

A sample of the risk weights specified in the Accord is shown in this table

Risk Weight	Asset Category
0%	Cash, gold bullion, claims on OECD governments such as bonds issued by the central government; other instruments with a full guarantee from an OECD government
20%	Claims on OECD banks and on OECD public sector entities, such as claims on municipalities or on Fannie Mae and Freddie Mac
50%	Uninsured residential mortgages
100%	All other exposures, such as corporate or consumer loans, less developed country debt, claims on non-OECD banks

EXAMPLE –

The assets of a bank consist of $100 million of corporate loans, $10 million of OECD  government bonds, and $50 million of residential mortgages. So based on the weights given in  the above table, the total of the risk weighted assets.

2) Risk Weighted Assets for Off-balance sheet Items

Though the concept of 𝑅𝑊𝐴 was natural for traditional balance-sheet exposures, banking  organizations also had many off-balance-sheet exposures. These include bankers’ acceptances,  guarantees, and loan commitments. A credit equivalent amount (𝐶𝐸𝐴)is calculated by applying a  conversion factor to the principal amount of the instrument. Instruments that from a credit  perspective are considered to be similar to loans, such as bankers’ acceptances, have a  conversion factor of 100%. Others, such as note issuance facilities (where a bank agrees that a  company can issue short-term paper on pre-agreed terms in the future), have lower conversion  factors. This table gives the credit conversion factors for traditional off-balance-sheet exposures.

Credit Conversion Factor	Off-balance-sheet Category
100%	Guarantees on loans and bonds, bankers acceptances, and equivalents
50%	Warrantees and standby letters of credit related to transactions
20%	Loan commitments with original maturity greater than or equal to one year
0%	Loan commitments with original maturity less than one year

• Traditional off-balance-sheet exposures were converted to 𝐶𝐸𝐴 by multiplying by one of  the  credit conversion factors shown in the previous table. The risk weight was then determined by  the nature of the counterparty. For example, a $100 million five-year loan commitment to an  OECD municipality would first be converted to a $20 million credit equivalent, and then be  assigned a 20 percent risk weight. Thus, its contribution to RWA would be only $4 million.

3) Risk Weighted Assets for over-the-counter derivatives

With respect to derivatives, Basel I offered authorities in each nation a choice between two  methods of computing a credit equivalent amount

a)Current Exposure Method

b)Original Exposure Method (only for interest rate and foreign exchange contracts)

In the current exposure method, the credit equivalent amount is calculated as

𝑚𝑎𝑥 𝑉, 0  + 𝐷𝐿

where 𝑉 is the current value of the derivative to the bank,

𝐷 is an add-on factor, and

𝐿 is the principal amount.

The first term in the equation is the current exposure. If  the counterparty defaults today and 𝑉  is positive, the contract is an asset to the bank and the bank is liable to lose 𝑉. If  the  counterparty defaults today and 𝑉 is negative, the contract is an asset to the counterparty and  there will be neither a gain nor a loss to the bank. The bank’s exposure is therefore 𝑚𝑎𝑥 𝑉, 0 .  The add-on amount, 𝐷𝐿, is an allowance for the possibility the exposure increasing in the  future. The riskier the derivative is, the higher the add-on factor 𝐷 will be.

Examples of the add-on factor, 𝐷, are shown in this table.

Remaining Maturity (yr)	Interest Rate	Exchange Rate and Gold	Equity	Precious Metals Except Gold	Other 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

life of four years. The current value of the swap is $2.0 million. Based on the previous table,  for a interest rate swap having life between 1 and 5 years, the add-on amount is 0.5% of the  principal so that the credit equivalent amount is $2.0 million plus $0.5 million or $2.5 million

If the interest rate swap is with a corporation, the risk-weighted assets are 2.5 × 0.5 or $1.25 million. If it is with an OECD bank, the risk-weighted assets are 2.5 × 0.2 or $0.5 million

In the original exposure method, nations could ignore the current market value of the contract  and choose whether to use the original or remaining maturity. For this method a sample of add-  on factors (D) as a percentage of principal is given in this table

Remaining Maturity (years)	Interest Rate	Foreign Exchange
< 1	0.5	1.0
1 to 2	1.0	5.0
> 2	1.0 + 1.0 × INT(M-1)	5.0 + 3.0 × INT(M-1)
M is the maturity and INT is the closest integer function

Capital And Risk Weighted Assets

EXAMPLE  – The derivatives book of  an international bank contains $300 million of  notional value of interest rate swaps with $100 million each having remaining maturity of 0.5, 1.5 and 2.5 years. Their market value is $30 million. The book also has $300 million of  foreign exchange swaps with a similar maturity profile and a market value of -$10 million.  Assuming all counterparties are private corporations, the risk weight is 100 percent.

•Putting all this together, the total risk-weighted assets for a bank with 𝑁 on-balance-sheet items and 𝑀 off-balance-sheet items is

where,

𝐿_i is the principal of the 𝑖^th on-balance-sheet asset

𝑤_i is the risk weight for the asset

𝐶_j is the credit equivalent amount for the 𝑗^th derivative or other off-balance-sheet item

𝑤^∗ is the risk weight of the counterparty for this 𝑗^th item

Netting

• Participants in the over-the-counter derivatives market have traditionally signed an International  Swaps and Derivatives Association (𝐼𝑆𝐷𝐴) master agreement covering their derivatives trades.  The word netting refers to a clause in the master agreement, which states that in the event of a  default all transactions are considered as a single transaction. Effectively, this means that, if a  company defaults on one transaction that is covered by the master agreement, it must default  on all transactions covered by the master agreement. Choices in these agreements permit  bilateral transactions with positive and negative values to offset one another. For example,  Bank A might enter an interest rate swap to buy protection from Bank B against an increase in  interest rates, and later enter another swap with an identical notional amount with Bank B to  sell protection. If rates did not move in the interim between these two agreements, their  combined impact on Bank A’s (and Bank B’s) net exposure and portfolio value is zero.

• Netting can substantially reduce credit risk. Consider a bank having three swap transactions  outstanding with a particular counterparty which are worth +$24 million, —$17 million, and + $8 million to the bank. Suppose that the counterparty experiences financial difficulties and  defaults on its outstanding obligations. To the counterparty the three transactions have values of —$24 million, +$17 million, and —$8 million, respectively. Without netting,the counterparty would default on the first transaction, keep the second transaction, and  default on the third transaction. Assuming no recovery, the loss to the bank would be $32 (=  24 + 8) million. With netting, the counterparty is required to default on the  second  transaction as well. The loss to the bank is then $15 (= 24 — 17 + 8) million.
• More generally, suppose that a financial institution has a portfolio of 𝑁 derivatives outstanding  with a particular counterparty and that the current value of the 𝑖^th derivative is 𝑉_i.
  • 1)Without netting, the financial institution’s exposure in the event of a default today is

• • 2)  With netting, the financial institution’s exposure in the event of a default today is

Without netting, the exposure can be considered as the payoff from a portfolio of options.  With netting, the exposure can be considered as the payoff from an option on a portfolio.

• The 1988 Basel Accord did not take netting into account in setting capital requirements. The  credit equivalent amount for a portfolio of derivatives with a counterparty under the Accord was

By 1995, netting had been successfully tested in many courts. The 1988 Accord was modified  to allow banks to reduce their 𝐶𝐸𝐴s when enforceable bilateral netting agreements were in place. The first step was to calculate the net replacement ratio, 𝑁𝑅𝑅. This is the ratio of the  current exposure with netting to the current exposure without netting.

The net replacement ratio is an average across all positions; although add-on factors and the  impact of netting may differ across types of derivatives, the impact of the latter is ignored. The credit equivalent amount was modified to

EXAMPLE –

• Suppose a bank has a portfolio of five derivatives with two counterparties, as described in the  following table

Counterparty	Type	Maturity	Notional	Market value	Add-on factor
1	Interest rate	2	100	-5	0.5%
1	Interest rate	3	100	0	0.5%
1	Foreign exch.	2	200	10	5%
2	Equity option	6	100	0	10%
2	Wheat option	0.5	300	-10	10%

Trading Activities And Market Risk

• While market risk (i.e., changes in market value of trading book assets) is the primary risk for the  trading book, it was not captured by the requirements described previously. The 1996  Amendment outlined two methods for measuring the capital charge for market risk –
  • 1)The standardized approach assigned capital separately to each of debt securities, equity  securities, foreign exchange risk, commodities risk, and options. No  account was  taken of correlations between different types of instruments.
  • 2)The more sophisticated banks with well-established risk management functions were  allowed to use an “internal model-based approach” for setting market risk capital. This  involved calculating a VaR measure and converting it into a capital requirement using a  specified formula. Most large banks preferred to use internal model-based approach because  it better reflected the benefits of diversification leading to lower capital requirements.

Under both approaches, capital charges were calculated separately for specific risk (SR) and  general market risk (MR) for each of the five categories. These were summed and multiplied by 12.5 so that the usual multipliers on risk weighted assets could also be applied to them.

Total capital for trading assets

• The value-at-risk measure used in the internal model-based approach was calculated with a 10-  day time horizon and a 99% confidence level, usually using a scaled one-day 𝑉𝑎𝑅 multiplied by underroot-10 . Correlations within a category of position were considered by the internal model, whereas  adjustments for correlations across categories were allowed at the discretion of the national  supervisor. Thus, market risk was given by

𝑀𝑅 = max(𝑉𝑎𝑅_t–1, 𝑚_c  × 𝑉𝑎𝑅_avg)

where

𝑉𝑎𝑅_avg was the average 𝑉𝑎𝑅 over the past 60 days and

𝑚_c is a multiplicative factor with a minimum value of 3. Higher values may be chosen by  regulators for a particular bank if tests reveal inadequacies in the bank’s value-at-risk model.  Given a multiplier of  3, the second term was usually larger than the 10-day 𝑉𝑎𝑅 computed for  the preceding business day (i.e., 𝑡— 1).

• Capital for specific risk, which was required for fixed income, equity instruments, and derivatives,  could be determined using either the standardized approach or the bank’s internal models.

In the latter case, the approach was similar to that for market risk, but the multiplier was 4  rather than 3 and capital for specific risk could not be less than half of capital calculated using the standardized approach.

• The 1996 Amendment created a new class of capital (i.e., Tier 3 capital), composed mainly of  unsecured subordinated debt with an original maturity of at least two years, that could be used to  meet part of the market risk capital requirement. However, only about 70 percent of the market  risk capital requirements could be satisfied with Tier 3 capital.

• The total capital a bank was required to keep after the implementation of the 1996 Amendment  was the sum of
  • a)credit risk capital equal to 8% of the risk-weighted assets (𝑅𝑊𝐴), and
  • b)market risk capital

Thus, the total capital required for credit and market risk is given by

𝑇𝑜𝑡𝑎𝑙 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 = 0.08 × (𝑐𝑟𝑒𝑑𝑖𝑡 𝑟𝑖𝑠𝑘 𝑅𝑊𝐴 + 𝑚𝑎𝑟𝑘𝑒𝑡 𝑟𝑖𝑠𝑘 𝑅𝑊𝐴)

where

𝑅𝑊𝐴 for market risk capital was defined as 12.5 ×  𝑚𝑎𝑥  𝑉𝑎𝑅_t–1, 𝑚_c  × 𝑉𝑎𝑅_avg

𝑅𝑊𝐴 for market risk capital was defined as sum of off-balance-sheet and on-balance-  sheet 𝑅𝑊𝐴s

•The  BIS  Amendment  requires  the  one-day 99% 𝑉𝑎𝑅 that a bank calculates to be back-tested  over  the  previous  250  days.  This involves 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 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 like to see both calculations.

Number of Exceptions	Value of mc
Less than 5	3
5	3.4
6	3.5
7	3.65
8	3.75
9	3.85
≥ 10	4

The Basel Accord: Basel II Variant

• The 1988 Basel Accord improved the way capital requirements were determined, but it does  have significant weaknesses.
  • Under the Accord, all loans by a bank to a corporation have a risk weight of  100% and  require the same amount of capital.
  • A loan to a corporation with a 𝐴𝐴𝐴 credit rating is treated in the same way as one to a  corporation with a 𝐵 credit rating.
  • Also, in Basel I there was no model of default correlation.

• Moreover, banking crises in the Nordic countries had demonstrated that systemic problems  could occur even in well capitalized banking systems. Meanwhile, there had been several technical  advances in market and credit risk measurement and management since 1987, signaling a  potential for more precise risk weighting and vastly imp roved risk management at all levels of  banking organizations.

• As a reaction to such concerns, In June 1999, the Basel Committee proposed new rules that  have become known as Basel II. These were revised in January 2001 and April 2003. A  number of Quantitative Impact Studies (𝑄𝐼𝑆𝑠) were carried out prior to the implementation of the new rules to test them by calculating the amount of  capital that would be required if  the rules had been in place. 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 further 𝑄𝐼𝑆.
• While retaining much of Basel I, Basel II contained four significant innovations:
  • Risk weight formulas for credit risk based on modern credit risk management concepts  and banks’ internal risk measures;
  • Required capital for operational risk, in addition to credit risk and market risk.
  • In addition to minimum capital requirements (Pillar 1), Basel II included specific  requirements for supervision related to capital and risk management (Pillar 2) and required  public disclosures (Pillar 3).
  • Repeated use of  Quantitative Impact Studies (QIS) to finetune the design of  the accord.  In each QIS, banks contributed detailed data which was then analyzed by supervisors.
• In the US, the Basel II capital requirements applied to “internationally active” banks. They  were not applicable for small regional banks which are regulated under Basel IA, which is similar to Basel I. In Europe, all banks, large or small, were regulated under Basel II.  Furthermore, the European Union required the Basel II rules to be applied to securities  companies as well as banks.

• As discussed, the Basel II is based on three “pillars”:
  • 1) Minimum Capital Requirements
  • 2) Supervisory Review
  • 3) Market Discipline
• In Pillar 1, the minimum capital requirement for credit risk in the banking book is calculated  in a new way that reflects the credit risk of counterparties. The capital requirement for market  risk remains unchanged from the 1996 Amendment and there is a new capital charge for  operational risk. Total Capital is calculated as

𝑇𝑜𝑡𝑎𝑙 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 = 0.08 × (𝑐𝑟𝑒𝑑𝑖𝑡 𝑟𝑖𝑠𝑘 𝑅𝑊𝐴 + 𝑚𝑎𝑟𝑘𝑒𝑡 𝑟𝑖𝑠𝑘 𝑅𝑊𝐴 + 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑜𝑛𝑎𝑙 𝑟𝑖𝑠𝑘 𝑅𝑊𝐴)

• Pillar 2 is concerned with the supervisory review process.
  • It covers both quantitative and qualitative aspects of the ways risk is managed within a bank. Banks are expected to keep more than the minimum regulatory capital to allow for  fluctuations in capital requirements and possible issues in raising capital at short notice.
  • Regulators in different countries are allowed some discretion in how rules are applied, but  overall consistency in the application of the rules is required.
  • Pillar 2 places more emphasis on early intervention when problems arise.
  • Supervisors have to encourage banks to develop and use better  risk management  techniques and to evaluate those techniques. They should evaluate risks that  are not  covered by Pillar 1 (e.g., concentration risks) and enter into an active dialogue with banks  when deficiencies are identified.

• Pillar 3 required more qualitative and quantitative disclosures, in the hope that pressure from  market  participants  would  help  improve  banks’  practices.  Qualitative  disclosures  included  aspects of  corporate structure, applicability of  the accord and approaches used, accounting  practices, and other matters. Meanwhile, quantitative disclosures included many characteristics  of a bank’s capital, exposures, and risk measures. 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.

Credit Risk Capital Under Basel II

• For credit risk, Basel II specified three approaches:
  • 1) The Standardized Approach
  • 2) ^{The Internal Ratings Based (𝐼𝑅𝐵) Approach –} 
    • a) The Foundation 𝐼𝑅𝐵 Approach
    • b) The Advanced 𝐼𝑅𝐵 Approach  However, the United States decided that only the 𝐼𝑅𝐵 approach can be used.

1)  The Standardized Approach

This approach is used by banks that are not sufficiently sophisticated (in the eyes of the regulators)  to use the internal ratings approaches. The standardized approach is similar to Basel I except for the calculation of risk weights. Some of the new rules here are summarized in this table

	AAA to AA-	A+ to A-	BBB+ to BBB-	BB+ to BB-	B+ to 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

• Some important observations are:
  • 𝑂𝐸𝐶𝐷 status of a bank or a country is no longer considered important under Basel II. In  Basel I, 𝑂𝐸𝐶𝐷 banks were implicitly assumed to be lesser credit risks than corporations. An 𝑂𝐸𝐶𝐷 bank attracted a risk weight of 20% while a corporation attracted a risk weight of 100%. Basel II treats banks and corporations much more equitably.
  • The risk weight for a country (sovereign) exposure ranges from 0% to 150% and the risk  weight for an exposure to another bank or a corporation ranges from 20% to 150%.
  • For a country, corporation, or bank that wants to borrow money, it may be better to have  no credit rating at all than a very poor credit rating. (Usually a company gets a credit rating  when it issues a publicly traded bond.)
  • Supervisors are allowed to apply lower risk weights (20% rather than 50%, 50% rather than 100%, and 100% rather than 150%) when exposures are to the country in which the  bank is incorporated or to that country’s central bank.
  • The risk weight for mortgages in the Basel II standardized approach was 35% and that for  other retail loans was 75%. For claims on banks, the rules are somewhat complicated.  Instead of using the risk weights in the previous table, national supervisors can choose to  base capital requirements on the rating of the country in which the bank is incorporated.

EXAMPLE –

• Suppose that the assets of  a bank consist of  $100 million of  loans to corporations rated 𝐴, $10 million of government bonds rated 𝐴𝐴𝐴, and $50 million of residential mortgages.

Under Basel I, it was $125 million, as seen earlier. Under standardized  approach of Basel II, it is $67.5 million, as calculated in the video.

• Adjustments for Collateral – There are two ways banks can adjust risk weights for collateral.
  • a) The first is termed the simple approach and is similar to an approach used in Basel I.
  • b) The second is termed the comprehensive approach. Banks have a choice as to which approach is used in the banking book, but they must use the  comprehensive approach to calculate capital for counterparty credit risk in the trading book.
    • a) 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.
    • b) Under the 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, (The adjustments depend on  the volatility of the exposure and the collateral.) 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.

EXAMPLE –

• Suppose that an $80 million exposure to a counterparty is secured by collateral worth $70  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%.

2)The IRB Approach

• The  model  underlying  the  𝐼𝑅𝐵 approach is shown in this figure.  Regulators base the capital  requirement on the value at risk  calculated using a one-year time  horizon and a 99.9% confidence  level. They recognize that expected  losses are usually covered by the  way a financial institution prices its  products. (For example, the interest  charged by a bank on a loan is  designed to recover expected loan  losses.) The capital required is therefore the value at risk minus the  expected loss.

• The value at risk is calculated using the one-factor Gaussian copula model of time to  default. Assume that a bank has a large number of obligors and the 𝑖^th obliger has a one-year probability of default equal to 𝑃𝐷_i. The copula correlation between each pair of  obligors is 𝜌. Then

where

𝑊𝐶𝐷𝑅_i (or 𝐷𝑅99.9_i ) denotes the “worst-case default rate” defined so that the bank is 99.9%

certain it will not be exceeded next year for the ith counterparty.

The one-year 99.9% 𝑉𝑎𝑅 is approximately

where

𝐸𝐴𝐷_i is the exposure at default of the 𝑖^th counterparty, and

𝐿𝐺𝐷_i is the loss given default for the 𝑖^th counterparty.

• Using the Basel Committee’s choices of a one-year time horizon for credit losses and a desire that capital be enough to absorb losses up to the 99.9th percentile of the credit loss  distribution, the formula is:

𝐶𝑎𝑝𝑖𝑡𝑎𝑙  = ∑  𝐸𝐴𝐷_i  × 𝐿𝐺𝐷_i  × 𝐷𝑅99.9_i   – 𝐸𝐿

where

𝐶𝑎𝑝𝑖𝑡𝑎𝑙 is expressed in dollars

• This table shows how 𝑊𝐶𝐷𝑅 depends on 𝑃𝐷 and 𝜌 in the Gaussian copula model. When the  correlation 𝜌 is zero, 𝑊𝐶𝐷𝑅 = 𝑃𝐷 because in that case there is no default correlation and the  percentage of loans defaulting can be expected to be the same in all years.

As 𝜌 increases,

𝑊𝐶𝐷𝑅 increases.

	PD = 0.1%	PD = 0.5%	PD = 1%	PD = 1.5%	PD = 2.0%
ρ = 0.0	0.1%	0.5%	1.0%	1.5%	2.0%
ρ = 0.2	2.8%	9.1%	14.6%	18.9%	22.6%
ρ = 0.4	7.1%	21.1%	31.6%	39.0%	44.9%
ρ = 0.6	13.5%	38.7%	54.2%	63.8%	70.5%
ρ = 0.8	23.3%	66.3%	83.6%	90.8%	94.4%

• Because the Basel Committee did not view loan loss reserves as Tier 1 capital, and yet loan loss  reserves were thought to be approximately equal to expected losses, the Committee chose to  make capital a function only of  unexpected losses (i.e., net of  expected losses). In cases where  loan loss reserves are less than 𝐸𝐿, a reduction in capital is made for the shortfall. This setup  allowed the Basel Committee to specify a loss percentile and an asset correlation 𝜌for each type  of asset. Each individual asset’s contribution to capital at any bank would then depend only on  the bank’s estimates of 𝐸𝐴𝐷, 𝐿𝐺𝐷 and 𝑃𝐷 for that asset.

Bank; Corporate, and Sovereign Exposures Under IRB

• For bank, corporate and sovereign exposures, Basel II assumes that 𝜌 and PD are related as

Since 𝑒^–50 is a very small number, this formula reduces to

As 𝑃𝐷 increases, 𝜌 decreases. This is because as a company becomes less creditworthy, its 𝑃𝐷 increases and its probability of default becomes more idiosyncratic and less affected by  overall market conditions.

• The relationship between 𝑊𝐶𝐷𝑅 (or 𝐷𝑅99) and 𝑃𝐷 is given in this table. 𝑊𝐶𝐷𝑅 is, as one  would expect, an increasing function of 𝑃𝐷. However, it does not increase as fast as it would if 𝜌 were assumed to be independent of 𝑃𝐷.

PD	0.1%	0.5%	1%	1.5%	2.0%
WCDR	3.4%	9.8%	14.0%	16.9%	19.0%

• The formula for the capital required for the  counterparty is

𝐸𝐴𝐷 × 𝐿𝐺𝐷 ×  𝑊𝐶𝐷𝑅 — 𝑃𝐷  × 𝑀𝐴

Here, 𝑀𝐴 is the maturity adjustment defined as

where

𝑏 =  0.11852 — 0.05478 × 𝑙𝑛  𝑃𝐷^2 , and

𝑀 is the maturity of the exposure.

• The maturity adjustment is designed so that, if an instrument lasts longer than one year, there is  a one-year credit exposure arising from a possible decline in the creditworthiness of the  counterparty as well as from a possible default by the counterparty. (Note that, when 𝑀 = 1,

𝑀𝐴 is 1.0 and has no effect.) The risk-weighted assets (𝑅𝑊𝐴) are calculated as 12.5 times the  capital required

𝑅𝑊𝐴 = 12.5 × 𝐸𝐴𝐷 × 𝐿𝐺𝐷 ×  𝑊𝐶𝐷𝑅 — 𝑃𝐷  × 𝑀𝐴

so that the capital is 8% of 𝑅𝑊𝐴, 4% of which must be Tier 1.

• Under the Foundation 𝐼𝑅𝐵 approach, banks supply 𝑃𝐷 while 𝐿𝐺𝐷, 𝐸𝐴𝐷, and 𝑀 are supervisory  values set by the Basel Committee. 𝑃𝐷 is subject to a floor of 0.03% for bank and corporate  exposures. 𝐿𝐺𝐷 is set at 45% for senior claims and 75% for subordinated claims. When there is  eligible collateral, in order to correspond to the comprehensive approach that we described  earlier, 𝐿𝐺𝐷 is reduced by the ratio of the adjusted value of  the collateral to the adjusted value  of the exposure, both calculated using the comprehensive approach. For derivatives, the 𝐸𝐴𝐷 is  calculated using the 𝐶𝐸𝑀 “current exposure plus add-on” approach of Basel I and includes the  impact of netting. 𝑀 is set at 2.5 in most circumstances.

• Under the Advanced 𝐼𝑅𝐵 approach, banks supply their own estimates of the 𝑃𝐷, 𝐿𝐺𝐷, 𝐸𝐴𝐷,  and 𝑀 for corporate, sovereign, and bank exposures. The 𝑃𝐷 can be reduced by credit  mitigants such as credit triggers. (As in the case of the Foundation 𝐼𝑅𝐵 approach, it is subject to a floor of 0.03% for bank and corporate exposures.) The two main factors  influencing the 𝐿𝐺𝐷 are the seniority of the debt and the collateral. In calculating 𝐸𝐴𝐷, banks  can with regulatory approval use their own models. As mentioned, in the case of  derivatives,  the model is likely to involve Monte Carlo simulation to determine how expected exposure  (after netting and collateral) will vary over the next year.

• The 𝑊𝐶𝐷𝑅  (or 𝐷𝑅99) is the default rate that (theoretically) happens once every thousand  years. The Basel Committee reserved the right to apply a scaling factor (less than or greater than  1.0) to the result of the calculations of the capital requirements given by the formula 𝐸𝐴𝐷 × 𝐿𝐺𝐷 × 𝑊𝐶𝐷𝑅 — 𝑃𝐷 × 𝑀𝐴 if it finds that the aggregate capital requirements are too high or  low. A typical scaling factor is 1.06.

EXAMPLE –

• Suppose that the assets of a bank consist of $100 million of loans to A-rated corporations.  The  PD  for  the  corporations  is  estimated  as  0.1%  and  the  LGD  is  60%.  The  a  maturity is 2.5 years for the corporate loans.

This compares with $100 million under Basel I and $50 million under the standardized  approach of Basel II, that was obtained earlier.

Retail Exposures under IRB

• 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. The capital requirement is therefore

𝐸𝐴𝐷 × 𝐿𝐺𝐷 × (𝑊𝐶𝐷𝑅 — 𝑃𝐷)

and the risk-weighted assets are

12.5 × 𝐸𝐴𝐷 × 𝐿𝐺𝐷 × (𝑊𝐶𝐷𝑅 — 𝑃𝐷)

𝑊𝐶𝐷𝑅 (or 𝐷𝑅99) is calculated as earlier. For residential mortgages, 𝜌 is set equal to 0.15 in  this equation. For qualifying revolving exposures, 𝜌 is set equal to 0.04. For all other retail  exposures, a relationship between 𝜌 and 𝑃𝐷 is specified for the calculation of 𝑊𝐶𝐷𝑅. This is

Because 𝑒^–35 is a very small number, this formula reduces to

𝜌 = 0.03 + 0.13𝑒^–35×PD

• This table gives the relationship between one-Year 99.9% WCDR and PD for Retail Exposures

PD	0.1%	0.5%	1.0%	1.5%	2.0%
WCDR	2.1%	6.3%	9.1%	11.0%	12.3%

EXAMPLE –

• Suppose 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, 𝜌 = 0.15 and 14.49.

Operational Risk Capital under Basel II

• The Basel Committee defined operational risk as the risk of  loss resulting from inadequate or  failed internal processes, people and systems, or from external events. After rogue trader losses at  Barings in the 1990s, the possibility of large losses from sources other than credit or market risk  became more visible. Three approaches to calculate capital for operational risk in Basel II are:
  • The Basic Indicator Approach – The simplest approach is the Basic Indicator Approach.  This sets the operational risk capital equal to the bank’s average annual gross income over  the last three years multiplied by 0.15
  • The Standardized Approach – This approach is similar to the basic indicator approach  except that a different factor is applied to the gross income from different business lines.
  • The Advanced Measurement Approach – 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. Operational risk capital is set equal to this loss minus the expected loss. One  advantage of the advanced measurement approach is that it allows banks to recognize the risk-mitigating impact of insurance contracts subject to certain conditions.

Example – Capital for the Basic Indicator and Standardized Approaches ($ billions)

• This table above provides an example of a bank’s gross income for each of  the eight business  lines specified in the Standardized Approach over a period of three years. It also shows the  operational risk capital levels each year for each business line under the Standardized Approach,  which are obtained by multiplying gross income times the business-line-specific multiplier.

Business Line	Multiplier	Gross Income			Capital
		Year 1	Year 2	Year 3	Year 1	Year 2	Year 3
Corporate Finance	18%	5	3	6	0.90	0.54	1.08
Trading & Sales	18%	1	-5	3	0.18	-9.0	0.54
Retail Banking	12%	20	25	30	2.40	3.00	3.60
Commercial Banking	15%	30	40	35	4.50	6.00	5.25
Payment & Settlement	18%	2	3	-100	0.36	0.54	-18.00
Agency Services	15%	1	1	1	0.15	0.15	0.15
Asset Management	12%	1	2	2	0.12	0.24	0.24
Retail Brokerage	12%	1	1	2	0.12	0.12	0.24
Sum		61	70	-21	8.73	9.69	-6.90

Negative capital may offset positive capital within a year, but years for which total estimated  capital is negative are ignored in computing the three-year average. Thus, under the  Standardized Approach, operational risk capital in this example would be

Under the Basic Indicator approach, total gross income for each year is multiplied by 15  percent, (again ignoring years of negative total gross income) and so the capital requirement in  this example would be

• Banks using the AMA approach are expected to estimate a distribution of operational risk losses  in seven categories that incorporates estimates of both the incidence of operational loss events  and their severity.
• AMA methodologies vary widely across different banks, but two broad approaches are most  popular:
  • A parametric and Monte Carlo approach, where data are used to parameterize the bank’s choice  of probability distribution for incidence (e.g., Poisson) and for severity (e.g., Weibull). These distributions are then used to produce large numbers of simulated loss observations from  which the value at the 99.9𝑡ℎ percentile can be read; and/or
  • Generate a moderate number of detailed scenarios in which losses occur, and then measure  operational losses in each scenario. Separate scenario analyses are often conducted for each  category of operational losses. Scenario analysis has the  advantage of  generating  informative narratives and being forward-looking. But the number of data points generated  is usually small and it is not obvious how to best convert such data into losses at the 99.9th  percentile. Hence, many banks use a combination of scenario and parametric methods.
  • The BCBS requires the inclusion of both expected and unexpected losses, and that the overall
  • program use internal data (at least five years of  experience), external data, scenario analysis, and  a consideration of the business environment and the bank’s controls. Though each supporting  element need not be included directly in calculations, the overall process must include all four.

• In recent years, required capital for operational at some banks risk was a material fraction of  total required capital, in part because the internal loss data that was required to be used under  the AMA included many large penalties for compliance failures, scandals, or misbehavior. As a result, the AMA approach has lost favor and is no longer permitted.

Solvency II

• There are no international standards for the regulation of insurance companies. In US, insurance  companies are regulated at state level with some input from the Federal Insurance Office and  the National Association of Insurance Commissioners. In Europe, their regulation is handled by  the European Union. The long-standing regulatory framework in the European Union, known  as Solvency I, was replaced by Solvency II in 2016. Whereas Solvency I calculates capital only  for underwriting risks, Solvency II considers investment risks and operational risks as well.

• There are three pillars in Solvency II.
  • Pillar 1 is concerned with the calculation of capital requirements and the types of capital  that are eligible.
  • Pillar 2 is concerned with the supervisory review process.
  • Pillar 3 is concerned with the disclosure of risk management information to the market.  The three pillars are therefore analogous to the three pillars of Basel II.

• Pillar 1 of Solvency II specifies a minimum capital requirement (𝑀𝐶𝑅) and a solvency capital  requirement (𝑆𝐶𝑅). If the capital of an insurance company falls below the 𝑆𝐶𝑅 level, the company should at minimum, deliver to the supervisor a plan to restore capital to above the 𝑆𝐶𝑅 level. The  supervisor might require the insurance company to take particular measures to correct the  situation.
  • ØThe 𝑀𝐶𝑅 is regarded as an absolute minimum level of capital. If capital drops below the
  • 𝑀𝐶𝑅 level, supervisors may assume control of the insurance company and prevent it from  taking new business. It might force the insurance company into liquidation, transferring its  policies to another company. The 𝑀𝐶𝑅 is typically between 25% and 45% of the 𝑆𝐶𝑅.

• There are two ways to calculate the 𝑆𝐶𝑅:
  • a) the standardized approach and
  • b) 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 also allowed  when the protection provided is considered equivalent. 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 (i.e., property and casualty), and health insurance.

• The internal models are required to satisfy three tests.
  • 1) The first is a statistical quality test. This is a test of  the soundness of  the data and  methodology used in calculating 𝑉𝑎𝑅.
  • 2) The second is a calibration test. This is a test of  whether risks have been assessed in accordance with a common SCR target criterion.
  • 3) The third is a use test. This is a test of whether the model is genuinely relevant to and used  by risk managers.
• Also similar to Basel II, requirements may be satisfied by a combination of Tier 1 capital (equity,  retained earnings, and equivalents), Tier 2 capital (liabilities subordinated to policyholders and  available for write-off in liquidations), and Tier 3 capital (subordinated to policyholders but not  satisfying the other criteria for Tier 2).