(Revised as of January 29, 2015)
A bank's capital, also known as equity, is the margin by which creditors are covered if the bank's assets were liquidated. A measure of a bank's financial health is its capital/asset ratio, which is required to be above a prescribed minimum.
1.Assets and Liabilities
When a bank creates a deposit to fund a loan, its assets and liabilities increase equally, with no increase in equity. That causes its capital ratio to drop. Thus the capital requirement limits the total amount of credit that a bank may issue.
It is important to note that the capital requirement applies to assets while the reserve requirement applies to liabilities. The reserve requirement imposes a lower limit on the amount of reserves a bank must own relative to the demand deposits of its customers.
2.For compliance,
A bank has to meet the Capital Adequacy Requirements (CAR) set by the regulator (OSFI in Canada);
The bank has to have the Internal Capital Adequacy Assessment
Thus CAR and ICAAP are two different sides of the same coin.
1)Capital Adequacy Requirements or Capital Adequacy Ratios
CAR can be expressed as the total amount(Capital Requriements) or Ratios(required Capital Adequacy Ratio =Required Capital/Asset). As there are different scopes of capital, there are different required Capital Adequacy Ratios.
The relationship between Capital Requirements and Capital Ratio is as follows:
Or Capital Requirement = Capital Adequacy Ratio x Risk Weighted Asset.
2)Classification of Capitals
The BIS rules set requirements on two categories of capital, Tier 1 capital and Total capital:
-Common Equity Tier 1 Capital is common stocks and retained earnings.
-Tier 1 capital is the sum of the above common equity tier 1 capital plus preferred stock: the book value of all its stocks-common and preferred stocks- plus retained earnings.
(Tier 2 capital is separate: loan-loss or undisclosed reserves plus subordinated debt*)
*Subordinated debt is long term debt that, in case of insolvency, is paid off only after depositors and other creditors have been paid. Thus it has been used like equity, but large part will be phased out.
-Total capital is the sum of Tier 1 and Tier 2 capital.
(Summary table)
Common Equity Tier 1 Capital (a) / Common Stocks+ Retained Earnings/Corporate Profits
Tier 1 Capital (b) / Above + Preferred Stocks=
All Stocks + Retained Earnings
Tier 2 Capital (c ) / Subordinated Debts and others / Subordinated debts:
Total Capital (d ) / = Tier 1 capital + Tier 2 Capital
= All Stocks + Retained Earnings + Subordinated Debts / (d) = (b ) + (c )
3) Risks Identification, and Computations of Risk Weighted Capital Requirements and Risk Weighted Assets
(1) Risk Identification
Pillar 1 Risks
(i)Credit Risk
Standardized Approach
Advanced
(ii)Operational/Operation Risk: Basic Indicator Method
Three year average of gross income x 0.15 (15%) x 12.5
(iii)Market Risk/Interest Rate Risk: Duration Gap Test - VaR
(iv) other risks
There are other new risks of Pillar 2, which are recently introduced, such as Liquidity Risk, Credit Concentration Risk, FX risk, and new items are added to existing risks, such as Reputational Risk being added to Operational Risk, Strategic Risk being added to Operational Risk.
Most risks require capital provision, but some risks, such as liquidity and reputational risk, do not.
(2) Computation of Total Mound of Risk- Risk Weighted Assets
Each identified risk may lead to some measurement. It may lead to the size of risk, or what is the amount of assets exposed to that risk. It is a computationof Risk Weighted Assets(RWA).
RWA = Risk Weight 1 x Amount of Asset with Risk Weight 1 + Risk Weight 2 x Asset with RW 2 + ……… + RWi x Asset RW1
For its calculation, we need a Risk Weight for each different kind of asset, which indicates the degree of vulnerability of each asset to the given risk.
(Table) Risk Weights for Different Assets are given as follows:
Asset / Basel IIRisk Weight
(See Note 1 below) / Updated Canadian
Risk Weight
(see Note 2: to be updated
From the OSFI website)
Cash and equivalents / 0 / 0
Government securities / 0 / 0.2-1.5
Interbank loans / 0.2 / 0.2-1.5
Residential Mortgage loans / 0.5 / 0.35
(0 for insured mortgage)
Commercial Mortgage Loans / 1.00
Ordinary loans / 1.0 / 1.00
Standby letters of credit / 1.0 / 1.00
Note 1:
Note 2: Other updated risk weight, refer to
How about the amount of Capital to set aside (Capital Requirements) for Operational/Operation Risk:
The BIS and governments, including Canada, require that 15% of the three year average of Annual Gross Income of the bankbe set aside:
Capital Requirement for Operation Risk = 0.15 x Annual Gross Income
*The Risk Weighted Assets for the Operational Risk is much larger than its capital requirement.
Risk Weighted Asset for Operation Risk = Capital Requirement for Operation Risk x 12.5.
Some risks may not lead to RWA, but simple numerical exposures.
Measurement
In addition to Pillar 1 risks, the newly revised ICAAP encompasses risks for which no capital is allocated, such as business risk, pension risk, and strategic risk.
Risk types according to the ICAAP processRisk type / Pillar 1 / Pillar 2
Capital is allocated / Contributes to calculated capital need?
Credit risk / Yes / Yes
Concentration risk / No / Yes
Market risk / Yes / Yes, plus additional tests
Market risk Interest rate risk in banking book / No / Yes, plus additional tests
Operational risk / Yes / Yes
Business risk: Earnings volatility risk / No / Yes
Risks in retirement benefits / No / Yes
Strategic risk: Business plans / No / Yes
No specific capital is allocated / Identified and mitigated?
Reputational risk / No / Yes
Liquidity risk / No / Yes, stress test
Strategic risk: Decision risk / No / Yes
* source: Swedbank’s ICCAP
Three risks should have Capital Requirements: Credit Risk, Operational Risk and Market Risk. Thus we should have;
Total Capital (Adequacy) Requirements for Pillar 1 Risks
= Credit Risk Requirements + Operation Risk Capital Requirements + Market Risk Capital Requirements
Total Risk Weighted Assets
= Credit Risk Weighted Asset + Operation Risk Weighted Asset + Market Risk Weighted Asset
Total Risk Weighted Assets for Pillar 1 Risks
= Credit Risk Weighted Assets + Operation Risk Weighted Assets + Market Risk Weighted Assets
= Credit Risk Weighted Asset + 12.5 x Operation Risk Capital Requirement) + 12.5xMarket Risk (Capital Requirement)
(4) The Statutory Minimum Capital Adequacy Requirements
Common Equity Tier 1 Ratio should be at least 3.5%(before 2015) to 4.5%(from 2015) of the total Risk Weighted Capital.
Tier 1 capital must be at least 4.5% (before 2015) to 6%(from 2015)of the total risk-weighted assets.
The total capital must be at least 8% of the total risk weighted assets. This is an internationally accepted standards. Thus it is called the ‘BIS ratio’ named after the international organization.
In Canada, the regulator OSFI requires that the bank should keep some additionalCapital Conservation Buffer as well. This is mandatory from 2016 in Canada, and is set to be 2.5%.
This means that from the year of 2016, the required minimumCanadian Capital Adequacy R ratios will be as follows:
The minimum CET1 Ratio with buffer is 4.5+2.5% = 7%;
The minimum Tier 1 Capital Ratio with buffer= 6 +2.5% = 8.5%
Theminimum required Capital Ratio with buffer in Canada= 8 +2.5% = 10.5%.
Summary table of minimum Capital Adequacy Ratios:
Bare Minimum Required Rate(International Standards) / Capital Conservation Buffer / Canadian Standards of
Minimum Required Rate for Business in the Canadian Financial Market
CET 1 Ratio / 4.5% / 2.5% / 7%
Tier 1 Capital Ratio / 6.0% / 2.5% / 8.5%
Total Capital Ratio / 8.0%* / 2.5% / 10.5%
Note: * this is the most commonly used and thus is called the ‘BIS ratio’. This is the minimum ratio of total capital to total risk weighted assets, which is set by the BIS as the minimum international standards.
In Canada, the minimum total capital ratio is not 8%, but 8% + the margin of “Capital Conservation Buffer of 2.5%”. In other words, the Canadian BIS ratio is 10.5%, which is the international standard of 8% plus the Canadian capital buffer of 2.5%.
The numbers could be confusing as many different numbers are floating around: 8, 8.5, 10.5, etc. Even for one category, Total Capital, there are different numbers, Canadian 10.5%, and BIS 8%, and so on: The Bank for International Settlement requires that the minimum total capital must be at least 8.0% of the total risk-weighted assets.This is the lowest acceptable common international standards for a bank for international business. Canada takes 8.0% in for the Total Capital Rate, but it adds 2.5%, and thus it is 10.5% for the total capital ratio. Singapore has the even higher number of 11% requirement for total capital ratio.
Two Examples of CAR, ICAAP, and BIS ratios
1)A full Example:
How to calculate the Total Risk Weighted Assets and the capital adequacy ratios?
Assume a bank has the following assets:
Cash and equivalents / $40m
Government securities / $80m
Interbank loans / $100m
Residential Mortgage loans / $200m
Commercial Mortgage Loans / $100m
Ordinary loans / $300m
Standby letters of credit / $80m
Total Assets / 900
And the annual total Gross Income is $20 million.
How much is the minimum amount of capital should a bank have in the form of the Common Equity or the Total Capital(Common Equity + Preferred Stock + Subordinate Debts)? Or What is the minimum Capital Requirement?
(1)Capital Requirement for Credit Risk
Take the approved Risk Weights as follows:
Asset / Credit Risk WeightCash and equivalents / 0
Government securities(AA credit ratings) / 0.2
Interbank loans(AA credit ratings) / 0.2
Residential Mortgage loans / 0.35
Commercial Mortgage Loans / 1.0
Ordinary loans / 1.0
Standby letters of credit / 1.0
The total risk-weighted assetfor Credit Riskis 0 x $40m + 0 x $80m + 0.2 x $100m + 0.5 x $200m +1.0x $100 m+ 1.0 x $300m + 1.0 x $80m = $600m:
Asset / Amount / Weight(what portion is risk?) / Risk Weighted Asset (RWA)
Cash and equivalents / $40m / 0 / 0
Government securities / $80m / 0.2 / $16 m
Interbank loans / $100m / 0.2 / $20 m
Residential Mortgage loans / $200m / 0.35 / $75m
Commercial Mortgage Loans / $100m / 1.0 / $100 m
Ordinary loans / $300m / 1.0 / $300 m
Standby letters of credit / $80m / 1.0 / $80 m
Total Assets / $900m / $600 m
Now, let’s talk about the minimum Credit Risk Capital Requirements which is set by the regulator: In order for a bank to do business, it has to have the minimum capital buffer against possible risks.
Recall,
Capital Requirements = Risk Weighted Assets x Required Capital Ratio
The cover the exposure of the above Credit Risk Weighted Asset of $600 m, how much capital is a bank required to hold for Credit Risk only?
Canada / Minimum Required Capital Rate for Credit Risk in Banking Business (%) / Minimum Capital Requirements (dollars)CET 1 Ratio / 7% / $ 42 m (= 600M x 0.07)
(Tier 1 Capital Ratio / 8.5% / $ 51m
Total Capital Ratio (international) =
BIS Ratio / 8% / $48 m(= 600M x 0.08)
Total Capital Ratio (Canada) / 10.5% / $ 63 m(= 600M x 0.105)
This table means that the bank should have the minimum of $ 42 m of Paid-up Capital raised through the sales of Common Stocks, $51 m of Common and Preferred Stocks, and $63 m of Total Capital (Common Stocks+ Preferred Stocks+ Subordinated Debts).
The Bank for International Settlement standard for the Total Capital Ratio is only 8%. The BIS’s Total Capital Requirement is $48 m only.
So far we have assumed there is only credit risk. In fact, however, that is not all of capital requirement, and credit risk is not all risks the bank is faced with. There are two additional risks, and there should be additional capital requirements.
(2)How about the amount of Capital to set aside (Capital Requirements) for Operational/Operation Risk:
The BIS and governments, including Canada, require that 15% of the three year average of Annual Gross Income of the bankbe set aside:
Capital Requirement for Operation Risk = 0.15 x Annual Gross Income.
Suppose that the average annual gross income is $20 million, the capital requirement for Operation Risk is equal to $ 20 m x 0.15 = $ 3 million;
(3)Market Risk
Changes in the market affect the net worth of some assets, particularly, the net worth of securities from the financial market.
We will ignore this Market Risk, and how to calculate the capital requirement for market risk.
Reasons: 1) Some banks are devoted to loans, and do not invest on market securities, and then there is no market risk; 2) How to compute Market Risk is an actuary exercise.
Duration gap test, and VaR may lead to the computation of Capital Requirement for Market Risk.
(4)Combining Credit Risk Requirement and Operation Risk Requirement
The Canadian Total Capital Requirement for two risks, credit and operation is $ 63 m + 3m = $ 66m……..(1).
The BIS total capital requirement is $48 m + $3 m = $51 m……..(2).
The bank has to raise another 3 million for this additional Capital Requirement for Operation Risk. That 3 million dollar has to be raised in the way to satisfy all level of required rates, or to keep the above table in tact: This means that this 3 million additional capital should be raised at least through Tier 1 Capital (Common and Preferred Stock sales). For instance, if the bank raises this additional 3 million dollars through borrowing of Subordinated debts, it may satisfy the Total Capital Ratio of 10.5%, but may not satisfy the Teir1 Capital Ratio of 8,5%.
(5) Integrated Formula for All Three Risk
As we have done, we may calculate capital requirements for each risk and add all the capital requirements up.
A more convenient and simple way is to integrate all three risk requirements into one formula:
The process requires some manipulation of converting Capital Requirement for Operation Risk and Market Risk into an equivalent of Risk Weighted Assets (so that in the formula, it can be converted back to Capital Requirement; one can get the Risk Weighted Assets times Required Ratio is equal to
In fact, the OSFI sets the integrate formula as follows:
If a bank is trying to find the amount of capital requirement, it can use the above formula:
For the minimum amount of common stocks (CET1 Capital) it needs: 1)You set the Required Capital Ratios at 0.07 or 7% for the above formula; And calculate the numerator which is in fact Capital Requirement by multiplying 0.07(require ratio) times the Denominator. This is how much of CCE Tier 1 Capital the bank needs.
For the minimum amount of Tier I Capital (all stocks) it needs: 1)You set the Required Capital Ratios at 0.085 or 8.5% for the above formula; And calculate the numerator which is in fact Capital Requirement by multiplying 0.085times the Denominator. This is how much of Tier 1 Capital(all stocks) the bank needs.
For the minimum amount of Total Capital (all stocks+ subordinated debt) it needs to do business in Canada: 1)You set the Canadian Required Capital Ratios at 0.105 or 10.5% for the above formula; And calculate the numerator which is in fact Capital Requirement by multiplying 0.085 times the Denominator. This is how much of Total Capital the bank needs to operate in Canada.
For the minimum amount of Total Capital (all stocks+ subordinated debt) it needs for international business or outside of Canada, say, in China: 1)You set the Required Capital Ratios at 0.08 or 8.0% for the above formula; And calculate the numerator which is in fact Capital Requirement by multiplying 0.085 times the Denominator. This is how much of Total Capital the bank needs in the international financial market.
Can we get the Canadian Tier 1 Capital Requirement (how much total stocks) and Total Capital Requirement(how much total stocks and subordinated debts) from this formula very quickly?
How much total capital (stocks + subordinated debts) should the bank have in Canada?
0.105 = Canadian Total Capital Requirement / ($ 600 M + 12.5 x $ 3 M) ;
and thus Total Capital Requirement = 0.105 times $ 637.5 M = $ 66 M….(3).
How much total capital should the bank have for business worldwide so that a foreign government in general may be satisfied?
0.08 = Canadian Total Capital Requirement / ($ 600 M + 12.5 x $ 3 M) ;
and thus Total Capital Requirement = 0.08 times $ 637.5 M = $ 51 M….(4).
You may note that (3) = (1), and (4) = (2). Which calculation method, out of Capital Requirements or Capital Ratios, you may use, you get the same figures for Capital Requirements.
Note One thing: Why multiplying 12.5 to Operation Risk(capital requirement) and Market Risk(capital requirement) in the formula?
If the denominator includes Operation Risk Capital Requirement, and Market Risk Capital Requirement, it would cause a problem.
For example, let’s use the BIS ratio of 8% or 0.08 for our illustration: If we put 0.08 = Capital Requirements / (Credit RWA + Operation Risk + Market Risk), it would not be right. Why? the Total Capital Requirement by BIS = 0.08 x (Credit Risk RWA+ Capital Requirement for Operation Risk + something about Capital Requirement for Market Risk). The second and their items do not make sense! As 0.085 times Operation Risk Capital Requirement is not Operation Risk Capital Requirement. The only way to have the right side component Operation Risk Capital Requirement to be added,as it is, nothing more or nothing less, to the left side of the Capital Requirement is by inflating it first. In other words, we have to offsetthe effect of the multiplier of 0.08 on the denominator of Operation Risk Requirement, and this can be done by multiplying 12.5 to Operation Risk Capital Requirement. Then, what would we call this, a new term, in the denominator? We may call it Operation Risk Weighted Asset. It sounds absurd, but it make a mathematical sense.
The 12.5 factor in the denominator came from this background. Should it be adjusted to for CET1 (0.07) and to about 10 for Total Capital (0.15=10.5%) ? Probably it should, but these formulas are only an approximation. Using 12.5 factor should be more or less O.K. for computation of all ratios.
One can find this amount is the same as the capital requirement we have got in disaggregation as found in (1).
(Extra questions)
How much amount of Common Stocks should the bank have to have operation in Canada?
The formula says, 0.007= Common Equity Tier 1 Capital Requirement / ($ 600 million + 12.5 x 3 $ million);
And solving for Common Equity Tier 1 Capital Requirement, we get