Minimum Capital Requirement(Basel Accord) In Banking

Capital Requirement and Basel Agreement

To study capital requirements and basel agreement, we need to have some prior knowledge about banking. We all know that the bank earns profit from loan it extends and investment it makes. For earning profit and lending activity bank receives funds from:

1. Deposits from depositors
2. Money borrowed from other financial institution
3. Investment from shares holder, in form of Equity
4. Funds from bundles of asset it may sell share in.

“Spread” can define as difference between Interest Rate with which bank lends money and rate at which it borrowed money is called Spread. With larger the spread comes higher profit. Bank only need to keep balance between volume of borrower and there Probability of default.

Depositor faces several risks and major of all risk is bank becoming insolvent or illiquid. When value of Asset become less than sum of the values of its liabilities plus Equity then bank become illiquid. Value of bank asset can fall due to various reason but main reason of diminishing asset values are 1) Credit Risk- which is risk that those to whom bank lent will not repay 2) Market Risk- where financial assets like stocks, foreign currency or option contract decline in value due to decreases in equity price or change in exchange rate, interest rate or commodity price 3) Operational Risk- Risk due to failures in internal processes or systems or fraud or damage to plant property & Equipment or system failure.

To reduce the chance of depositor losing their money, each bank is required to maintain certain level of capital (Equity). The amount of capital a bank is required by its regulator to keep is called Regulatory Capital. Also the amount of capital a bank wishes to keep to maintain a probability of insolvency that it consider appropriate is called Economic Capital.  The level of both capitals should be almost same. So regulate this capital Basel Accords are been set up to calculate and determine minimum capital a bank must hold.

We now need to understand Basel Accords- where we will start from BASEL 1 (1970), BASEL 2 (1996) and BASEL 3 (2018-2019).

Prior to BASEL 1

During 1970 capital amount bank can hold were internal decision of bank and were largely unregulated. But during 1970 and 1980 several countries reduced amount of regulation that applied to banks and further due to advancement of computer technology funds movement become easy and risk started to spread between different countries. As banking industry become competitive and financial systems become increasingly interdependent- this could trigger failure of any large bank in one country impact financial system of another country due to their financial interlink. Further banks tried to increase their balance sheet to lend more loans become exposed to granting risky loans and increase chances of insolvency increase.

BASEL 1

BASEL was first setup handle repayments from Germany to other country for settlement following World War 1. But it had second purpose to bring stability into international banking markets, to discourage excessive risk taking by banks and to eliminate differences in competitive advantage by banks in some countries (especially Japan) to offer cheaper international loans than other countries.

BASEL1 required that internationally banks should hold at least 8% of the sum of risk weighted assets (RWAs) as Regulatory Capital.

                                                                                                       (1.1)

Where, RC= Regulatory Capital

Ai=Asset i (e.g. Home loan etc)

i= 1, 2, 3….I

RWi = risk weight for asset i

Risk weight were supplied by BASEL committee where home loan has weight value 0.5 and corporate loan has weight 1(this asset included off-balance sheet exposures). Further it was discretion of national regulators to increase regulatory capital depending upon fund exposure to different risk like Investment Risk, Interest Rate risk or Exchange rate risk. BASEL only specified amount of regulatory capital for Credit Risk.

Capital requirement were made of two type:

1. Tier 1 capital consisted of paid up equity and disclosed reserves.
2. Tier 2 consist of undisclosed reserves, Asset revaluation (Change in market price of asset), provisions and hybrid instruments and lastly there are limits being applied to each segment.

Weakness of BASEL1

BASEL1 only focused on Credit Risk and ignored loss of asset value due to unexpected changes in exchange rates or unexpected changes in interest rates.

BASEL1 treated many types of loss as equally likely e.g. exposure to private companies and exposure to fixed asset were given same risk weight.

It omitted any reduction in risk for portfolio effects e.g. two exposures in a portfolio is likely to be less than sum of individual risks to each exposure but this was not taken into account.

Accord did not take into account relationship between maturity of loans and risk of default, there is always higher risk for longer maturity loans.

BASEL1 also avoided taking into account difference in amount of loan that is repaid in event of default or amount that may be owed when a loan is expected to default.

Difference between risk weight for home loan(0.5) and personal loan(1.0) were not in alignment so bank made more home loan as it required lesser capital relative to internally assessed risk other loan where risk weighting were higher.  This was called “Regulatory Arbitrage”.

BASEL1 Amendment

BCBS proposed various changes in BASEL1 but implemented only 2 changes:

(1) Added requirement for capital to include amounts for Market Risk this were included in Tier3. The type of capital bank needed to hold were amended to include Tier 3- supplementary capitals which consist of subordinated loans with maturities of 2 to 5 years. This Tier-3 capital will only be used for market Risk.  

(2) Amendment allowed each bank to choose between standard regulatory charge based on fixed parameters or values from an internally computed model, subject to certain requirements.

BASEL1 still did not allow banks to use internal models for credit risk prediction (especially PD) – BASEL1 with Amendment did not include capital for operational risk and did not consider ways in which supervisory process or market competition could reduce risk. These weaknesses of BASEL1 were rewritten in BASEL2 which came into force in 2006 and will be in force till 2020.

Before we start our detailed article on BASEL2, we will try to understand reasons for 2007-2008 shocks of financial system during which bank did not have inadequate capital and will highlight key reason for BASEL2 failure. Many banks had to raise large amounts of additional capital in short time that respective government had to step in to provide this capital to avoid banks being unable to pay depositors.

Below are few reason and weakness in BASEL 2:

The proportion of Risk weighted Asset that banks kept as capital was thought to be too low. Capital component was not sufficiently liquid and also BASEL2 did not ensure banks had sufficient short term liquidity.

BASEL2 meant that when the macroeconomics is depressed and proportion of loans that default is high, then bank mush have larger amount of capital. But during such stressful condition raising capital is relatively difficult and expensive.

BASEL2 still allowed “Regulatory Arbitrage” as the risk weights differ from those indicated by internal models.

Basel 2 Diagram

Basel2 has three set of requirements known as Pillars.

Pillar1 relates to minimum capital requirements and relates to minimum capital bank need to hold for Credit Risk, Market Risk and Operational Risk.

Pillar2 relates Supervisory Review Process and risks like Credit Concentration risk.

Pillar3 relates to Market Discipline.

Pillar 1 minimum capital requirements

Pillar1 – Here the most important to understand what constitutes “Capital”? Capital under Basel2 specifies 3 tiers according to their liquidity (where liquidity means how easy it is to turn the capital item into cash without major reduction in its underlying value).

Tier1 (core capital) consists of paid-up common stock + preferred stock + disclosed reserves from post-tax retained profits – goodwill and Tier1 capital must exceed 4% of RWA.

Tier2 (supplementary capital) consists of undisclosed reserves (profit not appearing in retained profit or reserves) + Asset revaluation reserves (reserves created when the values of assets held by bank increase) + General provisions(loss provisions on asset) + hybrid instrument + subordinate term debt with original time to maturity of at least 5 years(this valuation cannot be more than 50% of Tier1 core capital). Lastly this rules can varied by national regulator and value of Tier2 is either less than or equal to Tier1 capital.

Tier3 (Unsecured Short-term subordinate Debt that is fully paid up and has original maturity of 2 years at least). Tier3 capital must not be more than 250% of bank’s Tier1 capital that is allocated to cover market risk as Tier3 capital only meet market risk & included with national regulatory approval. But from above segment we need to subtract (1) increase in equity due to securitization exposure (2) investment in non-consolidated subsidiary bank and financial activities (3) Investment in capital of other banks and financial institutions (discretion of regulator) (4) minority investment in financial activities.

Now we will explore each segment of Pillar1 one by one:

Credit Risk for Minimum regulatory capital requirements:

AS we are aware that each bank must hold regulatory capital at least as large as sum of minimum regulatory capital requirement (MRCR).

Regulatory Capital >= MRCR (Credit risk) +MRCR (Market Risk) +MRCR (operational risk) (1.2)

To compute Risk Weight bank need regulatory approval between 2 approaches: Standardized approach and internal rating-based approach.

Standardized Approach:

Here risk weights are given by Accord. For sovereigns, banks and corporate the values of weight depends on risk rating given to obligator/borrower by external credit rating agency. This External credit rating agency need to meet certain criteria and approved by national regulator.  Real issue happens with off balance sheet item where one need to converted to “credit exposure equivalents” by multiplying the value of the exposure by credit conversion factor (CCF). Default rate range may differ between External credit assessment institutions (ECAI). So national regulators has to map and make adjustment to ensure consistency.

Risk weight of 150% when specific provisions are less than 20% of outstanding amount of loan.

Risk weight of 100% applies when specific provision are no less than 20% outstanding amount of loan or no less than 50% with supervisor discretion.

There are some criteria which needed to be looked at especially for retail exposures where risk weight is 75%.  This are (1) Exposure should be to individual person or persons or to small business (2) One revolving credit or lines of credit must be Overdraft or credit card, a personal loan or lease or small business loan (3) Maximum total exposure to one counterparty must be no more than 1 million (4) Asset must be sufficiently diversified that 75% risk weight is appropriate (as shown by standard no one borrower having loans that total more than 0.2% of regulatory retail portfolio).

Internal Rating-based Approach IRB approaches are subjected to regulatory approval this approach focuses on risks of bank’s particular portfolio than standardized weight. IRB requires using formula which intended to indicate capital equal to value of losses that bank may make on average over 1000 year.

Consider a portfolio:

Di            = 1 (i defaults)

                = 0(otherwise), Di =Random Variable with Bernoulli distribution with probability (p) of default.

Di            ~Bern (1; p).  Probability of default is denoted by PDi for loan i and is then P (Di=1).

Li             = Loss made on loan i

ELi           = Expected loss from loan i

LGDi        = Loss given default for loan i (LGD is proportion of balance of a loan that is outstanding at time of     default that is never recovered by bank)

EADi        =Exposure at default loan i.

If we assume that PDi, LGDi and EADi are uncorrelated. Then for a portfolio of N loans the total loss is given by

                                                                                                                (1.3)

The minimum value within this distribution such that probability of getting such greater loss is no more than (1-q) is known as value of risk (VaR) at confidence level q of that distribution, we can also denote it by VaRq(L_N) or α_q(L_N). This is simply the q^th  quantile of that loss distribution. Accord wish bank to compute the amount of capital which is equal to loss that would be expected to occur on average once every 1000 years, it needs banks to compute VaR_99.9(L_N).

It is possible to calculate expected loss and to compute LGD_i, EAD_i, and PD_i.  So amount of money to cover that loss can be included in interest paid by each borrower. This are included as provisions. But real challenge is to predict unexpected deterioration in repayment behaviour called as unexpected losses. So for unexpected losses we cannot have provision but instead we can have bank capital being used.  So Accord gives formula which is used to compute value of unexpected losses with probability of 0.001 that the actual losses will be larger than this.  To compute formula we will use single borrower and later aggregate portfolio.

Accord formula is based on asymptotic single-risk factor (ASRF). 

Let A_{i, T} =Value of firm asset at end of month t=T.

A_{i, 0} = Value of firm asset at beginning of period at t = 0.

Return on assets for firm’s          ln (A_{i, T} / Ai_{, 0}) = r_i  

And we standardized this by ri     =       (ri- E (ri))/αi where αi = std of possible ri values.

Assumption: 1) Asset returns depend linearly on a (standardized) factor, Y that is common to all obligors and on standardized idiosyncratic element that is specific to firm I, εi.

                Ri = * εi                                         (1.3A)

 Pi denotes correlation between Y and Ri. The factor which could be observable or unobserved – in short there could be vector of many factors but in ASRF model it is a single factor.

2) Model assume ϵi and Y are not correlated and also ϵi and ϵj are uncorrelated as well. Which says that the correlation between returns for two obligator depends only on the common factor Y. Conditional on Y the asset returns of any two obligator are independent.

3) Y and ϵi are both normally distributed in our assumption so does ri.

This brings us back to point raised earlier that at end of period if value of firm’s assets is less than its liabilities, it will not repay its liabilities- the owners cannot exercise their call option to buy the assets of firm by repaying loan. However in argument under ASRF model it says that a firm will default when asset returns fall below some threshold value, ki.

PD_i = P (r_i < ki) = (ki)                                    (1.4)

r_i ~ N (0, 1) and = cumulative standard normal distribution.

Hence                                   ki = ^-1 (PD_i)                                                                       (1.5)

PD_i = unconditional (on Y) that firm I will default. So if we knew for specific firm PD_i = 0.05, then we could find k_i by computing ^-1 (0.05) and from standard normal distribution table we get k_i = -1.645.

From     (1.4) and (1.5) we know that PD_i depends on Y. The PD, conditional on specific value of Y, denoted y, is

                                P (D_i = 1І Y = y)   =             P (r_i < k_i І Y = y)

                                                                =             )

                                                                =             P (  )                             (1.6)

                                                                =              )

                Since for borrower we wish PD_i to be at 99.9^th quantile value, we set Y at value such that there is 0.001 probabilities that the PD_i is greater than implied value. Since Y is negatively related to asset return (by assumption) this means that there is 0.001 probability of lower value of Y. In VaR term this means we set Y at its (1-q)^th percentile, where q is 99.9, that is y =  

Noting that  (Y = standard normally distributed). We are setting y = –^-1(q).

Substituting (1.5) into (1.6) we gain

^-1 (PD_i) + ^-1 (q))/                                 (1.7)

Where in accord q = 99.9

Given assumption of independence between LGD_i and EAD_i, expected loss for individual loan is

E (Li) = E (Di)*LGDi*EADi = PDi *LGDi * EADi                                                         (1.8)

If LGDi and EADi were fixed, we could find VaR_99.9 (ELi) value (which is VaR_99.9 value for expected loss distribution) for the obligator by substituting (1.7) into (1.8) to give

E (Li | α_q (Y)) = VaR_99.9(E [Li]) = PDi (α_q(Y)) * LGDi * EADi                                                 (1.9)

So amount of capital to cover unexpected losses is then equal to E (Li|α_q (Y)) less expected losses. The accord then multiplies the resulting expression by 12.5, being the reciprocal of 0.08, the proportion of RWAs that must be held as capital. Result will be risk weighted assets:

RWAi     = 12.5 * ULi

                = 12.5 * EADi * LGDi (^-1(PDi) + ^-1 (0.999)])/)) – PDi                                 (1.10)

For loans to corporate , sovereigns and banks , but not retail loans, the expression to right needs to be multiplied by maturity adjustment which is positively related to both length of loan and PD of loan. The argument for its inclusion is that longer term loans have higher chance of default.

The Maturity adjustment is given by:

MA_i = (1+ [(Mi – 2.5) * b])/ (1 – 1.5b)                      Mi = length of loan

b = (0.11852-0.05478*ln (PDi))²

Till now we consider single borrower.  Now let us explore portfolio of loans. The ASRF model makes some assumptions:

• There are finite numbers of loans in portfolio and their size distribution is such that no exposure accounts for more than some very small proportion of total exposure. Such a portfolio is said to be “Infinitely Fine grained”.
• Dependency between loans is due purely to one systematic risk factor as in model (1.3A).

The Basel formula tries to indicate the amount of capital equal to unexpected losses of portfolio. So we need VaR at 99.9% of loss distribution, L_N.

A few useful results follow from assumption of ASRF (1) Idiosyncratic risks of individual obligators are diversified away because ϵi and ϵj are uncorrelated. So only source of risk for portfolio is systematic risk.  As number of equally sized exposures in portfolio increases, the value of portfolio loss L_N  tends towards expected value, conditional on value of factor, E(L_N І Y).  Put it another way, when the factor has a particular value, the expected portfolio loss from the theoretical model tends to the observed loss as number of loans in portfolio tends to be infinity. (2) VaR of expected portfolio loss conditional on factor, VaRq(E[L_N І Y]), equals the expected portfolio loss conditional on VaR of factor,

E(L_N І VaRq(Y)). Putting this in place, if we have a portfolio of an extremely large number of equally sized loans, the VaR of actual losses on the portfolio at, say 99.9% equals the VaR of the expected losses, predicted by the model when the value of Y is at VaR at 99.9%. It is exactly this that Basel formula represents.

Risk Weighted Assets are subject to maturity adjustment for sovereigns, banks and corporate.