In considering the requirements for a satisfactory minimum regulatory capital requirement we need to reaffirm the purpose of regulatory capital outlined in Section 4. This is to ensure that a firm is able to survive a potentially systemic shock and still have sufficient net worth following the systemic event to be able to provide a prudent level of additional collateral to underwrite any required central bank funding without exposing the central bank itself to the risk of loss. From this it is clear that the capital to which the minimum requirement relates should be resources that are available to the firm to absorb losses at the time that they arise. This means that the only form of capital to which the proposed regulatory standard should apply should be unencumbered shareholders funds together with any stock which can be converted into equity at the option of the firm.

This is not to suggest that regulators should be indifferent to other aspects of a firm's liabilities - and in particular the availability of appropriate amounts of secure, subordinated long-term funding. Indeed, as we have argued in Section 4, we believe that regulators should pay considerable attention to arrangements of this type which help to underwrite the firm's ability to continue to fund itself during a crisis. However, we believe that it is essential to distinguish between regulatory requirements which exist to ensure that the firm has an appropriately conservative funding profile and minimum capital adequacy rules which exist to ensure that the firm is able to absorb any stress losses and still continue in business as a solvent entity. With respect to capital rules therefore the requirement should apply solely to shareholders funds and instruments that can be converted into equity.

If we accept this definition of capital, then in order to derive a suitable regulatory capital requirement we need to be able to assess

• the maximum amount of equity capital that could be depleted in a suitably defined stress scenario (the firm's 'equity at risk'); and

• the amount of equity which the firm should still be required to hold following such an adverse stress event (the regulatory multiplier).

- Calculating regulatory equity at risk

As we have argued in Section 6 above, we believe that the approach to calculating the regulatory capital requirement should be based on the same methodology that firms are increasingly using to assess their own risk bearing capacity which compares the firm's earnings potential (i.e. their projected earnings over a given reference period) with measures of the potential stress losses that the firm might face. This requires a methodology which will allow us to identify in a generic manner the potential sources of risk to a firm's earnings and to derive suitably conservative measures of the stress which might impact these factors.

In this context we can start with the following simplified model of a firm's earnings process which expresses the firms prospective earnings E(Rp_t+1) as follows:

E(Rp_t+1) = E( DP_t+1 + Y_t+1 - C_t+1)

Where:

E(Rp_t+1) is the forecast value of earnings in time t+1
DP_t+1 is the change in the value of the firm's portfolio of assets in time t+1
Y_t+1 is the value of the firms business revenues in time t+1, and

(It should be noted that for this purpose, business revenues include the fee, spread or 'edge' which a firm captures as part of its trading or lending activities. This can be compared to the premium which an insurance company charges for underwriting a risk. The income derived from the portfolio term ?Pt+1 solely reflects income derived from changes in the valuation of the assets already in the firm's portfolio)

C_t+1 is the costs which the firm incurs in time t+1

As we explained in Section 4, this only gives rise to a regulatory concern if Rp_t+1 is in fact negative. As our earnings equation demonstrates, this situation could arise if any of the three components of earnings - the value of its portfolio of assets, the ongoing business revenues or the costs - differ materially from their predicted value. An alternative way of thinking about this term is that the risk of loss derives from the following three broad classes of risk

• portfolio type risks, (essentially credit and market risk);
• strategic business risks, (the risks that the business is unable to capture the revenues which it anticipates); and
• operational types of risk, (the risk that the costs associated with handling the business materially exceeds what was anticipated)

In order to satisfy regulatory concerns about the risk posed by stress events using this methodology we need to derive a sufficiently prudent measure of the total amount of equity that is at risk in a firm to such events. This means that we require appropriate measures for the following

• a conservative estimate of E(Rp_t+1), say (Reg E(Rp_t+1))

• a measure of the potential stress loss that could impact the firm's credit and market risk portfolios to give a measure of (Stress DP_t+1)

• a prudent estimate of the extent to which business revenues could fall below their anticipated level in particularly adverse circumstances to give a measure of (Stress Y_t+1)

• a methodology for determining the potential 'stress' increase in its cost base that the firm could face as a result of its exposure to operational risks and other cost factors to give a measure of (Stress C_t+1)

On this basis we can then say that the amount of regulatory equity at risk (RER) in the firm is represented by the following term

RER = - ((Reg E(Rp_t+1)) - (Stress DP_t+1) - (Stress Y_t+1) - (Stress C_t+1))

We recognise that each of the component terms of this measure gives rise to potential difficulties of measurement and that there is likely to be considerable debate about the precise measures which would be appropriate if the Basel Committee were to consider adopting a methodology of this type. Nevertheless, we do not believe that the challenge of deriving a common methodology for deriving these values would be insurmountable. For example, the current regulatory capital requirement for market risk (three times 10 day 99% VaR) can be seen as a possible stress measure of the type we would envisage for the market risk component of (Stress DP_t+1), and that this could be further refined to incorporate the liquidity factors which we referred to in Section 4. Similarly, much of the current discussion about the developing discipline of credit risk modelling relates to the appropriate type of sensitivity analysis and stress tests which firms should apply to their portfolios and should lead to a convergence of thinking on a common measurement methodology.

With respect to the other terms in the equation, we would suggest that these might best be based initially on historical earnings trends and volatility analysis. Thus, for example, the regulatory earnings assumption (Reg E(Rp_t+1)) might be the lower of the previous year's earnings and an average of the past three years' non portfolio related earnings. The term (Stress Y_t+1) could be estimated by looking at the observed volatility of business revenues, and using a selection of the worst months during the observation period as an indicator of how revenues might be reduced during a stress period. Similarly, a review of actual operational losses and adverse cost movements could form a suitable basis for estimating (Stress C_t+1).

We include as an Annexe to this paper an illustration of how a measure of this type could be constructed. However, it should be emphasised that this is purely for illustrative purposes, and we do not seek in this paper to make any concrete proposal for a quantitative measure of RER. Our purpose is rather to outline how a measure of this type could be derived and to outline its advantages over the existing Basel Committee methodology as a basis for setting minimum regulatory capital requirements.

- Setting the minimum capital requirement and the regulatory multiplier

If a commonly agreed measure of this type could be established for calculating the amount of regulatory equity that was at risk, the final step in setting an appropriate minimum regulatory capital standard would be to determine a suitable regulatory multiplier which should apply to this number.

As we have already discussed, the need for such a regulatory multiplier arises because:

• any firm which suffered a loss as large as its RER calculation would need a certain amount of remaining equity in order to maintain its liquidity and to assure the market that it still had sufficient shareholders funds to continue in business;

• the firm would need to be able to continue in business for a minimum period of time, and potentially to continue to absorb losses, whilst it restructured its business or recapitalised

• in the event that the firm needed to obtain lender of last resort funding from the central bank it would need to have sufficient unencumbered assets to provide appropriate margin against any funds which it used to secure its borrowing

The ultimate decision on the appropriate amount for such a multiplier will inevitably be a matter for regulatory judgement and will be a direct consequence of the regulatory time horizon which we discussed in Section 4. Our initial sense would be that an appropriate value for the multiplier would be somewhere between three and five. The justification for a multiplier of three would be that this would ensure that a firm which in fact suffered a loss as large as its RER calculation would still have two thirds of its shareholders' funds available after the loss to continue to support its business and to provide security to its lenders. On the other hand, we believe it would be difficult to justify a regulatory multiplier in excess of five, since this would be sufficient to enable the firm to survive a further four years of similar stress losses before its shareholders funds were depleted - a level of comfort which should be more than adequate for the regulators. Moreover, we believe that it is just as important from an economic perspective to ensure that the minimum regulatory capital standard is not set too high as that it is not set too low.

A final, technical consideration that arises from our proposed approach is how a suitable minimum capital standard might be set for a firm whose RER calculation resulted in a negative number - i.e. where, despite cautious estimates of revenues and with appropriate estimates of stress losses, the firm would still operate profitably. This is neither an illogical nor an undesirable result of our proposed approach. Indeed if a firm is operating in a manner where it could not suffer a loss of equity under any reasonably foreseeable circumstances over the relevant calculation period (which we assume to be one year) the rationale for the regulators to require a minimum capital for that firm is limited. Nevertheless, we also recognise that the circumstances affecting a firm can change relatively quickly and consequently that there is a case for setting an absolute minimum capital requirement for all firms. Our proposal in cases of this type would therefore be to set the minimum requirement by reference to the absolute amount of the gross loss calculation, for example by setting a base requirement of the sum of the stress loss calculations. (An example of how this floor might work is also included in the Appendix)