Bankers are increasingly discovering that the goal of their business life is not necessarily to maximize ROA (return on assets) or even ROE (return on equity). Rather, fulfillment is achieved by maximizing the unpronounceable RARORAE (risk-adjusted return on risk-adjusted equity). From all indications this is the variable that is most closely linked to the long-run behavior of equity values.

RARORAE, which, sounded syllabically, evokes memories of a college cheer, can also be styled RAROEE (risk-adjusted return on economic equity). Economic equity is one of at least three kinds of equity a bank needs to consider. It is, quite simply, the amount of the shareholders' stake that economic analysis discloses is required to cover the bank's risk of earnings volatility, which is the possible deviation of returns from their expected or average amount.

Economic equity is thus the amount of capital protection that is objectively required, as opposed to what the regulators say is needed (Tier 1 equity) or the amount that the accountants reckon the bank actually has according to GAAP (book equity).

A Question of Tolerance

But how much equity is objectively required? The answer depends quite importantly on the risk tolerance of the individual institution. This risk tolerance is proxied by the bank's credit rating, but since the rating agencies are at times incorrect, the proxy is something less than perfect.

Nonetheless, ratings provide a convenient representation of degrees of risk tolerance. If a bank aspires to a triple A credit rating, it must have an equity-risk ratio similar to that of other triple-A institutions. But if the bank aspires to only a triple-B or A rating, its equity needs will of course be more modest.

Avoiding the Untenable

In turn, the rating to which the bank aspires should be a function of its business mix. If it wishes to lend to large corporations and must fund itself primarily in the market for purchased monies, then the bank needs an excellent credit rating. Obviously, lending to customers whose average credit rating may be higher than the bank's is an untenable situation, a guarantee of negative spreads. What's more, banks with lower than double-A credit ratings are effectively precluded from some types of derivatives business and therefore find it difficult to serve the needs of a large-company borrower population.

By contrast, regional banks with a portfolio of middle-market loans funded primarily with core deposits are much less likely to need an elevated credit rating. Even if they sport only a single-A or a triple-B designation, such banks will generally be more highly rated than their average borrowers. And the fact that they have few risk-sensitive funds providers and little need to engage in the derivatives business would seem to underscore the sufficiency of a comparatively low credit standing.

A Perverse Transfer

Indeed, it can be argued that it would be foolish for these banks to aspire to a premium credit position. Given that the FDIC does not yet charge insurance fees that are appropriate to the true riskiness of banks (although it will shortly introduce a modicum of differentiation into insurance schedules), banks whose equity levels are high enough to warrant, say, double-A or triple-A status end up paying far too much for insurance, while those with lower amounts of equity support end up paying far too little.

Under these circumstances, banks with overgenerous equity cushions are in effect transferring income from their shareholders, via the government, to the shareholders of riskier institutions.

Thus the amount of equity needed at the bankwide level is that required to provide the degree of protection against downside earnings volatility which is consistent with the institution's risk posture and corresponding credit rating. In turn, the amount of downside earnings volatility is determined by the interaction, or covariance, of three basic types of risk - unexpectedly large loan losses (credit risk); unanticipated movements in interest rates, exchange rates, or other market prices (market risk); and unforeseen operational errors or fluctuations in demand or output (operational risk).

Once it has figured out how much equity is needed to offset these correlated risks, the bank can provide answers to a number of significant questions. For example, what should be the institution's hurdle or required rate of return? If the bank chooses to assign enough equity to provide the amount of protection against earnings shortfalls that is appropriate to a triple-A company, then its required rate of return will obviously be lower than if its equity allocation were more modest. That is, since the bank is less risky, the marketplace will accept a lower rate of return without discounting its stock price.

On the other hand, a bank with an equity level appropriate to a triple-B rating must set a more aggressive hurdle rate in order to avoid being penalized by the market. However, since this institution is more leveraged than the triple-A bank, it will have a somewhat easier time attaining this more ambitious hurdle rate.

Additionally, the equity assignment at the bankwide level answers the question of what yield curve should be used to transfer-credit all internal funds generators and transfer-price all internal funds users. Quite obviously, the choice of yield curve should be consistent with the method of capitalization, meaning that a bank which earmarks enough equity for a triple-A rating should use a triple-A yield curve for transfer pricing purposes.

Parceling Out Equity

Having decided on the amount of equity needed by the overall bank, the institution must then parcel out this equity to individual business lines, customers, and products in proportion to their contribution to the bankwide risk of earnings volatility. In so doing, it must take into account the shape of the distribution of possible losses resulting from each risk type.

In business where this shape is normal (a bell-shaped distribution), assigning equity equal to one standard deviation from the loss mean will protect the bank from loss fluctuations most of the time (if, of course, the future replicates the past). And equity equal to three standard deviations will provide protection nearly all the time.

Skewed Distribution

The rub is that, in some businesses, the loss distribution is not symmetrical or bell-shaped. For example, loan-loss rates are not normally distributed since these rates cannot fall below zero. Because the loss distribution in the lending business is a bounded one, adequately protecting the bank against earnings volatility will require equity equal to more than three standard deviations.

On the other hand, the covariance, or portfolio, effect noted above would appear to mitigate equity requirements for each risk type. That is, an equity allocation for any business must take into account the covariance among the three major bank risks - credit, market, and operational. And if these risks are less than perfectly correlated with one another (which they are), then the bank will need less equity to support, say, its credit risk than if this risk were its only source of earnings variation.

Once the bank has determined how to parcel out its equity, what does it do if the calculated amount of economic equity in, say, the commercial-loan portfolio falls short of what the regulators require (4% Tier 1 equity)? Does it simply ignore the economic calculation in assigning equity to individual loans?

That would seem to be foolish. The purpose of the economic-equity exercise is to determine the real risk of an asset, which, as noted, is its contribution to the earnings-volatility exposure of the entire bank. The bank should use this economic calculation to help price loans by incorporating a volatility premium (equal to the needed amount of equity times the hurdle rate), thereby helping to differentiate loan pricing according to risk.

If the bank uses a regulatory-equity basis for pricing loans, it will inevitably distort the pricing process. Nor is this expedient necessary. As long as lending is not the only bank business and rigid regulatory rules do not apply to every bank business, the bank can find ways to assign the excess of regulatory required over economically needed equity to other bank activities.

Correcting the Imbalance

As noted at the outset of this article, a bank must contend with three types of equity - book, regulatory, and economic. The crucial relationship is that between book and economic equity since this determines whether the bank's risk posture is consistent with its risk philosophy or tolerance. A bank that has more book equity than is economically needed is a low-risk entity, in effect assuming less risk than its target credit rating and volatility exposure warrant. By contrast, a bank whose book equity falls short of what is economically needed is a high-risk institution, in effect assuming more risk than is consistent with its target credit standing and volatility exposure.

The methods available to each to these institutions to correct the imbalance between risk goals and risk positions depend in turn on the relationship between the amount of their book and regulatory required equity (see the chart). The low-risk bank needs to assume more risk, provided there is a satisfactory risk-return tradeoff available.

If it has more book equity than the regulators demand, this bank has a choice. It can acquire another bank with attractive prospects but less book equity than the regulators require and perhaps less book equity than is economically needed. Alternatively, it can expand into whatever component business earns an adequate return on economic equity, regardless of the business' need for regulatory equity.

If, however, these opportunities do not exist, the institution, being endowed with a surplus of book equity, has the luxury of considering a heftier stock dividend or a stock-buyback program, either of which should bring book equity back in line with both economic need and regulatory directive.

A troublesome Complication

A complication arises if this low-risk institution finds itself with less book equity than the regulators demand. Then it must either raise more equity or shuffle its business mix, even though it has more protection against volatility risk than its current business profile demands.

Since the bank already has more book equity than is economically needed, an equity offering is probably not a good idea. Instead, the bank should disinvest in those businesses that require a lot of regulatory equity but may have a low return on economic equity, either because returns are low - e.g., some types of letter-of-credit business - or because the requirement for economic equity is high - e.g., LBO lending. Such a step will help close the gap between regulatory required and book equity without damaging the bank's return potential.

At the same time because this bank needs to increase its risk quotient without raising its requirement for regulatory equity, of which it is short, it can increase its exposure in businesses that need economic but not regulatory equity.

For example, the institution may decide to take on additional market or interest-rate risk, which, at least for the time being, consumes economic but not regulatory equity and may, under certain circumstances, provide a high return on the economic equity it absorbs.

Another option is to gravitate toward a riskier (but only if commensurately more profitable) mix of customers in businesses where the requirement for regulatory equity is insensitive to the level of risk - e.g., commercial lending.

Raising Equity

The second type of institution mentioned above - one whose economically required equity exceeds its book total - must either shed risk or raise more equity. That's because it simply doesn't have enough of a cushion to support its risk tolerance and earnings volatility exposure.

Unlike the low-risk entity, this type of bank should probably consider an equity offering. It can raise equity without economic as opposed to accounting dilution if it can be sure of employing the funds in investments that generate a positive net present value - i.e., earn high returns on economic equity. Absent this assurance, however, this bank shouldn't go to market.

This institution's residual options once again depend on the relationship between its book and regulatory required equity. If book equity exceeds the amount demanded by the regulators the bank can concentrate on ridding itself of assets with low economic returns and high economic-equity needs without regard to their usage of regulatory equity. But if book equity is less than regulatory requirements, the bank should divest itself of assets and businesses with low returns on economic equity and high requirements for both economic and regulatory equity.

As can be readily seen, correct policy choices depend to a large degree on determining the rate of return being earned on the concept of equity that is most significant but also least transparent - economic equity. Therefore a high priority for the future is to formulate a risk philosophy that will suggest a target credit rating and to acquire a clearer grasp of the earnings volatility risk in the overall bank and its component parts.

This, in turn, provides a basis for determining the proper allocation of economic equity for the bank as a whole and any of its parts and therefore the true rate of return on any given loan, transaction, relationship, or line of business - credit or non-credit.

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