One of the bigger of the big issues about which bankers worry is capital structure determination: figuring out the right mix of debt capital -- or deposits of all kinds, subordinated debt, and so forth -- and equity capital to put behind earning assets.

Currently, most use a combination of judgment and regulatory signals to identify the ratio of equity capital to earning assets at which the positive benefit of decreasing the ratio -- or earning a higher return on equity -- just balances with the negative effect. The downside is greater exposure to the risk that an unplanned shortfall in net revenues -- revenues less noninterest costs -- will cause a collapse in earnings, damage to the bank brand, and subsequent decreases in demand.

A growing group of "advanced" banks use a different framework, which goes by various names. One of the most widely used is risk-adjusted return on capital. Another is value-at-risk analysis.

The key premise of the risk-adjusted return designers is that the balancing guidelines offered by the conventional framework are somewhere between vague and silent about the right way to measure and manage risk, with the result that they really can't tell a bank what the right ratio of equity capital to earning assets is for its business units or itself.

The key aim of the risk-adjusted return designers is to offer guidelines that can tell a bank what this ratio is. But do they succeed in this aim? Their answer, of course, is yes. My answer, however, is different.

Before I turn to why, let's first look at their three guidelines.

First, recognize that "right" means a ratio which, if chosen, would limit to a small target percentage -- say, 0.2% -- the probability that for the bank and each unit the equity capital, or cushion, will get wiped out in the event that a net revenue shortfall pushes the earnings needle significantly into the negative zone. Recognize, too, that for a domestic bank it is some combination of business, credit, and interest-rate risk that exposes the bank and its units to the possibility of large negative earnings.

Second, determine the overall downside risk to earnings for each business unit and then the 0.2% probability floor for negative earnings. After that, roll these floor numbers up in a way that takes into proper account cross-unit diversification effects. Let's say the resulting sum of negative earnings floors turns out to be 7% of the bank's earning assets.

Third, specify the equity cushion ratio as 7%. This is equivalent to telling the bank that if it sets this ratio at 7%, there will be just an 0.2% chance that in the worst-outcome negative earnings will exceed $700 million for every $10 billion in earning assets. Adjust planned earnings to reflect the interest charges implied by this ratio.

Finally, calculate the ROE. The bigger the required cushion ratio, the less this ROE will be. Thus, ROE can be described as risk adjusted.

This clearly represents an improvement over the traditional approach to capital structure management. But just as clearly, there are some significant shortcomings. As a consequence, there are grounds for thinking the equity ratios it produces may not be right.

One is the fact that the framework takes a bottom-up approach to what is a top-down issue. It puts the cart before the horse.

The horse for the corporate bank is determining first the downside variability of consolidated net revenues (given all cross-unit diversification effects on this variability), and then the overall equity ratio therefore necessary to keep consolidated earnings from falling below the 0.2% probability floor. The cart is determining what each unit's equity ratio should be, relative to the overall ratio.

A second shortcoming is the framework's apparent assumption that most or all of the bank's business units are mismatching asset and debt maturities, with the result that interest rate risk must be a key driver of the bank's desired equity ratio. In fact, most banks confine mismatching activities to their treasury units, thus managing away most interest rate risk.

Third, linked to the second shortcoming, is the way the framework handles the relationships among equity capital ratio, interest charges, and risk. When risk-adjusted return is illustrated (for example, by Bankers Trust), the planned level of interest charges, given the level of earning assets, is assumed to be the same for all possible equity ratios. But for successively lower equity ratios, planned interest charges in a matched funding regime obviously get larger and larger. As a result, the probability gets larger and larger so that a particular shortfall in net revenues will cause earnings to go negative. Put another way, the risk of below-the-floor earnings increases not just with increases in downside variability, but with increases in the ratio of debt to earning assets.

The fourth shortcoming, which is linked to the third, is the decidedly odd part risk-adjusted return has written for ROE in the balancing drama. Risk is the star; ROE appears only at the final curtain, when it is given a number.

If the drama is scripted properly, ROE co-stars. It increases, and at an increasing rate, as the equity ratio decreases. Indeed, it is because of this positive effect of financial leverage that banks want to push the equity ratio down as far as they can without exposing themselves to danger.

In short, it appears that any capital structure advice that the current version of risk-adjusted return gives a bank will be questionable at best. Is there a different and simpler framework -- a "revised risk-adjusted return" -- that does better? And if there is, what guidelines does it propose?

There is, and there are two guidelines.

First, estimate from historical data, after eliminating smoothing adjustments, downside variability of net revenues. Second, in the light of this estimate, determine the smallest possible equity ratio that is "safe" by a 0.2% probability standard or any other standard the bank chooses. If this ratio is above what the bank takes to be the regulatory minimum -- say, 5% -- don't go lower; otherwise choose 5%.

If a bank is typical in terms of the ratio of net revenues to earning assets, how low will this safe equity ratio be? Judging from what we know about the consolidated net revenue variability of large banks in general, the odds are high that the bank will decide that the 5% standard gives it -- subject to an important proviso -- the right balance between risk and ROE, given the cost of equity capital.

That proviso, of course, is that the bank will support the balance by pricing individual loans to reflect the best possible readings of their credit risks.

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