Despite the substantial improvement in the bank stock market since last summer, that market continues to signal difficulties for many institutions. While the mean of values has risen, so too has the volatility of values around the mean, reflecting continued investor confusion and concern over the health of the financial sector.

The KMV Corp. of San Francisco has built a model, perhaps the best in its class, that assesses default probabilities. The model measures the amount of negative equity volatility required to depress the value of any given bank's assets to the point where it just equals the amount of the current debt, which is the point of default.

According to the model's January reading, the expected probability of default in the riskiest quartile of those global banks with assets of more than $75 billion, which had risen from 17 basis points in July 1998 to a peak of 33 basis points in September, fell to 24 basis points in January 1999, still some 40% above its level of six months earlier.

The default likelihood of the next 50% of global big banks doubled, from 9 to 18 basis points, from July to September before settling back only modestly, to 15 basis points in January. And the default likelihood of the least risky quartile of institutions moved from 4 to 10 basis points and then dropped to 8 basis points during the same six months. Clearly, default expectations, while down from their late-summer levels, remain quite elevated.

There are 15 U.S. banking institutions among the group of global entities with assets of more than $75 billion. How have these fared? On the whole, better than their European and Asian brethren and, in some cases, spectacularly. BankAmerica Corp., for example, dramatically pared its loss probability from the September 1998 peak. It now sports a default frequency of only 6 basis points, which ties it with Fleet Financial as arguably the second- and third-safest big banks in the country.

According to the KMV model, National City Bank of Cleveland is currently the country's safest, with a loss probability of only 5 basis points. That default frequency probably merits an AA rating, which National City gets from one rating agency but is being denied by others that are perhaps a bit laggard.

Others among the biggest banks have also done well, but a notable few still need considerable improvement. Indeed, three show default propensities high enough to merit ratings that are less than investment grade.

It can be argued persuasively that most of these 15 banks need an AA rating in order to maximize their opportunities in the counterparty business. What would they have to do to secure it? Two obvious options suggest themselves: raise more equity to support the level of current riskiness or reduce the level of that riskiness.

Let's consider the equity option. How much capital would it take to reduce the default probability of the other 14 U.S. banks to that of the safest, National City? In total, these 14 would need to raise their market capitalization by some $240 billion, or 42% of their January total.

For institutions like Fleet and BankAmerica, which, as noted, have default likelihoods almost as low as National City's, the amount to be raised would sum to less than 5% of current capitalization. Five banks would have to raise capital equal to between 40% and 60% of their current total, and four institutions would need to almost double or more than double their present market equity endowments.

It seems that perhaps two-thirds of the 14 banks are recapitulating the classic pendulum movement. In the late '80s they were seriously undercapitalized. By the mid-'9Os, they had become overcapitalized. And by the late '90s they are, once again, seriously undercapitalized.

If the equity option proves unpalatable, banks that aspire to an AA rating can always reduce their risks, thereby obviating the need for extra capital. Two risk factors stoke the current upsurge in default frequencies: a rise in leverage and an increase in the volatility of bank asset values.

In the KMV methodology, the volatility of bank asset values is an inferred magnitude, representing that portion of equity volatility which is not explained by observed changes in leverage.

During a good part of 1998, whatever bank-investor dissatisfaction existed was traceable in large measure to the heady rise in bank assets rather than to any growth in uncertainty over the future value of these assets. In late summer, however, asset volatility began rising: One standard deviation from the mean of values rose from 4% to 5% and, at some banks, even to 6%.

One method of attacking both the leverage and the asset-volatility problems is to sell loans, or pieces thereof (especially large commercial obligations, which are generally quite fungible). Sale lightens footings, and structuring the sale in such a manner as to eliminate or reduce exposures that are most closely correlated with those remaining in the portfolio reduces the bank's average loss correlation, thereby damping asset-value volatility.

A second risk-reducing approach is not necessarily to sell the loans but only the risks embedded in them to investors that, for one reason or another, are "short" these types of risk. This method involves the use of credit derivatives, about which much is said but little is understood.

Many banks are reluctant to use credit derivatives either because of lack of familiarity or because of unwillingness to surrender a portion of their spreads. Yet by giving up some return, banks can often reduce risk more than proportionally, thus raising their return per unit of risk-the variable that, over any meaningful time frame, determines their stock price.

A third method of risk reduction is to restructure the bond portfolio in order to improve diversification by both increasing the number of obligors as well as by once again offsetting loss correlations in the book of funded and unfunded loans. This approach is arguably the most palatable of the three and, as such, will form the subject of our next article.

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