Measuring Risk, Both Expected And Unexpected

Most bankers are now aware that their stock prices are determined not by their reported returns on equity - numbers that the marketplace profoundly distrusts - but rather by their risk-adjusted ROEs. They are therefore making efforts to measure risk at the bankwide, line-of-business, customer, product, and even, in some cases, at the facility level.

As is now well known, risk must be subdivided into two components - expected and unexpected. Adjustments for expected risk should take into account the economic cost resulting from losses that occur with average frequency. Adjustments for unexpected risk should allow for deviations from this average - that is, the volatility of economic losses.

In the credit area, the first type of adjustment requires that banks incorporate into loan prices risk charges that reflect the typical loss, less recoveries, in different loan-risk categories, plus the administrative and interest expenses that occur when these loans fail to perform.

The second type of adjustment requires that banks set aside a portion of their capital to ensure institutional viability when losses become unpredictably large. The cost of this capital, equal to the size of the capital cushion times the amount the bank is required by the marketplace to earn on this capital, should also be reflected in the loan price.

Close, but No Cigar

Oliver, Wyman & Co. finds that while many banks are making laudable efforts to adjust for risk, these adjustments are as yet insufficiently differentiated. As a result, banks continue to misprice loans and miscalculate their returns. The lack of appropriate risk discrimination or gradation is to be found both in the level of risk provisioning for expected loss and in the level of capitalization for unexpected loss.

The consequences of a relatively undifferentiated approach to risk assessment can be illustrated in the following example. Consider two banks, one an undifferentiated and the other a highly differentiated risk assessor. The undifferentiated bank posts risk-provisioning charges that vary quite narrowly, from 50 to 125 basis points. It assigns capital to all loans at one rate, the regulatory standard of 4% equity. Its more discriminating counterpart has risk charges that vary from 10 to 300 basis points. And its capital assignments range from as little as 1% to as much as 15%.

Each bank can book either a low-risk credit, which carries a net interest spread of 50 basis points, or a high-risk credit, which commands a net interest spread of 300 basis points. To which of these loans would the two banks gravitate?

Calculating the Equity Benefit

The undifferentiated risk assessor views the calculus as follows: The low-risk loan is assigned its lowest risk charge of 50 basis points and, like any other loan, a capital charge of 4%. So the revenue of 50 basis points must be adjusted for the fact that 4% of the money needed to fund the loan comes from interest-free equity that displaces borrowed funds.

If the marginal cost of funds equals 8%, then the benefit from using 4% equity amounts to 32 basis points. Therefore revenue plus equity benefit equal 82 basis points. Net of the 50-basis-point risk charge and, say, 10 basis points in operating costs, the income from this low-risk loan sums to 22 basis points pretax and 14 basis points after tax. In consequence, the risk-adjusted ROE (14 divided by 400) amounts to only 4%. The loan is viewed as undesirable.

By contrast, the high-risk credit seems quite attractive. It sports a net interest revenue of 300 basis points. And since the bank assigns the same 4% equity to this loan as it does to all others, revenue plus equity benefit equal 332 basis points (300 plus 32). Net of, say, 50 basis points in expenses (reflecting the obvious fact that it costs more to monitor a high-risk than a low-risk credit) and the bank's highest expected-loss risk charge of 125 basis points, the pretax on the high-risk credit comes to 157 and the after-tax to 102. Based on its view of risk, the bank rushes to book this loan because its ROE amounts to 26%.

A Radical Difference

The other bank sees matters in a quite different light. Striving to allocate capital according to true economic risk, the bank assigns only a 1% capital cushion to the low-risk credit and a 10-basis-point provisioning charge. Thus the pretax amounts to 50 (revenue) plus 8 (capital benefit) minus 10 (expected-risk charge) and 10 (expenses), or a total of 38. The after-tax therefore comes to 25, which, given only a 1% capital levy, of course yields an ROE of 25%, not the 4% calculated by the other bank. This bank quite naturally rushes to book the low-risk credit.

Correspondingly, it spurns the high-risk credit that the other institution found so attractive. That's because, being a discriminating risk assessor, it loads the high-risk loan with its highest provision of 300 basis points and its highest capital allocation of 15%.

Hence pretax income (revenue of 300 plus equity benefit of 120 minus operating cost of 50 and risk provision of 300) equals 70. And an after-tax of 46 divided by 1500 yields only a 3% return.

Which bank is right? On Sept. 12, this writer published an article in this space detailing a new method for assessing loan default probabilities based on stock price movements. This method, whose record for predicting loan defaults has been proved far superior to that of the rating agencies, identifies a range of default probabilities for 5,000 companies that goes from as little as 2 basis points to as much as 20%.

Discrimination Pays

Based on this research, one would have to conclude that a schedule of expected losses that varies from 10 basis points to 300 basis points is more apt to be correct than one that moves from only 50 to 125 basis points. While the above example is obviously hypothetical, it would appear that the more differentiated risk provisioner is probably on the right track, while the less discriminating institution is more prone to err.

And since we know that unexpected losses tend to be proportional, though not linearly proportional, to expected ones, a bank that varies its capital assignments by as much as 14 percentage points unquestionably comes a lot closer to economic reality than one that mechanically applies the regulatory standard of 4%.

Thus the more discriminating lender is more likely to opt for a loan whose risk-adjusted return is high enough to satisfy the marketplace, which, if this situation is broadly generalizable, will respond by bidding up the bank's stock. Indeed, this bank can increase shareholder wealth even if it somewhat undercuts prevailing prices for the low-risk credit, thereby increasing its market share in this loan category. By contrast, the bank whose concept of risk adjustment is insufficiently graduated will probably continue to bid for loans with inadequate returns, causing investors to further discount its stock price.

Changing the Market's View

The point of this exercise is as simple as its homely example. Until banks become as sophisticated in measuring the cost of risk as many have recently become in measuring the cost of loan funds and in assigning the appropriate amount of noninterest expenses to each loan asset, they will not be able to alter the marketplace's rather negative view of the industry's prospects.

Understanding the cost of risk presupposes a methodology for assessing both expected and unexpected losses. It is Oliver, Wyman & Co.'s view that the expected losses of both public and private companies can be estimated from the volatility of the former's stock prices, as indicated in the article of Sept. 12.

It is also our view that the unexpected loss of a loan and therefore its appropriate capitalization can be derived mathematically from (1) its expected loss, (2) the correlation between this loss and those of the other loans in the portfolio (these correlations can, in fact, be deduced from the observable correlations in company stock returns), and (3) the size of the loan in relation to that of the portfolio.

Those banks that investigate this method can acquire the knowledge needed to price efficiently, to identify their more profitable customer and product segments, to differentiate service levels according to profit potentials, to gear compensation packages to these same potentials, and, in the final analysis, to enter or exit whole lines of business.