Everyone's trying to figure out which banks are most likely to have hard-to-value assets on their balance sheets. I call these "hard-to-value" rather than "toxic" assets because what ever their value might turn out to be they're not like a chemical dump.

New proposals appear every day. They range from setting up a "bad bank" to buy the assets, to running "stress tests" to see which banks would most likely fail/survive simulated worst case scenarios. One way to frame this problem is to assess the probability that any given bank holds a significant percent of hard-to-value assets in its portfolio.

In principle, there's simple a way to calculate that probability. First, select a set of banks. There must be at least three in the set. Then track down two bits of published data: net earned income and market cap. Net earned income is a bank's "revenue" -- what it earns from its performing assets. A bank's market cap is, well, what investors think its worth.

Here's how it works. Look up the revenue and market value of each bank for the last 36 quarters and calculate its market shares -- of value and revenue. Then subtract each bank's share of revenue from its share of value and calculate the standard deviation of the differences over the 36 quarters. Finally, divide the differences by their standard deviation. The result is a standard normal variable (mean 0 and standard deviation of 1). Call it an Asset Quality Index [AQI]. This index has three very useful properties. It's based on just two numbers that offer management very little wiggle-room. It's easy to calculate. And, more important, it's a probability.

The higher the AQI value, the less chance a bank has a significant proportion of hard-to-value assets in its portfolio. The lower the index the more likely the bank is to have them in its portfolio. This chart shows what eight of the countries biggest banks looked like in the 4th quarter of 2008 (click to enlarge):

Wells Fargo Company (NYSE:WFC) is 6.5 standard deviates above the expected value of the AQI. Put another way: using the Student t-Distribution, the probability that WFC has significant hard-to-value assets in its portfolio is less than 0.00003. The Mellon Bank of New York (NYSE:BK) with an AQI of 3.3 -- also is above the expectation. The probability that BK has a significant proportion of hard-to-value assets in its portfolio is 0.004. Apparently, there is nothing to worry about in either of these cases.

Goldman Sachs (NYSE:GS) is in high positive territory pushing the 2 sigma limit. Even so, the chances loom larger. The probability that GS has a significant proportion of hard-to-value assets in its portfolio is 0.07. American Express (NYSE:AXP) is even more problematical. With an AQI of 0.4, the probability AXP has some hard-to-value assets in its portfolio is 0.35. These probably are credit card assets.

Now things get much darker. The chance that J.P. Morgan (NYSE:JPM) has a significant proportion of hard-to-value assets in its portfolio is 0.54. The chance that Morgan Stanley (NYSE:MS) has some of these assets jumps to 0.81. As far as Citigroup (NYSE:C) and Bank of America (NYSE:BAC) go, look out below! The probabilities these two giants have significant hard-to-value assets in their portfolios are 0.98 and 0.99 respectively.

This is a handy, if unexpected, way to assess the probability that any bank has a significant proportion of hard-to-value assets in its portfolio. It might be a good idea to run this analysis on the financial institutions in your portfolio in order to pinpoint the risky ones in your neighborhood.

What do you think? As always your comments are welcome.

**Full Disclosure: I bought shares of Citigroup at a buck fifty and Morgan Stanley at six fifty -- for my grandchildren.**

**Disclosure: **The author is long C, MS. The author wrote this article themselves, and it expresses their own opinions. The author is not receiving compensation for it. The author has no business relationship with any company whose stock is mentioned in this article.