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Bank of America Made \$168 Million Last Quarter, More or Less

A bank's earnings are a quantum event; they are entirely probabilistic, and the answer you get depends on who's doing the observing.

Bank of America reported earnings this morning, and here is your fun quiz on those earnings. It has one question. The question is, was Bank of America's income last quarter:

1. more than zero, or
2. less than zero?

I mean, right there in the headline of the earnings release, you can see that Bank of America made \$168 million last quarter, which is a positive number with nine whole digits. It had to pay \$238 million of dividends to its preferred stockholders, though, so after those dividends it lost \$70 million, a negative number. So right there it's a mess.

How did it make that \$168 million or whatever? Well, you know, it's a bank, it makes loans and stuff, so it gets paid some interest. Specifically it got paid \$12.9 billion in interest last quarter. Also it charges fees for credit cards and mergers or whatever; those fees probably came to around \$8.1 billion. 1 And it made about \$2.9 billion in various trading-related ways, selling bonds and stuff, and other miscellanea. 2 So total revenue was about \$23.8 billion. 3 So Bank of America's earnings, under generally accepted accounting principles, were about 0.7 percent of its total revenue.

Or put another way: Earnings is the change in value of your assets, minus the change in your liabilities. Bank of America has about \$2.1 trillion of assets. (You gotta keep the m's and b's and tr's straight here.) So that \$168 million of income was 0.008 percent of assets.

How much precision do you think that \$168 million number has? Like, if I made \$168 million, I would know about it. Depositing \$168 million in my bank account would be a dramatic change to my bank account. If you asked me how much money I had in my bank account, I would say "\$168 million!" though there would probably be more exclamation points. I would be wrong -- I have some money in my bank account now, so adding \$168 million would produce a number that is ever so slightly more than \$168 million -- but I'd also be close enough for any reasonable purposes. The money I have in my account now would be a rounding error.

Bank of America's earnings are a rounding error. If Bank of America's measurement of its revenue was off by one percent, then that would more than wipe out (or double) its net income for the quarter. If Bank of America's measurement of its assets was off by one percent of one percent, then that would more than wipe out (or double) its net income for the quarter.

Is it conceivable that Bank of America's measurement of its assets could be wrong? Well, as of June 30, Bank of America had \$27.7 billion of "assets and liabilities where values are based on valuation techniques that require inputs that are both unobservable and are significant to the overall fair value measurement," a technical term meaning that Bank of America takes its best guess about how much those assets are worth. 4 Again: If that guess was off by one percent, that would more than wipe out (or double) Bank of America's net income for the quarter.

Or: Bank of America has \$891.3 billion of loans on its balance sheet. Some of those loans will go bad. Bank of America currently expects that about 1.69 percent of them, or \$15.1 billion worth, will go bad, so it reduces its assets for accounting purposes by \$15.1 billion. 5 If in fact Bank of America should have increased that number to 1.72 percent, that would wipe out its net income for the quarter.

I submit to you that there is no answer to the quiz. It is not possible for a human to know whether Bank of America made money or lost money last quarter.

None of this is meant to make fun of Bank of America, really. This is true of every bank, every quarter, to a greater or lesser degree, 6 though usually their earnings are a bit more distinguishable from zero. A bank is a collection of reasonable guesses about valuation. It is a purely statistical process. There is no objective reality. At best, there is a probability distribution, a reason to reject the null hypothesis with some level of confidence. If a \$100 billion bank announces \$5 billion of earnings this quarter, there is a high (not 100 percent!) probability that it made more than zero dollars. If a \$2.1 trillion bank announces \$168 million of earnings, that probability is like 50.1 percent. Did Bank of America make money last quarter? Maybe! It's an ever-so-slightly biased coin flip.

And that's ignoring the accounting thing! In addition to being a collection of guesses about valuation, a bank is also a collection of conflicting accounting regimes. Even if you assume that all of Bank of America's guesses about valuation are 100 percent correct, you can't really answer the quiz. Like, right in the headline, there's the \$168 million in GAAP net income, but also a loss of \$0.01 per share -- or negative \$70 million of income applicable to common shareholders. Which should you care about? Both? Neither?

After those two conflicting numbers on the Consolidated Statement of Income, you can turn the page and get the Consolidated Statement of Comprehensive Income, which is more comprehensive. (But shorter!) It has a different number: Bank of America's comprehensive income was negative \$636 million. Basically the difference comes from the fact that banks have three different types of assets:

1. Mark-to-market assets: If their value goes up (down) during the quarter, that's income (loss) for the bank. This includes most of the \$27.7 billion of assets valued based on unobservable inputs, as well as lots of more regular trading assets.
2. Available-for-sale assets: If their value goes up (down), that's not net income (loss), but it is comprehensive income (loss) on the next page.
3. Held-to-maturity assets: If their value changes during the quarter, the bank can mostly ignore that for all purposes. 7 There are a lot of these assets. In particular, loans tend to be held to maturity. Remember there are \$891.3 billion of loans.

So if you count the changes in value of some of Bank of America's assets (along with the fees and interest and so forth that are more straightforwardly "income"), you get income of positive \$168 million, or negative \$70 million, depending. If you count the changes in value of some more of those assets, you get negative \$636 million. If you count the changes in value of all of Bank of America's assets, you get a number that hahahahahahaha come on, you are not going to find in any accounting statements, that is crazy. That is the most secret of secret sauces, plus it's not like Bank of America knows that number either. 8

So you get at least three numbers -- positive \$168 million, negative \$70 million or negative \$636 million -- using just U.S. generally accepted accounting principles. But why stop there? Other accounting principles are sometimes accepted. There is tax, for instance. Bank of America had \$663 million of tax expense this quarter, on \$831 million of pre-tax income, which looks a bit like an 80 percent tax rate. This is not because the tax rate applicable to Bank of America is 80 percent. It's because tax accountants get a different number for Bank of America's income than GAAP accountants do. For instance, if Bank of America paid a 35 percent tax rate, then its pre-tax income, for tax purposes, was \$1.9 billion, and its post-tax income, under tax accounting, was \$1.2 billion. Positive \$1.2 billion. Why not. 9

Or regulatory capital. Bank of America's common equity tier 1 capital went down by \$1.6 billion this past quarter. Some of that is dividends -- it accrued about \$526 million in common dividends -- but most of it is not. It's just that regulatory capital and GAAP measure income differently in some respects. And the same in other respects. This is very confusing. It's so confusing that Bank of America got it wrong by \$4 billion earlier this year. Or by \$2.7 billion. Depending how you count!

So even ignoring valuation questions, Bank of America's net income was between negative \$1 billion and change (capital accounting) and positive \$1 billion and change (tax accounting), with the +\$168/-\$70 million GAAP numbers clustered around the rough midpoint.

A bank's earnings are a quantum event; they are entirely probabilistic, and the answer you get depends on who's doing the observing. You make some guesses with some degree of statistical likelihood, and then you apply one of a half-dozen accounting regimes to the guesses, and you get a number, and then you're like, ooh, look at this number, it's so numeric.

But it's not a thing in the world. It's just the output of applying your rules to your inputs. But your inputs are fictions, and your rules are fictions, so it's very silly indeed to treat your output as a fact.

A bank is a collection of contracts that provide for future cash flows, and the value of those contracts depends on your guesses about the future cash flows. 10 The rules give you some guidance about how to guess -- with different rules providing different guidance for different purposes -- and then you get some smart people to make the best possible guess. A bank's income statement -- and balance sheet -- is just a set of social conventions about predicting the future. How much money did Bank of America make in the second quarter of 2007? It says here \$5.7 billion. But how good did the predictions about future cash flows embedded there turn out to be?

Isn't that great? 11 What you make of it depends on your priors, on the story you bring to banking. There's a sense in which it supports the Anat Admati story: If a bank's earnings and capital are just estimates of a statistical distribution, you want it to have lots of (estimated) capital, so that its odds of having negative (actual) capital are very low or zero. But there's also a sense in which it supports the story that the aim of banking is to conceal risk: The process of taking all of a bank's contracts, ignoring most of them, estimating the change in value of the rest, summing the estimates and producing a single (preferably positive!) number that you call a bank's "earnings" is sort of a soothing process. It might even persuade a casual observer not to look too closely at the roiling uncertainty that underpins that number. Because banks are magic, and if you look too hard at how the magic happens, you might stop believing in it.

This column does not necessarily reflect the opinion of Bloomberg View's editorial board or Bloomberg LP, its owners and investors.
1. Adding "Card income," "Service charges," "Investment and brokerage services" and "Investment banking income" from page 4 of the supplement. Absolutely no science here; those things are not all fees by any stretch, but we're simplifying.

2. Again that's just adding categories from the supp -- "Equity investment income," "Trading account profits," "Mortgage banking income," "Gains on sale of debt securities" and "Other income" -- without any claim that it's "right."

3. It reports net revenue of \$21.2 billion, which is net of interest expense.

4. Comparable numbers for this quarter aren't available yet, but, you know, it's not vastly less.

5. I mean, that's its provision for credit losses, which is not quite the same thing as the percentage of loans it expects to go bad.

6. So JPMorgan had a robust \$5.6 billion of GAAP income this quarter, on \$2.5 trillion of assets. Its asset value would have to be wrong by a whole quarter of a percent to wipe out that net income.

7. Ha, very loose, there are other-than-temporary impairments and so forth. More on this topic here.

8. Which is not really their fault; it's not like regular businesses mark all their assets to market either.

9. This oversimplifies dramatically. For one thing, BofA pays income taxes in many jurisdictions. For another, even better, thing, the \$663 million in its financials is not its tax for the quarter. It's not the check it wrote to the IRS. It's its GAAP tax for the quarter. It's tax accounting filtered back through GAAP accounting. In my limited experience, GAAP tax accounting is more than twice as maddening as GAAP accounting, or tax accounting, on their own.