Bad Arithmetic Proliferates

Wow. That was my reaction on waking to a dreary Hong Kong morning, logging onto the Internet, and finding that Paul Krugman's flawed model on overpaying for toxic bank assets had grown wings. A blog site dangerously named “self-evident” had taken a Krugmanesque approach to show how taxpayers could get shafted under the Geithner plan. Scarily, the link appears to be spreading like wildfire through the blogosphere.

Okay, I don't like the Geithner plan either. But at least we should get the criticism right.

This blog entry, penned by Nemo, does have an admirable cleverness in that it tries to impale the Treasury Department on its own “Geithner Plan for Dummies” fact sheet. The Geithner plan of course proposes a partnership of public and private funds to buy the bad assets clogging up U.S. bank balance sheets. Here's the quick-and-dirty version of the Treasury Department example of how the program would work:

A private investor wins the bid for a pool of mortgages with a bid of $84 (of the face value of $100). The FDIC guarantees $72 of financing. Of the rest, the government puts up half ($6) and a private investor half ($6).

Now here’s Nemo:

Let’s flesh this out by repeating it 100 times. So say a bank has 100 of these $100 loan pools. And just by way of example, suppose half of them are actually worth $100 and half of them are actually worth zero, and nobody knows which are which. (These numbers are made up but the principle is sound. Nobody knows what the assets are really worth because it depends on future events, like who actually defaults on their mortgages.)
Thus, on average the pools are worth $50 each and the true value of all 100 pools is $5000.
The FDIC provides 6:1 leverage to purchase each pool, and some investor (e.g., a private equity firm) takes them up on it, bidding $84 apiece. Between the FDIC leverage and the Treasury matching funds, the private equity firm thus offers $8400 for all 100 pools but only puts in $600 of its own money.
Half of the pools wind up worthless, so the investor loses $300 total on those. But the other half wind up worth $100 each for a $16 profit. $16 times 50 pools equals $800 total profit which is split 1:1 with the Treasury. So the investor gains $400 on these winning pools. A $400 gain plus a $300 loss equals a $100 net gain, so the investor risked $600 to make $100, a tidy 16.7% return.
The bank unloaded assets worth $5000 for $8400. So the private investor gained $100, the Treasury gained $100, and the bank gained $3400. Somebody must therefore have lost $3600…
…and that would be the FDIC, who was so foolish as to offer 6:1 leverage to purchase assets with a 50% chance of being worthless. But no worries. As long as the FDIC has more expertise in evaluating the risk of toxic assets than the entire private equity and banking worlds combined, there is no way they could be taken to the cleaners like this. What could possibly go wrong?

In an update, Nemo admits that his example is “totally unrealistic.” Further, he says, “It was not meant to be realistic; it was meant to be illustrative.”

But what does it illustrate? Consider this excerpt: suppose half of them are actually worth $100 and half of them are actually worth zero, and nobody knows which are which. He claims his principle in constructing the example is basically sound because no one knows what these assets are worth. True, but -- BIG but -- that’s different from saying they’re all worth full value or nothing and there's absolutely no way of knowing which are which.

Here’s the type of “real world” that Nemo’s auction would illustrate well:

Buyers for the assets bid blindly. Either they aren't allowed to review what they are bidding on (sorry, no peeking), or it’s impossible to make ANY estimation of their value (think about it: if you have no chance of telling the difference between a $0 and $100 asset, you’re basically in the Land of Perpetual Fog). So they essentially buy a lottery ticket. Joe Hedge Fund says, “I’ll put a $6 investment on 35-46-91,” knowing he’ll either profit big (it’s worth $100) or go bust (it’s worth nothing).

Absurd? Hugely. This doesn't illustrate anything real world at all. If you want to come up with a model for overpayment, you would do best to start with a few realistic baseline assumptions about how the bidding will work. Motives of private investors are simple: they want to make money, and the more of it the better.

So they might craft their bid by first running economic scenarios, tweaking variables a little this way and that way. In the spirit of Nemo’s example, let’s say they run the scenarios 100 times on an asset worth somewhere between nothing and $100. And let's say its true worth, known only to God, is $50.

One hundred data points result. Most are likely to be clustered around $50. The farther out you go toward the extremes ($0 and $100), the fewer points you find. Let’s say that between $17 and $83 you find 90 percent (and that’s likely a conservative figure) of the outcomes.

No Wall Street investor worth his salt would bid anywhere near $84, knowing that there’s a 90 percent chance he’s overpaying, based on his own number-crunching. (Note: This assumes that taxpayers and private investors share profits and losses, let’s say 50-50, in BOTH directions, at least until that FDIC backstop kicks in on the way down).

Is there a simple way to illustrate the magnitude of the real overpayment problem? I don't think so (it’s fairly sophisticated unfortunately), but the takeaway seems to be that
(1) as long as the profit gains (and losses) are divvied fairly and
(2) there aren’t ways to “game the system”
overpayment will be modest, maybe a few percent?

The Geithner plan’s real problems lie elsewhere, such as with the chasm that currently exists between the market price for these assets and what the banks have booked them for. The plan risks being a high-profile dud, with blaring trumpets and scurrying about at the front end ... and no assets at all changing hands after all is said and done.