Krugman is skeptical. The fact that the loans are non-recourse, he writes, would mean that investors would likely take greater risks since their losses are capped, costing the taxpayer dearly. I know... he won a Nobel Prize and I didn't. But he's wrong and I'm going to prove it.

Here's the example Krugman cites:

Suppose that there’s an asset with an uncertain value: there’s an equal chance that it will be worth either 150 or 50. So the expected value is 100.Here is what he means. A bid of $130.50 makes the average outcome of the scenarios $0. That is the breakeven point... a higher bid than that will, on average, result in a loss:

But suppose that I can buy this asset with a nonrecourse loan equal to 85 percent of the purchase price. How much would I be willing to pay for the asset?

The answer is, slightly over 130. Why? All I have to put up is 15 percent of the price — 19.5, if the asset costs 130. That’s the most I can lose. On the other hand, if the asset turns out to be worth 150, I gain 20. So it’s a good deal for me.

In another post, he explains that "two-state numerical examples" are the natural way to think about these things. Really? Just out of curiousity, what would happen if we went to a three-state numerical example?

Huh. When you add a middle scenario, all of a sudden the breakeven point has gone down to $116.28. Of course, in real life outcomes don't isolate themselves into two faraway islands. What if we kept on adding scenarios...

Wow. It looks like if we modelled this more like real life the overbidding Krugman writes about diminishes. If there were an infinite number of scenarios between $50 and $150, as there would be in real life, the degree of overbidding might even be reduced to single digits.

Let's also ask ourselves: is the spread of uncertainty likely to be as wide as Krugman's example? Think about it. There's a 3x spread between the high value and the low value. This would be like saying that a security with a face value of a dollar could as easily cost 25 cents as 75 cents. Remember that investors will have information about the payment history and location and credit history of the borrower, and remember that they have a wealth of prior experience on how similar borrowers have performed before. Isn't it likely they will be able to make far better projections than that? What if we narrowed the scope of uncertainty?

That makes a huge difference. Now the rational investor is only overbidding by just under 5%. But okay, let's say we overshot when we narrowed the spread of the scenarios. After all, no one can really predict economic performance, and that will certainly be a significant variable. Let's widen the scenarios a little to say... 40% on either side. But let's not pretend that there's an equal chance of getting extreme scenarios as opposed to the middle scenarios. Let's weigh the scenarios on a bell-shaped curve, giving more weight to the likelier middle scenarios, and less weight to the unlikelier extreme scenarios:

Still, a rational investor is only overbidding by around 5%. But I hear you say: 5% of a trillion bucks is an awful lot of money. It sure is. But there are other factors we have not considered yet.

First of all, the FDIC loans are low-interest... but they're not no-interest. The government will be making some money on the loans that do happen to perform.

But more importantly, there is a fallacy in our calculations. We're pretending investors are eager to risk capital just for the sake of breaking even. That's crazy. On the day the Geithner plan was rolled out, Bill Gross of PIMCO went on CNBC saying he expected returns in the "low teens." For any investment where the entirety of your capital is at risk, that is the minimum you should expect. So the bids are going to be lower than the breakeven price; they need to factor in their profit. Notice also that profit expectations increase as the range of uncertainty we mentioned above, the risk, increases.

Nor should we forget that it's not cheap to pore over loan tapes and make calculations that are far, far more sophisticated than the ones we've just done. Expenses will be at least 1%... probably more. Lower the bid by that amount. (Meanwhile, our government will have no such expenses.)

Together, these underbidding effects will dwarf any overbidding due to the capped losses. While there is no guarantee that the U.S. will not lose money on this deal, it is far likelier that we will profit. As many economists before, Prof. Krugman has let his theory come untethered from reality.

**Update:**I forgot to decrease the cap amount as the bid decreases! Still, that doesn't change the numbers too much. In the final case, I still have a number just slightly above 5%. I'll update with correct numbers later.

**1:32PM:**The numbers are now corrected.