Wednesday, March 25, 2009

For Übergeeks Only: Why Krugman Is Wrong

A couple of days ago, Paul Krugman wrote a widely cited post where he argued that the Geithner plan would amount to a huge subsidy for banks. The taxpayers, he fretted, would once again be taken to the cleaners. To fill in some background: in the Geithner plan Treasury funds are combined 1:1 with private equity; together they go to the FDIC and obtain a non-recourse loan six times greater than the original principal. Private investors decide how to invest while the Treasury piggy-backs on their expertise, splitting the proceeds with them.

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.

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.
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:
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.


Anonymous said...

Interesting post. I have a few thoughts:

The "correct" underlying price of the security should already account for the return necessary to get someone to hold it. These securities will pay interest and principal, just not the amounts originally envisaged. But if you pay 100 for a security that is paying a coupon of 6% on a face value of 200, you're getting a 12% current return. Even if, e.g., that 6% pay rate drops by .5% a year for four years due to defaults and then you sell at 2/3 of par because the worst risks have been cleared out, you make 13%. Something reasonably close to a 0 expected value, different from "breaking even", should be expected.

Second, there will need to be overbidding, because the bank's marks on these securities are well above your breakeven price. And any premium paid to the seller is exactly offset by a loss to the FDIC on its loan, if you model that side of the transaction, so I don't see how the government is going to make money. In fact the difference between the banks' values and the market's for these securities is far more than 5%. If the program only results in premiums of the magnitude you're talking about here, the market won't clear. Of course, since the premium is purely a function of the leverage , it can be set arbitrarily high, but then you're no longer talking about $50 billion on $1 trillion of assets.

Finally, relying on the "wealth of prior history of how similar borrowers have performed before" is what got us (via the rating agencies) into this mess. Post-2005 underwriting standards and loan structures were fundamentally different from what had come before and we have no idea what the unprecedented massive levels of negative equity among homeowners will do to default rates. I wouldn't count on narrowing the scope of uncertainty too much.

Wagster said...

Thanks, Anonymous. You make some excellent points.

On your first point... I have a feeling this is a definitional difference on what "correct" price is. My point is just that there is a profit + expenses margin, and that my hunch is that the overbid premium will be less than that. I'm not denying that there is a subsidy, just that the Treasury will *probably* profit despite it.

On your second point, I agree that the market won't clear. There will be lots of sellers left on the sidelines. Why would the banks sell if it left them insolvent? They will prefer to continue their zombie ways, hope for a miracle down the road, and Geithner will have to think of some other solution. But at least at that point we'll have a better idea of the valuation of this stuff. The way I see it, when your computer doesn't start, you try the easiest solution first... is it plugged in? When you've exhausted the easier solutions, then you take it to the shop. (Tangentially, let's not forget that the FDIC will be making some returns on the portion of their loans that do perform.)

As to your last point, I acknowledge that the numbers-crunchers have not dressed themselves in glory recently. But we have three years experience with a falling market. I have no professional experience with this, but my wild-assed guess is that 40% uncertainty on either side, as with my last scenario, is probably not too much to ask.

Finance Guy said...

YES! Delighted that someone else got this point about the essential flaw in Krugman’s model. Krugman parries that academic economists simplify all the time blah blah binomial etc. He's right, as long as your simplification broadly and conceptually conforms to reality. But Krugman’s doesn’t at all.

The problem: Krugman creates a very simple model to illustrate how much bidders will overpay. Any model, no matter how simple, must conceptually align with the thinking of bidders (after all, they do the overpaying, not the guy holding the assets).

So how will they arrive at a bid? Krugman’s model (implicitly) assumes they will look at the outcome as a roulette wheel: black I win (150) red I lose (50). Following that thinking, they bid slightly more than 130. Now here’s the beauty of his mistake: Even if your assets actually do end up worth either 150 or 50 (let’s say, by some magic bit of strange chance), he’s still wrong. Why? Because the BIDDERS (the overpayers) don’t know that. They’ll still bid as if they’re in the real world, and the eventual value of the asset will lie along some bell curve (as you suggest).

So the only way Krugman is right: if the auction is such that the bidders believe at the outset that the value will end up either 50 or 150 and not anything in between (or, to be more precise, they believe it will end up at either end of two extremes)! Krugman’s a really smart guy; I think he just got a bad donut with his morning coffee or something.