This is a second attempt to explain in clear english and with a little arithmetic what is so bothersome about Paul Krugmans attack on the Obama/Geithner plan. Krugman makes a very strong statement that he backs up with hocus-pocus.

Leave on one side the question of whether the Geither plan is a good idea or not. One thing is clearly false in the way it’s being presented: administration officials keep saying that there’s no subsidy involved, that investors would share in the downside. That’s just wrong. Why? Because of the non-recourse loans, which reportedly will finance 85 percent of the asset purchases.

Ok, so Administration officials are lying about a plan that will actually subsidize banks. How do we know that? Because, according to Krugman, a little arithmetic shows that a collection of loans or securities that should by all rights be worth $100 each can be purchased for as much as $130 each by a smart buyer who breaks even on the deal by exploiting Federal loans for the purchase. But the numbers don't really show that at all.

A huge number of assumptions are packed into one sentence framing the issue.

Let me offer a numerical example. 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.

For now, pretend "expected value" means "average". Krugman is supposing that there is a collection of "assets" which, somehow we know to be either worth $50 or worth $150 with an equal chance of either. The investor is going to use this knowledge to game the system and take the sucker FDIC to the cleaners according to Krugman.
Here's the logic. I buy two assets and get one good one and one bad one. The actual value is $50+$150=$200. If I bid $130 each, the FDIC lends me (5/6) of the price, about $108.3, the treasury and I invest $10.8 each,  then on the good one I make a profit: I paid $130 and got back $150 which is enough to pay back the loan to the FDIC, get back my investment and keep $10 extra. On the bad one I lost everything - my entire investment. So I pretty much break even on the deal, but the poor FDIC got hammered recovering only $50 from their $108 loan. Sucks to be them. Great to be the banker who just got paid $260 for assets worth $200. But is this really going to happen?

  1. Krugman is modeling the plan as a sale of individual assets, but that is not the plan. The plan is an auction of pools of assets and the pool structure protects the FDIC a lot. Suppose that the Feds did not permit you to buy a single asset but made you buy pools of TWO assets each. If you price each asset at $130, you have to buy a pool for $260. In this case there is a single FDIC loan for 5/6 of $260 which is about $216.  This is key: one loan of $216 not two loans of $108. Whenever a good asset is packaged together with a bad asset the FDIC gets nearly its entire loan back - the value of the pool is $200, and the FDIC takes every penny to end up with a loss of just $16 while you lose over $20. Sucks to be you. If we then go to a  asset pools with 4 assets each, and the pools will be enormous not just 4 assets, things get even rosier for the FDIC. This table shows how 16 pools would be distributed if we assume things are random. The last column tells how many pools of this type (with that many good and bad assets) would be in the 16 pools.

    good assetsbad assetsValuePools

    With this set of pool, the break even bid is $105 - a 5% subsidy to banks if we accept the rest of the silly premise and still have expected value of $100.

  2. Ignoring pools, how likely  is it that the Treasury plan will start with an auction of a large number of apparently identical assets, 50% of which are worth 3 times what the other 50%. Because the 3x values is no accident, if bad and good assets are closer in value, the break even point changes dramatically. For example, if bad assets are worth $80 and good assets are worth $120, then the break even point is $104. If assets are pooled by 4, then the safe bid is $100.20 - a big 2/10 of a percent subsidy to the banks.
  3. If the good and bad assets have such different values how is it that they won't be distinguishable by either the Feds or another investor? Why a second investor? Because if the second investor has a good reason to believe the good asset is good, the second investor will happily bid say $140 for it so of our 2 bids at $130 each, we will only succeed on the bad asset - losing everything.
  4. What is the motive of the investor to take a risk to break even? Because if the investor is unlucky and gets 2 bad assets (more on that below) or has incorrectly forecast value (maybe the good ones are worth only $130) then its easy to lose money here - and these assets may have to have to be held for a long time to get returns anyways. Investors are more likely to bid low to increase their, you know, profit. Krugman's model is based on the idea that the goal of the investor is to win the auction, but the goal of the investor is actually to  either make a lot of money or not lose any money. Low bids works here.
  5. Does the investor really not understand what "expected value" means? Expected value of $100 does not mean that if you buy 2 of these assets one will be good and one bad. The probability of a flipped coin landing heads is 50%.  Suppose we have a bet where I win $2 on heads and lose $1 on tails. Then the "expected value" of flipping the coin is $0.50 (h/t Reino) - a great deal for me. But I just flipped a penny 4 times (I really did) and got 3 tails and one head - I lost $1 (no you can't have it). What's wrong? Am I cheating myself? No. The "expected value" is something we expect if we can keep trying until the probabilities beat down random variations. "Expected value" is the average eventually (or in the limit). If I can keep flipping the coin, eventually I'll break even. So for the investor to use the scheme Krugman is proposing, he or she has to have confidence that there will be enough assets purchased to reach the average. That's a bet that AIGFP might have taken, but presumably AIGFP will not be allowed to invest on these (I hope!).
  6. This is an auction, not a coin flip. The investor has to take into account that other, maybe luckier, investors are also bidding. If Investor A is just randomly buying, hoping to live on the expected value, and Investor B is picking, say, 3 good ones to every bad one, Investor B is destroying the distribution by removing more good assets than bad  assets. Suppose there are 10 assets, 5 good and 5 bad. If Investor B buys 3 good ones and one bad one, then there are 2 good and 4 bad assets left for Investor A and the "expected value" for A is now just over $80 , not $100. In fact, Investor B can make a profit buying these things for $120+ while A will lose money on $80.

So Krugman's arithmetic shows a highly unlikely possibility for ripping off the Feds. And the possibility of ripoff also depends on all sorts of unknown details. For example, we don't know how much the FDIC will charge for its loan insurance but we do know it will charge and that is something not accounted for in the model. We don't know how vigilant the FDIC third party evaluator will be, but we do know there will be one. We don't know how many asset pools will appear - the banks could quite possibly just chicken out of offering anything. Of course, there is a subsidy built into the plan, a subsidy of the investors but it's hard to see how that translates into a subsidy of the banks or a ripoff of the government (we share any profits). Maybe there is some detail I don't know or maybe the actual auctions will be done in such a way as to allow banks to indirectly buy their own assets (that would be a ripoff of the taxypayer and it is forbidden in the plan). But Krugman's model does not give any substantial reason to believe the plan is horrible.

In the end, what bothers me about Krugman's argument is that it really depends on the assumption that Geithner/Obama's goal is to find a way to give money to banks. If you start from that you can find a statistical model that supports you - just as AIG FP and Moody's found a statistical models that supported them. There is always a model which will tell you what you want to believe.

UPDATED. Two people who actually know some economics agree

Originally posted to citizen k on Sun Mar 29, 2009 at 04:12 PM PDT.

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