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Krugman and Sachs probability theory (with Table)

by rootless2 Sat Mar 28th, 2009 at 09:54:08 AM EST

Krugman and Sachs make an expected value argument as if each asset was covered by a non-recourse loan. But the Geithner plan is based on pools. Let use Krugman's numbers of $100 face, $50 bad, $150 good with an even distribution. If you are able to assure 50/50 distribution, then $130 is investor break even since the investors 1/12 investment of about $10 makes $10 profit on the good assets and loses $10 on the bad ones. I'd say that nobody would be stupid enough to make investments on this type of basis, but reliance on Moody's AAA ratings convinces me otherwise. However the loans are not being sold individually, but in pools. If we minimally pool in sets of 4 then the investor only earns profit on sets with majority good loans and loses money on the even and majority bad loan sets. Binomial distribution then tells us that the break even bid is $105 (oops!)

Here is the calculation using Krugman's assumptions, but supposing that assets are pooled in groups of 4. If we purchase at 105.6, Each pool costs 4*105.6 = 422.4 the FDIC loan is 5/6*4*105.6 = 352 the investor puts in 1/12*105.6*4 and the Treasury matches The first column has the purchase price The second column has the number of good assets in the pool the third is the net equity left over when the FDIC loan to the pool is repaid. The fourth is the investor return from the pool minus the original investment (the most the investor can lose is 4times the investor equity per asset). The fifth column is the frequency of pools with that number of good assets according to the binomial distribution. And the final is the investor result for pools of that type. So with 16 pools, the investor must bid under 106 to expect to break even, granting Krugman's idea of an investor as someone using Moody's theory that previous performance is a guaranty of future results.

4 248 88.8 1 88.8
3 148 38.8 4 155.2
2 48 -11.2 6 -67.2
1 -52 -35.2 4 -140.8
0 -152 -35.2 1 -35.2
Thanks to Migeru for posting the link to Krugman,

Links and quotes from Krugman and Sachs would be useful...

You're assuming everyone is right up to date on this discussion.

by afew (afew(a in a circle)eurotrib_dot_com) on Sun Mar 29th, 2009 at 05:00:13 AM EST
See Krugman's Geithner plan arithmetic (March 23, 2009)
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.

Most economists teach a theoretical framework that has been shown to be fundamentally useless. -- James K. Galbraith
by Migeru (migeru at eurotrib dot com) on Sun Mar 29th, 2009 at 05:03:30 AM EST
[ Parent ]
The peculiar ideological contradictions of this moment of time involve an utterly orthodox neo-classical economist, propounding exactly the kind of silly statistical models that got us into this mess being regarded as the Prophet of the left!
by rootless2 on Sun Mar 29th, 2009 at 10:33:41 AM EST
[ Parent ]
... orthodox economist. Why, he won a Bank of Sweden Prize in Honor of Nobel, for work involving making a slight novel set of assumptions unanchored in reality and working out the mathematico-logical implications of those assumptions, and so clearly he is a heterodox firebrand.

I've been accused of being a Marxist, yet while Harpo's my favourite, it's Groucho I'm always quoting. Odd, that.
by BruceMcF (agila61 at netscape dot net) on Sun Mar 29th, 2009 at 05:58:54 PM EST
[ Parent ]
Krugman self-servingly links to a much, much better discussion in a later post: Great minds (March 23, 2009)
Felix Salmon links to a post by Nemo offering a numerical example of the subsidy provided by the "Geithner put." I like it -- because it's almost identical to my own example. That's not a criticism, by the way: the natural way to think about these things is in fact in terms of simple two-state numerical examples.
Here are the links to Nemo's articles on the Geithner plan.

self-evident » The "Geithner Put", part 1

Step 1: If a bank has a pool of residential mortgages with $100 face value that it is seeking to divest, the bank would approach the FDIC.

Step 2: The FDIC would determine, according to the above process, that they would be willing to leverage the pool at a 6-to-1 debt-to-equity ratio.

IMHO, if a bank approaches the FDIC with a pool of residential mortgages that it is seeking to divest, the FDIC should forthwith add the offending bank to this list.

self-evident » The "Geithner Put", part 2

Step 1: Treasury will launch the application process for managers interested in the Legacy Securities Program.

Step 2: A fund manager submits a proposal and is pre-qualified to raise private capital to participate in joint investment programs with Treasury.

Step 3: The Government agrees to provide a one-for-one match for every dollar of private capital that the fund manager raises and to provide fund-level leverage for the proposed Public-Private Investment Fund.

This one is about making (hedge) fund managers work for the treasury as if their skill set were critical to getting us out of this mess.

Then he addresses the kinds of criticism of his first post that rootless2 presents in this diary

self-evident » Fun with uniform distributions

(Update: If there are too many numbers and equations below, Mike at Rortybomb has created a fantastic post illustrating the principles graphically. And he even uses lognormal distributions like a real financial engineer.)

In my earlier post on the "Geithner Put", some people objected to my model as unrealistic.  Which is true.  So, using ideas from Andrew Foland (via private mail), I decided to grind out the math for a uniform distribution. Yes, a Gaussian might make more sense, but I doubt the answers would be all that different.  And besides, that might not lead to a nice closed-form solution.

Anyway, here is Andrew's model.  Assume lots of identical assets.  Assume each has an unknown value uniformly and independently distributed between m-a and m+a.  In other words, m is the average value and 2a is the range of possible values, and everything in the range is equally likely.  Let k be the "leverage factor"; i.e., the fraction of the purchase price that consists of equity.  So for 6:1 leverage, k is 1/7.

And finally

self-evident » On bags and their holders

OK, so we know that high-leverage non-recourse loans may result in the lender losing a lot of money to the borrowers. The transfer is large when the leverage is high and when the value of the assets is very uncertain. The transfer is largest when the possible outcomes are heavily weighted toward the extremes; what statisticians call "fat tails" or "platykurtosis". (If these terms mean nothing to you, relax; I am just throwing words around that I barely understand myself. This is a blog, after all.)

Perhaps the leverage and probability distributions are such that there will be no massive subsidy. More sinisterly, perhaps the transactions will not be at arm's length, and the banks (and in particular, their creditors) will effectively be both the buyers and the sellers fleecing the FDIC/Fed, and the whole point of this complicated structure is to hide this from the average person. Interfluidity has an excellent piece espousing this view. I am not quite so cynical as to think he is right, but nor am I so trusting as to think he is wrong.

Regardless, we know that the FDIC and Federal Reserve are making these loans. So what happens, exactly, should one of these organizations lose a lot of money?

Most economists teach a theoretical framework that has been shown to be fundamentally useless. -- James K. Galbraith
by Migeru (migeru at eurotrib dot com) on Mon Mar 30th, 2009 at 04:23:24 AM EST
[ Parent ]
so the result is that until we see the actual terms of sales and actual items on sale, we have no idea. Which was my objection to Krugman in the first place. His reasoning depends on the assumption that Geithner wants to subsidize banks and then, via some weak math hand waving arrives at the conclusion that Geithner wants to subsidize banks.

if you assume uniform distribution, MANY assets, and big value gaps, then it is possible that the auction may be a disaster, but that's not the same as proving that the auction is a ripoff.

by rootless2 on Sat Apr 4th, 2009 at 04:06:11 PM EST
[ Parent ]
by rootless2 on Sun Mar 29th, 2009 at 09:30:28 PM EST

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