The Geithner Plan: Quick Numerical Example

Calculated Risk links to video of Austan Goolsbee of the White House Council of Economic advisers, discussing how the Geithner plan aligns the incentives of the public and private sector participants.  I had dubbed this idea a fib but Goolsbee makes it sound plausible: “if the private guy makes money, the government makes money. If the private guy loses money, the government loses money.”   CR links to an example that explains how this plan could still see the private guys make money and the government lose money but it doesn’t explain how the price gets set, which is sort of the crucial issue.  So, here’s a simple numerical example that shows how the price gets set.  The point is probably pretty obvious, but I found it self-instructive to work through the figures.

The two keys to understanding why public and private incentives are not aligned are (i) Assets with uncertain payoffs will be auctioned off in small lots, so private investors can (and will) purchase many different lots (ii) The asymmetric incentives such that private investors get a higher rate of return on the investment in the cases when the assets deliver a positive return.

As described here, the conditions of the Geithner plan are a bit different than described in my earlier post. The government will put up 93 percent of the funds, six-sevenths in the form of debt with the remaining one-seventh equity component equally split between the government and private investors.

Now consider the case of a bunch of ex-ante identical assets, each of which pays off either zero or 100 with equal probability.  A large number of these assets come up for sale, so by the law of large numbers the average payoff will be 50.  How much would the assets sell for under Geithner plan conditions? Suppose private investors purchase each asset for X.   In this case, half the time, their profit will be -X/14, while the other half of the time their profit will be 0.5(100-X).

This implies an average profit of 25 – (2/7)X.  Comparing this with the initial investment of X/14, we can calculate the rate of return on this strategy as a negative function of X.  Suppose that the rate of return needed to be 10% for participating private investors.  In other words that  (25-(2/7)X )/ (X/14)    = 0.1.  In this case, we can solve to get that the purchase price will be X=85.4.

So, here’s how the spoils get divided out.  The public-private consortium buys the assets for 85.4, with 79.3 coming from the taxpayer and 6.1 coming from the private investors.  The private investors get back an average of 6.7 to give them their 10% return.  But since the pool of assets only pays out an average of 50, the average return for the taxpayer is 50 – 6.7 = 42.3, implying an average return for the government of -47%.

One can re-do the calculations using other probability distributions and private sector rates of return but these figures suggest that the Geithner plan conditions could work to boost prices for these assets by about 70%.

The one caveat here will be a familiar one from the early days of the meltdown: Correlated risk across the pools of securities.  If these securities are all correlated, then perhaps there are scenarios under which all of them produce very poor payouts.  This may require higher risk-adjusted rates of return than the 10% used here, and this may limit how much private investors will bid.

Update: It may be useful to clarify that the 10% return for private investors in this example is not supposed to represent some supra-normal return earned by these investors.  Instead, this is just assumed to be the required rate of return for taking on a risky investment of this sort.  I see now that some can intepret this story as “public gives subsidy to hedge funds, hedge funds then make out like bandits”.  The problem here is the classic public finance issue of the incidence of a tax or subsidy. Just because a particular industry is taxed or given a subsidy, that doesn’t mean that they bear all the cost or obtain all the benefit.  In this case, the assumption that there is a 10% rate of return, which gets enforced in a competitive auction in which the funds bid against each other, means that the subsidy gets transferred in full to the banks selling the bad assets.  It’s the banks that make out like bandits from this deal, not the hedge funds.

20 replies on “The Geithner Plan: Quick Numerical Example”

I am not sure how to interpret your analysis but it seems incorrect to me; at least by the theories of classical finance. According to the Modigliani-Miller theory, the method of financing an asset purchase has no effect on the value of the asset. The fact that the debtholders would be left with losses if the underlying asset values go down will be correctly impounded in the required yield on the debt at time of issuance. The value of the entire asset cash flow package is unaffected by how the asset flows are divided up among claims.

The only taxpayer-provided subsidy in the Geithner plan is in the (possible) underpricing of the non-recourse debt issued as the largest part of the funding package. I could find no explicit statement that this debt will be deliberately underpriced. I suspect that it will be underpriced to some degree; in fact I believe that some underpricing is probably appropriate to produce the desired outcome. A modest underpricing hardly seems a major flaw in the plan. The US Federal Reserve (along with the Bank of England) is in the midst of a deliberate policy of quantitative easing in an attempt to inject massive new liquidity into long-term debt markets. The Geithner plan, if it incorporates some debt underpricing, accomplishes this in a targeted way, getting right in where the biggest debt market liquidity problem lies (commercial banks holding toxic assets tied to mortgages and thereby reluctant to lend).
Note also that the debt pricing subsidy (if there is one) provides absolutely no benefit to the hedge funds etc who purchase these securities. If the auction market is competitive the entire subsidy accrues to the banks selling the toxic assets. Your blog entry makes it sound like the hedge funds are benefitting at the expense of the taxpayer – this violates basic asset pricing theory, unless you are claiming that the auction will be rigged or noncompetitive for some reason. The hedge funds competing against one another should in theory eliminate all abnormal expected returns from the deals.

Krugman is on your side (which has me a bit worried about the soundness of my beliefs) but the Geithner plan seems to me a reasonable partial solution to the toxic debt problem for US banks.

Quick response to Greg’s comments:

1. Indeed, in my example, the debt is deliberately under-priced (my example actually assumes a zero interest loan to keep things simple) and so definitely doesn’t correspond to the MM theorem. As Colm McCarthy discussed in his earlier post on this, if the debt was priced at a market value then a government intervention wouldn’t have any effect at all.

2. I did not imply (or certainly didn’t mean to imply) that the hedge funds benefited from the subsidy—they just have a required return of 10% in this example (I just plucked this figure out of the air) and that’s exactly what they get. The example is indeed intended to illustrate in a (supposedly) simple way how the subsidy gets transferred completely to the US banks by upping the price for the assets.

On the merits of it, basically it’s a deliberately opaque way of overypaying for assets. I suspect that if Joe Sixpack could see that, they would not be in favour of this deal. Note also that media reaction along the lines of “the markets received the plan well” — thus implying it’s unambigously a good deal — misses the point. Of course it’s good for bank stocks. It’s a big lump-sum transfer from the taxpayer at a time when the alternative could well be nationalisation.

Hope this clarifies.

Gregory, the critical issue is the ‘underpricing’ of the debt. A hedge fund specialising in distressed assets (I love ‘legacy’ assets – legacy sounds like a long-forgotten great-aunt in Australia left you an unearned surprise – beats ‘toxic’ anyway) cannot raise debt at the moment at all, I suspect, and certainly not six times leverage at any kind of tolerable rate. The extension of FDIC cash to the new vehicles at a rate that persuades them to buy is underpriced by definition.

I can forgive Krugman for being a Democrat – he opposed the Paulson scheme of which this looks like a minor variant, as Karl Whelan argues, and he is critical now of Greithner. On the face of it, this is a transfer from taxpayers to bank shareholders. Whether it is enough to make the banks whole is another issue – perhaps not.

I don’t know how to (i) bail out insolvent banks (ii) leave them in shareholder ownership and (iii) protect taxpayers, all at the same time.

I think Daniel Gross asks the right question: why can’t individual investors get a piece of this deal, if it’s so great?

Can’t I put some of my pension plan, savings, 401(k) or other investment income to work buying these instruments if I want to? If a law were needed to allow this, it would sail through both houses in the current climate.

A lot of negative reaction to the Geithner plan seems to pivot on the fact that this is a “good deal for private investors”. Well, huzzah — aren’t we all private investors now? Might there even be a case that people whose retirement investments were plundered or wiped out in bankruptcy are at the front of the queue when and if these debts are recovered, in whatever part?

Oh, I’m sorry, does that idea make the Geithner plan private tranche look less attractive? Put me down for less, then. At a lower price. I’m sure the market will make this work.

In response to Ben, I’d like to emphasise again that there is no reason to think that this will line the pockets of the hedge funds. The point is that the subsidy means that the hedge funds can obtain a normal hedge-fund rate of return even if they pay more the current market value for the assets. It is the banks who are getting the good deal—the competitive auction format means that the value of the subsidy gets transferred to the banks—not the hedge funds.

The fact that Slate commentators and the like misunderstand this shows that Geithner plan is probably too complicated for the public to fully understand. And I suspect the administration is perfectly happy with that state of affairs.

Well, then I can at least take comfort in the fact that the Obama administration can so effortlessly create a perfect, inertialess, frictionless method of moving capital!

It seems to me that if the Geithner Plan yields something that involves a quantifiable investment risk which is worth evaluating and subjecting to scrutiny and equations, then it’s something that private investors should have access to, or serious questions should be asked.

If there isn’t, then there’s no risk to analyze and there are no numbers involved, and a numerical example makes no sense — it’s just Michael Lewis’s example writ large and way too late: “You have a dog, and I have a cat. We agree that they are each worth a billion dollars. You sell me the dog for a billion, and I sell you the cat for a billion. Now we are no longer pet owners, but Icelandic banks, with a billion dollars in new assets.”

Final comment for Ben. I also see no reason to restrict the potential pool of private investors. They shouldn’t expect, however, that the “frictions” in the process are going to line their pockets with supra-normal returns.

The method of financing is important to look at because if the banks find a way (i.e. loaning to a hedge fund or setting up a purpose vehicle) to use this special deal to buy the toxic debt from themselves using government bailout loans, it gives the government all of the downside, and banks will have every reason to overpay for those assets. It’s just a more convoluted version of TARP.

Can’t believe that you (and countless others) are buying into this bad model for how overpayment will work.

Consider: YOU assume an asset that pays either 0 or 100, randomly (because of this feature, the bidder cannot distinguish AT ALL between something that is VERY SOUND and something that is UTTER CRAP — how realistic does that sound for starters?). This “simplification” is then used to construct an example of taxpayers being fleeced.

Whoa. Back the truck up.

You are assuming a distribution with two fat ends and no middle!?!? When an ACTUAL BIDDER crunches scenarios on how much a security is worth (which is what he will assuredly do before bidding, to get comfortable with the range of possible values), he will in reality wind up with a FAT MIDDLE and two skinny tails (0 and 100 will be RARE OCCURRENCES in the data set). So he’s most likely to conclude the asset will end up with a value between say 40 and 60, if the true unknown worth of the asset is 50.

So if he bids even 61 he has a good chance, say 3/4, of losing money.

I can’t believe this bad arithmetical model is all over the Internet. Your model does not approximate anything in reality … the bidders will NOT risk losing money 3/4 of the time. When they model the distribution curve of likely outcomes, do you REALLY think it will be dumbbell shaped with an invisible bar in the middle? I supposed your example works well if we change this to a ROULETTE WHEEL investment. Your math is correct as far as it goes but it purports to reveal … absolutely nothing about the real world.

Krugman has made the same mistake. Surprising.

I don’t like the Geithner plan either because I think nothing will happen. There won’t be massive overpayment (unless there’s some wrinkle I’m unaware of) and the banks will keep the crap and on we go … argh.

Hey your blog is great; I like it a lot. It’s just driving me nuts that this bad model is proliferating, against all sense, and that P. Krugman (who I greatly greatly respect) is the first guy who apparently trotted out a version of it.

The problem of the model, in a nutshell, is that it only works if you have BIDDERS WHO MAKE THEIR BIDS ON THE EXPECTATION THAT ALL ASSETS WILL BE WORTH ALL OR NOTHING AT THE END OF THE DAY (in other words, they think they’ve got a lottery ticket). If the bidder (in a more realistic scenario) thinks he has an asset of some uncertain value that could be worth 0 or 100 (or any point in-between), he will model the range of outcomes to arrive at a bid … and in the end will make a much smaller overpayment than 30% or 40% (maybe a few percent because of FDIC subsidy? dunno).


Karl, while I don’t think this model for overpayment works, there is another way to look at this that would result in potentially HUGE overpayment. It just occurred to me. It’s based less on the risk element (big pocket U.S. protecting investor on the way down) than on the time value of money OVER LONGER PERIODS (these CDOs are 10-year or 5-year yes?). Assume almost all the money to invest is essentially “free” to borrow — then how much would an investor pay for a stream of income (which is how mortgages are structured) say $10 million a year over 10 yrs.? If he needs a 5% annual return, and his borrowing cost is 5%, then he’d pay about $100 million yes (inflation not accounted for true). But if his money is essentially free (assume for simplicity that he gets 100% free financing though is liable for the first 7% of downside), and he needs a 5% return, what would he pay? About $200 million or twice as much yes? This is a huge overpayment. (Note: I don’t know quite how these securities are structured exactly so I may be off somewhat here but I think basic argument is sound)

Now the question: how does the taxpayer get screwed? Unclear. Because: there are a couple of nebulous things here. (1) If you sell the asset before the 10 years are up, do you then split up profits etc. and the government exits the financing? If so, there is a big incentive not to resell these things, because without the government subsidy they’re worth far less. (2) So in that case: how do you split the yearly income stream?

I’m just banging this out, top of head but seems like big overpayments could be baked in here.

Whoops. One quick addendum: Not $200 million cause he’s splitting profits with his government partner. If he’s in a 50-50 split, that puts us back to $100 million … argh … this is gnarly stuff without knowing more details. I desist.

Perhaps a less snarky response might help.

Nobody thinks that this is an accurate description of the likely distribution of returns. It’s just a model intended to illustrate a general principle without making things too complicated. (This is the way academic economists think through lots of issues). The basic result would be replicated for a more general distribution because the asymmetry between downside and upside risk means that the mean payoff to investors has to be greater than the mean of the underlying distribution. But to work through a numerical example with a realistic distribution is the kind of thing best left for academic papers rather than blogs.

Snark point taken. Apologies. But I still think the overpayment issue isn’t that much a risk problem. I think it’s more likely a cost of money problem — i.e., the private investor is basically getting an $X million interest-free loan over the life of the asset (as much as five or ten years?) To be fair, without knowing more details, it’s hard to tell how much overpaying this results in.

I know that what you’ve come up with is just a model to illustrate a general principle, and of course it has been simplified. Here’s my problem (snark off, and also disregarding the whole “cost of money” point): You’re trying to illustrate a conclusion about how much investors will overpay. That means your example (however simple) has to align with how Joe Bidder will look at these assets.

Consider it this way: Even if you create a simple model where all assets wind up worth $100 or $0, the key thing is what Joe Bidder thinks. He’s the one overpaying. So if he thinks he’s living in your model, he will overpay a lot more, knowing he’ll either get a winning lottery ticket or a loser. But if he thinks he’s in a more real-world model (subtle point: even if he’s actually in your model, that doesn’t matter: what influences his bid is simply which model he thinks he’s in), where the assets could have a number of values from $0 to $100, he’ll approach his bid entirely differently.

The fact that he knows he’s not in your model then means he will use a “best guess” kind of model. He will crunch scenarios and wind up with a distribution of outcomes. He will figure the true value lies near the fat middle and will bid near there. The trouble with your model is that it really doesn’t illustrate how much a real bidder would overpay (unless, again, he is convinced that he’s bidding in an “all or nothing” auction). And I think that the problem is conceptual, not granular, with all due respect.

love the cartoon …. and I’m embarrassed that not more than 1 hour ago I emailed Roubini’s RGE (who I am a great follower of) to point out an error they might wish to correct

Note to Flawed Approach – I did this privately and politely
If we’re all too critical, this could curb lateral independent thinking which could lead to group-think which, in turn could lead to herding (was going to say sheeish but I’ve never ‘heard of a herd’ of sheep!) behaviour which could lead to irrational exuberance – or infintie bullishness (I’m momentarily mixing my metaphysical mammary metaphors) – which could lead us to boom and bust – and sure then where would we be?

Definetely time for bed

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