## Making a Prediction

Kevin Drum asks a question about the numbers Nemo and I wrote:

But it’s a pretty important question that some financial engineering types should spend some more time on. If, in the end, the toxic waste gets overvalued by 10% or less, that’s not too big a deal. If it’s overvalued by 50%, it’s a disaster. Not only will taxpayers likely lose a lot of money, but no one outside the auction will have any faith in the prices. And since price discovery is one of the goals of Geithner’s plan, lack of faith would be disturbing indeed.

This is very valid. I played around with a toy model as a teaching tool for how options work in this case. I didn’t mean to imply a specific value for overbidding – but why don’t we try to answer this question? If I’m wrong, you don’t even know who I am anyway.

I’m going to continue to use the lognormal distribution. A lot of the binomial modeling (It’s either 30 OR 80) increases the volatility and doesn’t seem natural to an actual rough guess. I am not a mortgage-value modeler, and know little of how the distributions play out in practice. But then again, I just want a ballpark – is it closer to 10% or 50%? This distribution will be good enough.

This is still a very difficult proposition because (1) nobody knows what these assets are worth and (2) provided we know what it is worth on average, we can still make a lot of extra money, perhaps more than from the assets, from the put option from the FDIC – and that depends on the volatility. And we have even less of an idea of how volatile the assets are. The volatility will come from the mortgages themselves, and also unemployment and falling GDP. It can also be gamed.

So I’m going to suggest a 2×2 matrix. 2 values of assets, 2 volatility estimates. The real values will probably be somewhere in-between them.

Asset Values

Bad: Paul Krugman is right. These assets aren’t trading because they are worthless, and everyone knows it. The \$1 trillion dollars in debt is actually only worth around \$350 billion; this is what we set our average value to.

Good: Well, relatively good. Obama’s team is right – with some government backing, people’s risk measures go from too adverse to just right, and we realize the assets weren’t that bad all along. The \$1 trillion dollars in debt is actually worth \$600 billion, and this will be our average value.

Volatility

Low: Unemployment decreases while never having gotten that high, GDP bounces back harder to make up for lost time, the regulators make sure that the hedge funds don’t game the process with the portfolio selections.

High: The opposite of Low happens.

Also: I’m going to assume a lower leverage on average (a lot of commenters said that was unfair) – let’s say on average the hedge fund pays 1/5th. Hedge Fund means both the Treasury and the Hedge Fund itself. They are damn good, so they know the distribution so they can bid to whatever value they like, and they bid to where, as wagster suggests, they receive a 12% return on their investments.

So what happens? With a trillion dollar notional, all dollars below are in billions:

This should be taken with a major grain of salt. However, looking at the range from the low ends to the high ends, we see the waste will be overvalued somewhere between 7-20%. I would say low-to-mid teens. FDIC will lose between \$30 and \$100 billions, which will be split between the hedge funds – remember they lost money on the asset itself! – and the banking sector. (Go ahead and add half the HF profits – which are from Treasury – back into the FDIC loses, if you want to think of the government as a single entity.) The over valuation isn’t as bad as I thought it would be, but the FDIC loses more than I expected.

Any quants out there have better clues?

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### 11 Responses to Making a Prediction

1. Chris Marino says:

Nice.

Minor quibble with your assumptions, but this echos my feelings on the program as well. IMHO, 12% return isn’t aggressive enough, and I’d be shocked if they were offered 5/1 leverage on some of the better pools…..

Nevertheless, my conclusion is the same. Considering what the program is supposed to accomplish (rescue banking system), these costs are not onerous. My fear remains that the pools themselves are bimodal and the bad asset auctions fail and the problem (as defined as crummy bank balance sheets) doesn’t really get solved. Stress test program then kicks in and then god knows what happens….

2. Kislaya Gautam says:

Intutively, how can FDIC loose while the HF and the treasury, who have put in the equity and thus the cushion to absorb the first loss, make money at teh same time?

3. Kislaya Gautam says:

The previous comment was based on the singel asset example that you have given. Over the portfolio, one can see how HFs acan make money while FDIC looses.

4. Mike says:

Kislaya – yeah, the single asset is an average asset, represented by a security pool. When they buy this security pool, it’ll be a big with hundreds/thousands of loans in it, of which are drawn from this distribution in my example. The high ones pay out; the low ones get cushioned by the FDIC.

Chris – I thought about bimodal/binomial distribution, as they are what Krugman and Nemo use to be illustrative. Remember that the loan value is capped at 100; if we “draw” a very very good state of the world – everyone is rich – they don’t pay extra on their mortgage’s total value. So as the volatility goes very high, we get a clumping low and a clumping at 100.

Extra: Note that mu has to decrease if I increase the volatility/sigma to keep the average =exp(mu+sigma^2/2) the same; since the median =exp(mu), increasing the vol while holding average constant lowers the median. Which is to say, if you crank up the vol, you’ll end up with a lot of 100s, and a normalish distribution around the very low end – so if you are worried about bimodal/binomial, picture a “Very High” volatility rating above and it’ll duplicate it.

5. Chris Marino says:

Mike, my point about being bimodal was more about the possibility that some auctions can fail. This model doesn’t capture that. I think for a given pool, your lognormal is fine. Across pools, maybe not so much.

This is why some were hoping for mandatory participation in the program.

Without that, it’s possible that only low volatility auctions clear, which is OK from a taxpayer subsidy point of view, but it’s not going to fix the problem (selling the bad).

6. Mike says:

Wow. Yeah. Ya know, I gave some thought to the optimal portfolio construction question for hedge funds, in light of how valuable vol will be to them, and that we are doing all this, in the words of the defenders, to make those investors risk-neutral in their expectations.

The optimal decision on the banking side is a whole other cookie. And I slept through all my game theory auction design classes back in school. Hmmm….what is their dual incentive to accept or not? That is also conditional on whether or not they think they are solvent, and how likely MtM and other regulations will be eased or strengthened.

That’s a really interesting question. Regardless of the answer, it would be better to form mandatory participation…

7. Mike says:

Joting down some equations, I get that:

– Solvent banks will sell off their subprime and crap exposures; in part to get rid of them at an inflated price. In part because their risk tolerance has lowered.
– Volatile loans will be higher priced than less-volatile loans – this makes sense from the option point of view; so solvent banks will really want to get rid of them, as the premium there is the highest.
– Insolvent banks will only sell if the bid premium is larger than the difference between their capital requirements and the capital of their portfolio.

In this case, it’s an obvious adverse selection; if a bank doesn’t sell their subprime loans, it doesn’t signal that they are healthy – it signals that they are even more fucked than we previously thought. That is the point that financeguy was getting at in the latest post I linked to. So I’m not sure if only low-vol loans clear – I think the opposite is true in a way.

8. Chris Marino says:

I don’t think there is an solvent/insolvent criteria here. Its going to be on a pool by pool basis, which depends on what they’re carrying it on their book for.

If they can book a gain they sell, otherwise not. Some good pools might have been written down too much already and they might be able to book a nice gain. Other crappy pools might still be on the books at an inflated price and even a healthy premium might not be enough for them take the bid since it will force them to realize a (further) loss. With no mark to market requirement for certain assets, they wouldn’t have to do this.

IMHO,the worst outcome would be having to provide outrageous premiums (much larger than your model suggests) to pry this crap loose.

As you say, It’s further complicated by the looming ‘stress tests’ which might force them to mark down assets further, in which case they’d probably take the bid.

All together, the whole situation is FUBAR. The stakes are enormous. Failure is not an option, but success could wipe us out as well….

That said, I do believe there are some smart dudes working on this and I hope that it plays out along the following lines:

1. FDIC doesn’t offer too much leverage to support wacky over bidding
2. Threat of stress test revealing insolvency forces banks to be realistic about values
3. They take the bids, some banks get whacked.
4. Securitization market gets back on its feet.

9. financeguy says:

10. Mike says:

Chris,

Your four point plan is exactly what I am rooting for. The stakes are incredibly high.

financeguy,

That is a really good question. I know the point of this from the defenders is to make a very risk adverse market “risk neutral”, and to piggyback the risk aversion and time frame of the government onto private investors. So I assume the hedge fund needs to have their cash in for the full term – hence why they are getting a great deal with the leveraging, and the non-recourse loan.

Now that it’s though of as a secondary market further down the line; if the Treasury has an option to buy out the hedge fund’s position 5 years out (or some such thing), I wonder if that would help with some of people’s worries – the left had of the government will then have sold the right hand a put option; it can be disregarded from the taxpayer’s POV (but maybe not smaller banks).

I’ll have to look into this. Keep up your great blog!

11. financeguy says:

Yeah Mike, you’re probably right. Hedge fund needs to have cash in for full term. Though you could make the argument that if you just need to “jump start” a flatlining market, it doesn’t matter whether they’re in full-term (in fact, if they can find a price to sell at early on, this could even be a double-over good thing: 1. it shows market becoming liquid 2. the FDIC can withdraw that particular low-cost guarantee and pull a little risk off the books).