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Some markets are not martingales.  It's not a really a violation of the EMH if you can't short them.  The current price is then a consensus of the longs, and those who are bearish don't get to express their opinion. Take houses.  When they are overvalued all you can do is stand on the sidelines and watch the slow motion train wreck.  If you could short them, they'd crash a lot faster, wouldn't be anywhere near as likely to bubble in the first place, and the shorts would be there to buy them when they fall to fair value.  I think deposits are like that too.  The fast money is long since gone, but no amount of intelligent consensus that Greek banks are going to die can drive out the stupid money.  So it takes time.

It takes so long because markets and governments must engage in price discovery. By "price", I mean the "strike price" of the implied bond market put on sovereign bonds and bank non-deposit funding. Governments (inc. central banks) would like that strike price to be as low as possible. In other words, they would like creditors to absorb as much in losses as possible without melting down. Markets, on the other hand, would like that put to be "at the money". In the case of the 2008 crisis, the dynamic of price discovery occurred from Aug. 2007 to the Lehman failure. Up until the GSE bail out, the put was "at the money" -- Bear's creditors were made whole. The big change with Fannie and Freddie was that preferred shareholders -- quasi creditors -- were wiped out. The strike price moved down (or rather, up the capital structure). In the case of Europe, we are at the stage again when the strike price is moving down; initially, though, only for debt of countries too small to matter (Greece and Portugal). The crisis is gaining momentum with concerns over Italy. The thought is that Europe cannot make good on an "at the money" put for something as large as Italian sovereign and bank debt. Once markets coalesce around that view, collateral haircuts will spike and a run -- like Gorton described for the 2008 crisis -- will begin.

The "put" offered to markets by governments is a political artifact. The question is for how long, and by how much, governments can ignore the desire of the polity to cancel that put. The U.S. reached its limit with the GSE's and then Lehman. Europe may reach its limit with Italy.

K makes a good point. This is a good argument for having futures or derivatives markets on existing assets: they're easier to short (and trade, more generally), so the price finding process is smoother and more effective.

There are many reasons why a roughly efficient market may trend up or down. One of them is the 'peso problem'--a small probability of a sudden jump in the opposite direction. For instance, this may happen if "everyone knows" that Greece/Ireland are going to default, but there is an enduring probability that the EU and IMF will decide to bail them out.

That's a very good question Nick. At this point I'm not even sure a messy Greek default would trigger an immediate domino effect in other countries. I remain convinced that the Eurozone will eventually be dismantled, but I have no idea when exactly. Will it be come this fall, in 2013 or by the end of the decade?

Where will the final blow come from? A "too big to save" country defaulting or a Northern European country having enough? My only certitude is that will come coupled with some form of banking crisis that will probably entail some kind of banking nationalization in a few countries.

I agree with K that this scenario is pretty un-hedgeable. But then it is very hard to gamble with the legal means of exchange for several hundred million people. Whether we like or not it is pretty much impossible to live a normal life (that is, without that much investable wealth) while totally avoiding the banking system. The same goes for most businesses. “As long as the music is playing, you've got to get up and dance”...

Nevertheless, there are several signs that ordinary Greeks are shifting their deposits out of the country as much as they can. Martin Wolf had a column about the "slow motion bank run" a couple of weeks ago. I heard the same things about Argentines a decade ago, a significant number of people had sheltered money abroad before the crisis. It has since become second nature for many Argentines to have money sheltered in Uruguay or elsewhere.

Good comments. I don't have anything useful to add.

There's always the possibility that something will change the trajectory. In the case of Europe, maybe they come-up with some kind of fiscal integration, or issue EU bonds, or ... Over time the number of longs willing to play chicken with fate dwindles until ... BANG!

"A 'slow motion bank run' is an oxymoron. And yet that seems to be just what has been happening."

I think that results from uncertainty over whether Europe will either exhaust its pool of "moral hazard", run out of stomach for increasing it or come to the conclusion that increasing it won't work anyway.

Moral hazard slows and clouds the development of the network effects inherent in bank runs and money demand. It also introduces the possibility that it may be costly to flee (i.e., if the policy responses work).

ISTM that in reaching a new equilibrium, a significant number of people who benefited from the old equilibrium but will not benefit from the new will resist change. That manifests in the political process.

It is also symptomatic in the employment area; in order to grow we need to create jobs, but most companies are unwilling to incur the expense of hiring and training new workers. They attempt to reach a partial partial by hiring away from competitors but in total the employment pool doesn't increase.

If nobody wants to expand net employment through hiring and training then we will have chronic unemployment.

It's all part of the human aversion to incurring losses.

Didn't Keynes remark that financial speculation was not an exercise in guessing some objective fact, but guessing what other people would guess (or guessing what other people would guess that people would guess....and so on)? An inherently uncertain and shifting process. The scene changes as the major players - bond dealers, private banks, central banks, governments act on the guesses about other guesses, which in turn....In short, there are no equilibria, just pauses while people catch up with the state of play or gather the resources to make the next bet. Add in slow diffusion of understanding about the actual state of play, aversion to abandoning one's current plans, need to convince internal audiences before acting, deliberate misinformation and so on - why would you expect things to be smooth or quick? As to the underlying trend, the drivers may not be economic at all, and are certainly a mix of politics, demography, resource availability and much else as well. Why should appreciation of these trends be universal, quick or complete?

In other words, a multi-party strategic game. Clauswitz had some good things to say about these before Keynes.

Greece is filled with people who have been predicting the painful crash of the debt-fueled economy for over 20 years now. (I'm one of them :-) )

But as my father told me the other day, "you can eventually be proven right but that doesn't change the fact that you were WRONG FOR 20 YEARS!"

And in the past 20 years, a whole slew of people grew rich (or at least very comfortable) in an "unsustainable" debt boom. As long as enough buyers of GGBs could be found, all was well.

So yeah, timing is everything...


It seems to me that what you are missing that the expectations of individuals flip at different points of time. And the confidence interval around those expectations will narrow with time (increasing the probability of action).

Just looking at aggregates is always misleading (I think I would like to have that as my signature theme).

More good comments.

reason's comment makes me think of Greg Mankiw's and Ricardo Reis's paper on sticky information and the Phillips Curve:

Most economics models (for simplicity) assume everybody has the same information, and that everybody is paying attention all the time. And if the simple model were literally true, so that the only thing going on in the world were what is going on in the model, then that assumption would make perfect sense. But people's lives are filled with 1,001 different things, and they can't think about all of them all the time. So they forget to change their car's oil. Or can't remember when they changed it last. And some, I have heard tell, buy a brand new BMW and never do anything except add gas, and drive it till the engine seizes.

The Mankiw Reis paper, by the way, explains why it takes so long for the economy to get to the long run Phillips Curve.

I don't have much original insight on this particular issue, but regarding the failure of the Law of Iterated Expectations, there does appear to be a literature on the phenomenon, essentially making the points by previous commenters about beauty contests and optimistic or pessimistic (or "smart" and "stupid") money, in the presence of some constraints. These can be a simple inability to sell an asset short, or limited risk bearing capacity, or possibly more fancy issues with agency problems. See for example "Beauty contests and iterated expectations" by Allen, Morris, and Shin or "Speculative dynamics and the term structure of interest rates" by Kristoffer Nimark. Both make the point that if the information sets of the agents are not nested, then the LIE does not in general hold. Neither paper includes a model of bank runs, however, just generic assets (in the second, specifically bond prices).

It seems that allowing bank runs in such a framework would be more difficult, however, since the point of a bank run is that there's a discontinuity (or at least a non-smooth transition) at the point when the bank runs out of money. You would also need to extend the standard three-period Diamond-Dybvig model to something with more complicated dynamics. Though it's maybe not describing exactly what's going on, a recent Econometrica by Angeletos, Hellwig, and Pavan ("Dynamic global games of regime change: learning, multiplicity, and the timing of attacks") seems to have some of the key ingredients of an explanation: the coordination issues of the Diamond-Dybvig model, heterogeneous expectations and learning, and limits on the size of individual actors (here modeled as simply limited availability of capital to withdraw). As usual with dynamic game theory papers in Econometrica, the results are complicated and messy and hard to interpret in terms of real world phenomena (I certainly didn't follow all the theorems), but the abstract seems to provide a flavor of what's going on in Europe. Their conclusions:

"We then show how the interaction of the knowledge that the regime survived past attacks with the arrival of information over time, or with changes in fundamentals, leads to interesting equilibrium properties. First, multiplicity may obtain under the same conditions on exogenous information that guarantee uniqueness in the static benchmark. Second, fundamentals may predict the eventual fate of the regime but not the timing or the number of attacks. Finally, equilibrium dynamics can alternate between phases of tranquility—where no attack is possible—and phases of distress—where a large attack can occur—even without changes in fundamentals."

It's not clear to me that this captures the situation precisely: for one, it predicts periods of calm interspersed with random panics, some but not all of which succeed, rather than a steady flow of withdrawals. I suspect that this is a function of the lack of a state variable tracking the size of the withdrawals needed to tip over into a panic, which should decline over time as people take their money out to place in an outside option. A 1970s-Krugman-style currency crisis model does generate a steady flow of withdrawals until a crisis hits, but that model is driven by a fundamental which is also steadily worsening over time essentially exogenously, which doesn't seem realistic in this case. Still, the basic logic of both that model and the Angeletos et. al. model suggest that in such a situation one should not be surprised to see relative stability and orderly transition for a while until some critical threshold is reached, at which point a slow drain becomes a frantic rush to the exits without warning.

Nick, Any comment on the question Krugman raised about Italy vs. Japan? It's true that Japan has it's own currency, and it's true that they COULD use monetary policy to reduce their debt burden, but there's no sign they are doing that, or will do that. So why isn't their debt situation as bad as Italy? One reason is the greater growth of the rest of the eurozone means they have to pay higher interest rates than Japan, even if there was no default risk in Italy.

"Expectations of what will happen at some fixed future time ought to follow a random walk (a martingale, to be precise), where the next move is as likely to be up or down"

You are assuming no new information is provided, right? If information is constantly being provided, you will updated your expectations in real time. Just assume that the measure with which you are taking your expectation is changing -- some Borell sets become heavier as new information is provided and other sets become lighter, so that the integral of your variable over all the sets is changing with the new information, and hence with time.

And don't all processes include gradual information discovery? So you would expect the law of iterated expectations to hold only in those cases where the estimated probability measure is constant -- i.e. if agents are never smarter tomorrow than they are today, about the likelihood of rain 3 days from now. But as market prices are themselves relevant information (in particular, higher interest rates make default more likely), then you would never expect the law of iterated expectations to hold in the debt markets. Rather, you expect the market prices to instantly adjust as new information is provided, but not 50/50 up/down.

While this can be true in theory:

"Solvency crises don't depend on multiple equilibria, but on changing fundamentals. "

this is not true for the euro crisis and in particular Greece. The fundamentals of Greece are not changing. Greece cannot pay its debt due to the structure of the euro, and wouldn't be able to pay them under any likely assumptions for the future. It wouldn't have been able to pay them months ago.

The fundamentals haven't changed for Greece at all. What has changed is the understanding of the investment community of what Greece is facing, and the politics of the bailouts.

The euro is designed to risk/threaten/cause sovereign defaults - it's regarded as a strength by people who think sound money is very important.

You may be confusing a spot rate with a forward rate. A forward rate for a specific fixed time period should be a random
walk. A spot rate, though, often has predictable trends.

Fmb: you are right, of course. I fudged this in my post, even though I understood the point. My reasoning is that the price at time t of a good to be delivered t+s periods in the future where s is fixed but large relative to the interval t, t+1, t+2 etc. over which we observe the trend, should be approximately the same as a forward rate for a good at some fixed future time T.

TC. That's the puzzle. If the fundamentals aren't changing, why is it taking so long for people to understand them?

RSJ: "You are assuming no new information is provided, right?"

I am assuming new information. The expectation, conditional on that new information, will change. But if we know we will get new information tomorrow, but don't yet know what it will say, today's expectation of tomorrow's expectation of Friday's rainfall will equal today's expectation of Friday's rainfall.

You lost me on Borrel sets.

Scott: I've been running it over in my mind. Nothing useful to report yet. Haven't really concentrated hard on it.

David: Wow! You've been reading some heavy duty stuff. What I get out of it is that a lot of different things can happen if you play with some of the standard simplifying assumptions a bit.

Even though Diamond-Dybvig is a 3-period model, I always interpret it as a sort of infinite period overlapping 3 generations of investments model, if you get my drift. There's a steady small stream of new investments just starting, and a steady small stream of old investments just finishing, and a big stock of existing investments still growing. The second period is long relative to the first and third.

Hi Nick,

I just had a conversation with a friend about this today.

1. The market isn't a truth mechanism, it's a voting mechanism. There is no falsity to truth arb you can create with the available financial products for the euro.
2. In this area economic reality (Greece insolvent) is impacted by market action. This is what Soros calls reflexivity.
3. Economics and finance are different. Finance is less important than politics at the level of nations, so the fundamentals (Greece is insolvent) is secondary to the politics (the euro can change its rules to make Greece solvent).
4. The ECB can make the problem go away at any time through the SMP. I argue it's caused the problem by insufficient use of the SMP.

"The market isn't a truth mechanism, it's a voting mechanism."

True to a large extent. But it's not one man one vote; it's one dollar one vote; the rich vote a lot more; those with a lot of liquidity can vote a lot more, and a lot of people proxy out their votes, with their agents then controlling a lot of votes.

I've been thinking about this recently with "probability" markets, like credit default swaps (CDS's) on US debt (insurance policies on the US not paying its bonds). There was a time when there really was a minute risk of US default on short and medium term debt, yet the implied probabilities from the CDS market were on the order of 1%. This seemed too high.

I think the market probabilities may be highly biased when it comes to tiny probabilities.

Suppose the true probability of country A's default is 1 in 10,000, and the market knows this. For the CDS market to reflect this, aside from transactions costs, you'd have:

Short: Get $1, and if it does happen you pay $9,999.

Long: Pay $1 and if it does happen you get $9,999.

Given that people are risk averse, far more would prefer to go long than short, so prices would be bided up and the actual implied market probabilities would be much greater than 1 in 10,000, even though the market knows the true probability is only 1 in 10,000.

In addition, there aren't many parties that would have pockets deep enough to go short for many dollars and have the credibility to back up their contracts.

Now, the people going short could diversify, but only to a relatively small extent. You can't find close to 10,000 such independent bets. And there are behavioral issues; how many people worth millions still buy collision and theft insurance on cars worth less than $100,000.

You always hear market implied probabilities being quoted as though they're so efficient and accurate, but there could be a big problem with this when the true probability is very small. I wonder if this is in the literature.

Nick, say that you are flipping a coin each day, but that on heads, the coin becomes more biased towards heads, and on tails, the coin becomes more biased towards tails.

This is like Greek Debt -- a higher probability of default raises interest rates, which increases the probability of default.

Now, over time, the probability of getting heads or tails will slowly converge to 1. Not necessarily monotonically. Prices will not follow a random walk, they will converge asymptotically to one of two values, and the casual observer may wonder why it is taking so long.

RSJ: What you are describing is not a price sequence. What you have is a sequence of probabilities of successive, different events. Those can do whatever you want, and are not martingales. An equilibrium price is a sequence of expected values (probabilities) of e.g. the *nth* coin flip. This *is* a martingale. Imagine that you have to keep guessing what the 100th coin flip is going to be. You observe the coins going more and more heads. If you don't take that trend into account when calculating the odds of the 100th coin flip and you therefore just monotonically increase your estimate of heads you are doing a really bad job. If there is a contract that settles on the actual probability of the 100th coin flip, I'll fleece you by buying it off you, thereby quickly bringing the price into line with rational expectations. From there on it'll be a martingale. Equilibrium prices (yes, there are lots of caveats for market failures as discussed by me and other above) are iterated expectations. Iterated expectations are martingales.

K, it's the same thing.

Imagine that B(K) is an instrument that pays out $1 if the K-th flip is heads.

The price of this contract will change as more information is revealed in exactly the manner I described.

And specifically, Nick was wondering why it was taking so long -- why prices of Greek debt were trending down -- apparently predictably -- when it seemed obvious that Greece would default.

So in our coin toss example, a sample path of prices for a contract that pays out $1 if the N-th toss is heads (where N is very large), will first start out at .50 but (assuming that the attractor is tails), will converge very slowly to zero, never actually reaching zero, as there is always a (decreasing) non-zero chance that there will be a succession of heads that will un-bias the coin.

Prices can appear to converge *very* slowly to zero.

Here is a realization of the biased coin example, in which at each stage, with a 1% positive feedback. E.g. If the current toss is heads, the probability of the next toss being heads is 1.01*current probability of heads.

If we take a contract that pays $1 if the 1000-th toss is heads, then this is a realization of the price series of this contract. Now think of this as being the price of Greek debt, slowly trending downward. After about the 400-th toss, the price seems to be following a predictable convex path (ex-post), but that does not mean that you can earn an arbitrage profit ex-ante. There is always the possibility of a string of heads to unbias the coin. We also know that this sequence *will* settle down a tail that is a predictable convex decreasing (or concave increasing) function.

We just don't know which one, and when the tail behavior will take over :)

Similarly, even know, there is the possibility (however remote) of some grand bargain on Greek debt that would either prevent default or increase the recovery value. Even though we know that this possibility is small and is likely to diminish.

Ex ante, when that price hits 0.05 (around the 776th flip), I can see, with a very high probability, where it's going. If you are buying at 0.05, I'm a seller. You are not incorporating all your information about the time series up to that point (i.e. the odds of heads is trending down), in making your estimate of the prob of the 1000th coin flip.  Once a real market gets going on trading your contract, the price process will look nothing like your graph.  Instead it will look somewhat like a log-normal random walk that happens to start at 0.5 and end at 0.01.

TC: with the "reflexivity" that sounds a bit more like multiple equilibria, and more like a liquidity problem interacting with solvency. "If other investors won't put the money up, the project won't have enough funds to succeed, and my own investment in the project is worthless."

RSJ: I *think* (not sure) that what you are talking about is in some way equivalent to the "Peso Problem". (I though another commenter had mentioned the Peso Problem above, but now I can't find it).

Well, judging by the markets today, it appears stuff has finally happened

Jason: unfortunately, yes. Though maybe it's better to get it over with? (Like when you are really hungover, and .... never mind; this is a family blog.)

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