The definition of a bubble is naturally elusive. Certain Fed Chairmen have been known to observe that while a bubble is usually apparent after the fact they are hard to identify in prospect. I don't agree with that statement, but it is true that there is no single metric that one can rely on to be able to say "aha! There is a bubble." Candidates include a change in the characteristic acceleration of prices (as described in considerably more detail in Didier Sornette's excellent Why Stock Markets Crash: Critical Events in Complex Financial Systems), a very high multiple of price to cash flows - whether that is in terms of a yield or a price-to-earnings multiple - or measures of investor eagerness/greed.

But whatever the measure, one part of the definition must be that in a bubble market, prices are considerably ahead (define "considerably"?) of what a dispassionate assessment suggests the probabilities and payoff matrix would be worth aggregated across all possible states of the universe. A key sign might be when investors believe the probabilities of poor payoffs are essentially nil, so that all possible outcomes are believed to be bullish and not yet in the price. Investors' classic overconfidence bias should not affect prices as long as the payoff matrix is symmetrical - over-assessment of the likelihood of poor outcomes is balanced by over-assessment of the likelihood of good outcomes - but if the view of possible winning and losing scenarios is skewed to include only winners, then the overconfidence bias could result in a bubble. Metaphorically: if there are lots of fat people on a boat but they're evenly distributed, it doesn't matter how fat they are. But if the fat people are only on one side of the boat, it matters.

This metaphysical musing is produced by my head-scratching about the market the last few days. To be sure, the Employment figures on Friday were better-than-expected and had hefty upward revisions; while not good on an absolute basis, they were certainly relatively better than had been expected. But that is small beer compared to what is happening in Europe. On Friday Fitch downgraded Italy and Spain and Dexia was nationalized, we think, over the weekend. Sarkozy and Merkel had another meeting and released a statement declaring their intention for carrying on an undertaking of great advantage; but no one to know what it is.¹ Specifically, they were not specific, but said they would be specific soon about a plan to support Europe's banks. Italy's parliament failed to approve the 2010 budget, which has already been spent, in a gesture of no confidence in Burlusconi, and the government in Slovakia fell when its legislature voted down the EFSF (this is a largely symbolic vote and it is expected to pass in a week or two, but the significance is that the government was taken down on support for bailouts). S&P cut the ratings of Spanish flagship banks Santander and BBVA by a notch to AA- with a negative outlook, and other Spanish banks were also downgraded. The U.S. Senate just passed a bill, although probably dead-on-arrival, designed to punish China for keeping its currency undervalued. I think it's called Smoot-Hawley, but if not then it probably should be. (Geez, folks, there are enough new mistakes to make that can send us down the tubes; do we really need to make exactly the same mistakes that we made in the 1930s?)

The initial cut at the Volcker Rule was released for comment today, and while it will surely be watered down...that's why they release it for comment...it appears both sweeping and vague. The regulators lamented that they couldn't define what will be permitted because it "often involves subtle distinctions that are difficult both to describe comprehensively within regulation and to evaluate in practice." Duh. When the dealer buys a billion 10-year notes from Fannie Mae at 1/256th of a point behind the current bid, they clearly aren't going to turn around and sell them all at the bid; they're going to hold some of the risk until the buyers come to them. But how much of that risk, and for how long, will they hold? That's a proprietary decision, and the dealer is now in a position indistinguishable in every way from what it would be if it bought bonds on a whim to make a short-term trade. Yeah, this is a hair that may be too fine to split.

The demonstrations are continuing around the U.S., although it isn't clear what the demonstrators stand for. On a recent trip to Tampa, at one demonstration I saw signs saying "End the Fed," "Afghanistan is not a good war," "Debt is slavery," and "End Congressional bribery." I haven't the faintest idea what these things have in common, except that the people carrying the signs are young, jobless, and cranky. Kind of like the early 1970s, I guess. Tune in, turn on, drop out, man.

I'm not avoiding reporting the good news. There's just nothing to report. Well, there are reports that Greece is likely to receive the next tranche of their bailout package when it is needed, despite the fact that they haven't come close to meeting the requirements of the bailout. Is it good news that the EU is caving in? I'm not sure.

And yet, stocks and bond yields are closer to their highs since mid-August than they are to their lows since then. 10-year real yields are at their highs since the late summer swoon (a whopping 0.20%). Are we at the cusp of a sudden acceleration in growth that will justify higher yields and higher equity prices?

I don't think so. But the alternative explanation is that stocks may be rising because Europe is about to collapse and US securities are considered safer destinations for all the liquidity that is being poured into the market. This, too, befuddles me. Does anyone think US securities markets will not be affected if the European markets crash?

I may well be wrong about the particulars. I generally expect institutions to display strong survival instincts and to therefore avoid blowing up for far longer than we would otherwise anticipate. So far, this has been the case with the Euro and countries in the Eurozone. But I am surprised at this point to see such little progress being made to preserve the institutions, and yet the markets reacting as if the institutions' survival were already assured. By "institutions" here I mean in a micro sense (banks) and in a macro sense (sovereign institutions and the Euro itself). I do not think we are out of the woods yet. If the VIX is able to break below 30 and stay there for at least a day or two, I may grow to believe in the stock market rally, but it seems to me it would be truly miraculous to have gotten this close to having the Euro implode without the stock market ever closing technically in bear-market territory down 20% from the highs!

¹ This is actually a classic line from a prospectus of a 1720 offering during the frenzy associated with the South Sea Bubble. See Extraordinary Popular Delusions & the Madness of Crowds. Some issuer actually raised money on this basis.