Tuesday, March 13, 2007

The Sordid Business of Predicting A Crash

First let me state that I am patently NOT in the business of prognosticating stock crashes. That said, please allow me to forecast one that, against all good, common sense, I believe, may be coming to a bourse near to you rather soon, in perhaps the next 30 to 40 trading days. And I say "good, common sense" because statistically predicting crashes is, for those who pursue it, a truly rotten profession. Far more difficult than trying to predict, say a "0" or "00" on the spin of roulette wheel (at a mere 1-in-37). It is more akin to 1-in-120 call, AT BEST, and perhaps a 1-in-500 or even 1-in-1000 longshot-of-a-call at worst, assuming of course that I do not need to accurately flag the precise day, but or days, but only the general vicinity in time.

Surely you will ask "why" I have embarked upon so ludicrous and statistically unrequited and unrewarding a path. The first reason in all honesty is that since I am not paid for this forecast, I cannot be fired for being wrong. Second, because I am master of my own fate, and because I am rather reasonably hedged and crash-neutral insofar as market exposure is concerned in my professional portfolios, I needn't worry about firing myself, for being wrong. Third, IF as a result of this rather bold and outlandish prediction, I turn out to be correct, then I shall have no problem (with all of my readers' testaments in hand), in pursuing a new (and leisurely!!) career as an ‘Investment Letter Writer’, one that I can pursue from a suitably comfortable location, be it surf-side or slope-side (for which the prices of said bricks & mortar will - no doubt - be dramatically reduced in the event).

The more skeptical amongst you will no doubt endeavor to ask, what manner of evidence I might possess to back up this apparently farcical and visceral hunch. And here, I will reveal to you, that which is of true value. It is not a secret of dark magic or of statistical smoke & mirrors, though it is somewhat obscure, and off the beaten path of ordinary observers. For "it" is buried deep in the cross-section of the distribution of stock-market returns, in particular, within the higher moments, which, I would hold out to my readers, have a remarkable tendency to (historically speaking) whisper things that are terribly important, be it "danger" or "opportunity".

To be more specific, I am referring to the cross-sectional skewness of daily returns in the investable portion of the US equity market, and, even more precisely, a three-month moving average of such a measure, systematically removing of course, the most extreme daily observations. Typically, this measure tends to have a negative sign, which if my feeble knowledge of statistics serves me right, implies that the associated tail risk of the distribution sports a negative sign, in relation to the average daily return (which has incidentally over the past 25 years typically been (small) positive. The kurtosis then, a sensitive cubed measure, relates to us just how far from the mean that [usually] negative tail lies. Periodically, in the US, this measure of cross-sectional skewness of returns climbs to positive territory, and, on a few even rarer occasions, the departure into the positive is rather greater and more elongated than at others. These, historically speaking, have coincided with, or presaged significant market events.

On some occasions (as one might expect), such a flip-flop into a state of highly elevated positive skewness has FOLLOWED extreme corrections such as those seen in the Aug through October period in 1987, the May through early October period in 1998, or the June 2002-> March 03 capitulation of the NASDAQ. On such occasions, it has been a benign signpost of recovery, signaling what momentum traders term: a breakout, or trend-continuation, of sorts. This is intuitive since, following a grand capitulation, with the veil of fear and uncertainty is lifted, gaps to the upside, recovering earlier losses, are unsurprising and tend towards continuation. Such moves are typically consistent with, and converge towards, some future sustainable intermediate-term equilibrium rather than away from it.

On other occasions however, such positive skewness periodically follows elongated positive return runs that resembles something like a melt-up. At such times, positive returns perhaps have induced panic buying, or panic short-covering that causes the tail-risk to have - at these instances – an uncommonly positive sign. Such was the case in April to August run-up in 1987, the second quarter of 1998, the fourth quarter of 1999 into the beginning of the year, and, yes, mid-February 2007. In fact, mid-February 2007 saw the most elevated measures seen I’ve seen in the US market since my data for this commences 25 years ago. Now I’ll admit that these may not be apples-to-apples comparisons since the nature and number of listings in the “investable” cross-section has changed over time, but nonetheless, the elevation recently witnessed is, in a single word, unprecedented.

None of this will escape practitioners, who can see it and smell it in the trenches, perhaps using other technical descriptive terminology or endogenous market indicators, but it is, nonetheless an additional systematic tell-tale, less commonly observed by most. Now add to this a kurtosis measure of the same cross-sectional returns. Somewhat expectedly, during selective panics, (for example the 2002 tech-wreck), skewness is highly negative, and kurtosis is highly elevated signaling a negative tail well-departed from the mean. During 1987, by contrast, or September 11th, the crashes were rather more democratic, and while skewness was negative, kurtosis was not nearly as elevated as at other times of less-universal panic. For during a crash the average return tends to be rather negative, with the tail not too far off the mean, as correlations tend to converge. Importantly, at both “significant tops” AND recovery rallies, kurtosis is typically diminished, or at a local minima. This may reflect investor behavioural preferences to take profits on large the positive tail, but it nonetheless has a subduing effect in keeping the tail closer to the mean on those occasions when the skewness does turn positive. Yet again, in mid-February, somewhat unprecedentedly, we have witnessed very elevated positive skewness AND reasonably elevated kurtosis. In my experience, this is twilight-zone stuff. All we need now is Rod Serling to tell us what it means.

My take is as follows: we are at a monumental turning point in America’s twenty-five year experiment in leverage, and systemic speed bump in Bretton Woods II. We are seeing the telltales of a liquidity-induced blow-off that’s been fueled by ever-easier credit and nearly free-money that - up until now - has fed nominal earnings growth, but that is on the cusp of rolling over, on many and diverse fronts due to systemic contradictions, inconsistencies and imbalances. Yet some high-rollers awash with investable funds and brass cojones seem to be betting that even more liquidity (the Fed "put", Bernanke's helicopter, whatever) will be thrown at it by authorities, that will assuage any drop in nominal prices. AND they must also believe that this liquidity, like that which has been thrown at markets since 2002, will continue NOT to spike rates, and NOT to puke the USD, and NOT cause the ire of Pelosi and her labour constituents, and so not fan inflation but further fuel yet another bout of asset price spirals such as those seen in commodities, stocks, Art, REITs, Credit Spreads, beachfront property, wine, Chelsea homes, and the famous Honus Wagner T205 baseball card. The era of risk anaesthitization is ending.

Understand, I am not a bear looking for an excuse to be bearish. Rather, I am looking at an indicator of an unusually rare market occurance, searching for an explanation, whose more plausible answer is pointing towards something eventful, with returns that are likely to be more volatile, and with a greater frequency of negative signs than those witnessed in the preceding four years. As an immediate forecaster of things bad, I must admit to being unnerved by the post-hiccup jack-in-the-box company of Mssrs. Faber, Edwards, and Tice, irrespective of their esteemed and cogent analyses. But IF the whispers of "the higher moments" again prove prescient, it is highly likely that the brief turbulence witnessed last week is but a proverbial “shot across the bow” presaging an episodic fit that will - in hindsight - be measured in months, and nominal losses into measured into double-digits.


RJH Adams said...

I reach for stat 101 and a database but am able to say that the property search appears to have been timed to perfection.


Anonymous said...

Bold prediction indeed. I have been wrong many times on the timing of this event. On the other hand, as we have discussed in the past, a three sigma event is a question of when and not if. Even a broken clock has to be right once a day. :))

As to if I agree with this prediction, I'm certainly looking forward to your first 'Investment Letter'.


"Cassandra" said...

I will tell you honestly that I prepared this post almost in its entirety in mid-Feb, and then without publishing it, went AWOL to the alps during the week of mayhem & chaos.

So I have had some time to meditate upon the TwilightZone-nature of the skewness of the cross-section of returns. And I have a satisfactory answer which I can hint at by posing the question: "Are the smartest guys in the room, actually the smartest guys in the room....?"

Clytemnestra said...

Hey, turn that frown upside down! Basel II implementation is going to boost bond returns through the magic of reduced capital requirements so if you still insist on investing in equities, you have to at least bring some alpha transport to bear. Once everybody gets in the act this reduces volatility at the cost of some increased skew and flatness, which is not ominous the way it would have been in the old days when the real active money was predominantly long. Market β is so Nineties.

Oh and there might be 1 little slip, kurtosis raises deviations to the fourth v. 'cubed measure.' I note this only because your post will be world famous after the imminent global cataclysm and you'll want everything to be just so.

OldVet said...

I am reeling in shock and have sent your message to my most trusted advisors forthwith! One has translated your message as "The thieves and morons have been stealing all the money and they're about to haul away their loot!" I've been Shorter than Short for weeks on the melancholy assumption that I would be insolvent soon and might as well go down fighting the Morons and Thieves.

I sent a meanly worded email to the Federal Reserve Board of Governors this week and asked them to quit shoveling cash to the crooks, to no avail.

To find our that skewness and kertosis are indicators! My God! Thanks, let's prepare the Dom Perignon! All I have to do now is wait. OldVet :)