The Sordid Business of Predicting A Crash

Cassandra Does Tokyo
March 13, 2007


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[1] 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 Ill 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 Americas 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.

Sordid Business of Predicting A Crash (con't)
April 5, 2007

Kurtosis in the daily cross section of US equity returns is as elevated and extended as it has ever been, YET the skewness remains highly positive, a truly anomalous circumstance. Historically, this has reliably foretold something ominous to come. Today, in answering the question I posed and whose answer I hinted at in my early March post of similar namesake, I will reveal why this happenstance exists. The answer is: "Private Equity".

Collectively, they [private equity], and the speculators who move security prices on the basis of rumours surrounding "who's next", are the ones responsible for the positively-signed, bountiful premiums, gapping certain stocks in the distribution higher in relation to the the rest of the distribution, which only inches forward. And as Stephen Ratner forthrightly said in his Bloomberg interview detailed below, they [his own private equity firm, Quadrangle] will continue to take things private so long as liquidity is abundant AND lenders are willing to buy debt at rates and on terms that, as Ratner says, make little economic sense from the perspective of the lender.

So in itself, the higher moments of the US equity market are whispering "bubble", though the bubble is seemingly located in the credit markets, with the equity market but a reflection thereof. This doesn't leave equity markets free and clear by any stretch of the imagination, for the chain of dependencies and linkages are many and complex, but it does explain the highly unusual circumstances of the higher moments. And by explaining away the fragile state of the higher moments, it perhaps takes the heat off of a collapse based upon unsustainable speculative internals, and pushes it towards the exogenous sustainability of the credit markets' extreme generosity and munificence.

Historically they have been related, and, as such, the higher moments of the US equity market may themselves be the tell-tale of the bell-ringing ebullience of us dollar-based credit markets.

http://nihoncassandra.blogspot.com/

Kurtosis risk denotes that observations are spread in a wider fashion than the normal distribution entails. In other words, fewer observations cluster near the average and more observations populate the extremes either far above or far below the average compared to the bell curve shape of the normal distribution.

Kurtosis risk applies to any quantitative model that relies on the normal distribution for certain of its independent variables when the latter may have kurtosis much greater than the normal distribution. Kurtosis risk is commonly referred to as “fat tail” risk. The “fat tail” metaphor explicitly describes that you have more observations at the extremes than the tails of the normal distribution suggests. Thus, the tails are “fatter.”

Ignoring kurtosis risk will cause any model to understate the risk of variables with high kurtosis. For instance, Long-Term Capital Management, a hedge fund cofounded by Myron Scholes ignored kurtosis risk to its detriment. After four successful years, this hedge fund had to be bailed out by major investment banks in the late 90s because it understated the kurtosis of many financial securities underlying the funds own trading positions.

Benoît Mandelbrot, a French mathematician, extensively researched this issue. He feels that the extensive reliance on the normal distribution for much of the body of modern finance and investment theory is a serious flaw of any related models (including the Black-Scholes option model developed by Myron Scholes and Fischer Black, CAPM developed by William Sharpe). He explained his views and alternative finance theory in a book: The Misbehavior of Markets.
The obvious question is, what if this deviation from ‘normal’ in stock market returns is the result of a concerted and sustained manipulation of the markets? The answer is seen is CDT’s paragraph which I have enlarged, regarding the assumptions required to maintain the market distortion, e.g. that this liquidity will continue to NOT spike rates, NOT to significantly erode the value of the US dollar, and NOT fall afoul of the changing political environment in the US as the middle class realizes it is being screwed, and that the social model is shifting from a democratic republic to an oligarchy.

What will limit the ability of Fed to continue to Ponzi scheme and continue to inflate asset bubbles? The answer is clearly the ‘value’ of the dollar, a subfunction of the full faith, credit and fear of the US and its debt of zero maturity which is the US dollar, otherwise known as dollar hegemony. When and if the dollar breaks, bonds and then stocks will quickly follow and the Ponzi scheme will be done. There will be no ‘deflation’ in terms of monetary deflation with a stronger dollar, excepting at the point of a gun (“Political [and economic] power grows from the barrel of a gun.” Mao ZeDong) or when we knock two or three zeros off the dollar and issue ‘new dollars’ as Russia issued ‘new roubles.’

To put all this simply and in summation, as we have been saying it now for four or more years, the limiting factor on the Fed’s ponzi liquidity scheme is the value of the dollar and the existing social and political structure of the United States.