As goes early-January, so goes Nothing

Salil Mehta is a popular statistician and risk strategist, who has developed a unique method to teach quantitative techniques. He blogs at Statistical Ideas.
We’ve started the year with a sizable downward market pattern, which is making market participants think in ill-advised ways.  Eight of the first eleven trading days (S&P 500) were negative.  If we use a binomial distribution model, it would show a 9% probability of seeing >8 down days of the first 11 days (focus on green color below).  So it’s rare, but not necessarily significant.  Note that throughout this article, we sometimes equally express 8 of 11 trading days as 8/11.  Now instead of the theoretical models that under-emphasize mathematical kurtosis in financial markets (Ch.3 of Statistics Topics, or here), if we examine the empirical market history, then we would appreciate a further case for how rare is such a pattern.  And of 64 prior years (from 1951 through 2014), only 6% of those years fit this criteria (focus on orange color below).  In science, we traditionally often rely on p-values of 5% to be significant; so 6% is not far from such threshold.  In any event, the actual probability may actually seem rarer still.  Since the last time we had such a pattern (>8 down days of the first 11 trading days) was 37 years ago, in the late 1970s!
Part of the reason there is a focus on the portion of initial trading days that have been down, is that the overall market performance over these first 11 trading days has been anything but remarkable.  YTD of -1.9%.  Over the same 64-year period (though 2014) the market has initially changed a similar -1.9% or worse, on 22% of those years (and the last of which were just a half-dozen years ago).  So nowhere near more exotic, for market participants to focus on versus the current “down days” pattern that only 6% of the years fit.Still, given the sizable downward market pattern, it is natural to ask: “What now?”  For example, does the initial downward S&P 500 pattern foretell something concerning the performance for the rest of January, or even for the rest of 2015?  It turns out that neither of these latter questions can be resolved by assessing these statistics from the initial trading days.  For more on how lay people and many professionals can insanely bungle their understanding of probability, see these articles from an endless well of the same: hereWall Street Journal, and Financial Times.  We’ll show in the comprehensive pairs of modeling charts below, how despite the sizable downward market pattern, there is little we can infer about the rest of the year, let alone for just the immediate rest of the month!  For amusement value, we identify the last year (2014) in red text color.  And to be excruciatingly thorough, we note that the impact of January versus the remaining 11 months is no different from the noise we see below.  What these charts show is that this adorable notion of “As goes x, so goes y” is basically a case of dangerous people abusing probability to confuse anyone into believing there is definitely a there there.

So sure seeing a drop in 8 of 11 initial trading days, and being down 2% for the year, is enough to create some short-term “panic” among market participants (focus on grey color of top chart above to assess the degree of personal, over-confidence we are continuing to head lower for the foreseeable future).  But as we have proven in various parts of this academic blog, all of this playing around with statistics that others do is simply a silly exercise.  Trying too hard with the markets just bloats one’s hubris and reduces the intelligence we should be having.  It also dangerously puts our financial interests at risk.  Look no further than the intraday FXCM business fiasco from last week, which had the potential to again destabilize financial markets we in Washington had worked hard to calm.  In the realm of probability, we should probe deeper into anyone’s suggestion of drawing a relationship (either in business, or anywhere else in life), where there are regular false positive errors occurring.  In this case, such errors are from over-emphasizing the importance of initial annual trading days, in order to in any way evaluate where the market is likely to go.


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  1. constantnormal commented on Jan 19

    There is nothing so entertaining as the attempt to recognize patterns in short-term chaos …

    L. Frank Baum said it a lot more clearly, using a lot fewer words:

    “Never give up. No one knows what’s going to happen next.”

  2. VennData commented on Jan 19

    Anything that market data can predict will he arbitraged away by computers trading at billions, trillions of per second faster than you.

    Notice how “technical analysis doesn’t work anymore.” The computers will arbitrage away anthing as prosaic as technical analysis if it ever really added value.

    But those that believe will not listen. So to make a social benefit that shifts resourxes from astrologers to sciejce-based thinkers. Raise taxes on day traders, lower them on scientists: get rid of carried interest preferences for crap shooting hedge funds and raise short term capital gains while lowering long term capital gains.

    Oh and raise taxes on the rich until there is some evidence of AGGREGATE loss on investment. No one or two headlined lod mouths.

    And no tax have can use the Western Banking system. Cash suitcases for you.

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