Example of Gambler’s Fallacy: The US Stock Market’s Rip on a Traditionally Down Day of September 30

I reiterate here that neither statistics nor seasonality determines the market’s outcome. 

The Bespoke Invest notes that one of the trading sessions with a notorious bias for negative performance has been September 30^th

While March 30th has traditionally been the day where the S&P 500 has been up the least, 9/30 is tied for fifth at 38%.  Since 1945, the S&P 500 has declined an average of 0.15% (median: -0.25%) with positive returns just 38% of the time on 9/30.  While the long-term performance of the S&P 500 on the last day of September has been poor, in recent years it has been even worse.  In the current bull market, if the stock market has been open on 9/30, it has traded down

Well, it turns out that positive returns of just 38% of the time on 9/30 prevailed last night…

Even more, US stocks came out strongly…

Why? According to this CNBC report which quotes an expert:"Nothing has changed fundamentally from yesterday to today except that most of the globe is rallying with weaker-than-expected data points, with the hope of more stimulus from central banks," said Ryan Larson, head of U.S. equity trading at RBC Global Asset Management.

Ah there you have it again…stimulus. So expectations of stimulus may have partly powered last night’s bounce.

The basic premise: Each session is different from any other session in the past. And all past sessions have different factors of influences in shaping the day’s outcome. So unless these sessions share same influences, those ‘trending’ numbers can be seen as just coincidental. 

This fascination with “trending” numbers, most especially applied to seasonality, in projecting future outcomes can be seen as the Gambler’s Fallacy

Investopedia explains: When an individual erroneously believes that the onset of a certain random event is less likely to happen following an event or a series of events. This line of thinking is incorrect because past events do not change the probability that certain events will occur in the future.

As example, again Investopedia: Consider a series of 20 coin flips that have all landed with the "heads" side up. Under the gambler's fallacy, a person might predict that the next coin flip is more likely to land with the "tails" side up.This line of thinking represents an inaccurate understanding of probability because the likelihood of a fair coin turning up heads is always 50%. Each coin flip is an independent event, which means that any and all previous flips have no bearing on future flips.