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I have fallen down a wikipedia rabbit hole and landed on the page titled "Seven States of Randomness". I won't yet attempt to explain in a sentence what it describes.

Though at the end of the History section the following text is written (with my emphasis)

Mandelbrot and Taleb pointed out that although one can assume that the
odds of finding a person who is several miles tall are extremely low,
similar excessive observations can not be excluded in other areas of
application. They argued that while traditional bell curves may
provide a satisfactory representation of height and weight in the
population, they do not provide a suitable modeling mechanism for
market risks or returns, where just ten trading days represent 63 per
cent of the returns of the past 50 years.

Which most likely requires reading most of the article to get the full context.

My question is, is this true? Or is it even fair to ask if this is true? Does anyone know where this quote originated from or is this just the made up "fact" of whomever wrote this wikipedia page? If it is true, is there a better less technical explanation of it somewhere?

Mild vs. Wild Randomness:
Focusing on those Risks that
Matter and A focus on the exceptions
that prove the rule are copies of the original article referenced by the Wikipedia page. The authors are well respected academics so I assume that they have some support for the statement but the article doesn't appear to explain exactly what they assumed.

For a plausibility check, according to this chart the total compound increase in the S&P 500 index from 1970-01-01 to on 2018-12-31 (48 years so close to the 50 years they quote though obviously a different 50 year period) is 2622.25% (I'm using the Change in Index rather than including dividends because that requires actual research). I'm also too lazy to find a quick source of the top 60 days by percentage change since 1970 but Wikipedia does have a list of the best day each year so we can ask "If you had been invested in the S&P 500 since 1970-01-01 (ignoring dividends) but missed the best day each year, how much would you have lost overall?" If we take the best single-day returns for every year since 1970 that would produce 440.05% growth. If we exclude those 48 days, the other 364 days must have produced 467.04% growth-- (1+4.4005)*(1+4.6704)-1 = 26.2225). So (rather approximately) half the growth in the index has come from the best single day in each year which is roughly in line with the claim.

I assume that Prof. Mandelbrot and Taleb did a much more thorough analysis than I did here. Clearly they were looking at a different time period than I am, they were probably looking at a different index, they weren't limiting themselves to the data they could easily grab from Wikipedia, etc. But it's interesting that you can get reasonably close to their number doing a back of the envelope calculation using a much different data set than they were working with.

I can't speak to the research methods used in that study but Taleb was likely trying to build on his "black swan" hypothesis by showing that the "black swan" trading days have the biggest impact on the market overall.

The math behind Mandelbrot's and Taleb's analyses always goes over my head, even though I'm a fan of Taleb's work from a philosophical standpoint.

Tony Robbins simplified this concept by enforcing the idea that you can't time the stock market. I'm not sure who did the research, but it shows that if you try to time the market and miss out on the top performing days, you ultimately underperform the market.

Image source: MarketWatch