# Power Laws & Investing Long Term

• 1 min read

- 401K
- Random
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_aioseop_keywords: Black Swan, S&P500, Long Term Investing, 401k
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I decided to download about 40 years of data on the S&P500 and analyze how many times the index made an explosive leap higher. The reason I did this was because of something I read in The (Mis)Behavior of Markets by Mandelbrot. In his book, Mandelbrot states that something like only 10 trading days account for some of the largest moves in market's history.

Although he doesn't provide the math for his claim, I decided to look at the positive % changes in the S&P500 and graph them. I looked at how many observations I had for the time period and then compiled them into positive ROC groups. The largest observation for positive ROC was for moves greater than 0% and less than 1%, which makes sense since we see lots of smaller moves over time.

As the long tail moves out, we see less greater ROC moves, with only 7 large moves of greater than 5% and less than 6%. What I didn't plot was one observation of a 9%

~~10%~~or greater move, so we even have one of those.In my opinion, and contrary to trading advice, it seems that if you want to catch large positive moves (and inadvertanely negative moves too), you'd have to remain invested for the long term. Maybe there is something to be said about this "Buy and Hold" strategy! :)