S&P 500 Weekly Gains And Losses Distribution (Strong Mean Reversion)

How does the return distribution of gains and losses look like in the S&P 500?

In this article, we calculate the average weekly gain in the S&P 500 and show you a distribution bar of the gains and losses. It turns out that the S&P 500 shows strong mean reversion: a weekly gain is most likely followed by weak returns, and weekly losses are followed by positive returns. 

Media is of course full of negative and scary articles and it’s easy to lose sight of the big picture.

S&P 500 weekly gains and losses distribution

But according to my calculations, a weekly fall (from Friday to Friday on the close) of more than 4% has happened 53 times since 1993. That is 4% of the sample, so it happens quite often (in my opinion).

Here is the weekly distribution in percent (for example 547 observations/weeks where S&P rose more than zero but less than 2%):

Weekly gains following a negative week

The table below shows the return the following week after weeks with negative returns (if S&P 500 for example this week fell more than 5% then the average return next week is 1.53%):

<0	<-1	<-2	<-3	<-4	<-5
0.40	0.48	0.38	0.33	0.63	1.53

For comparison, the average weekly return over the whole period is 0.2%. In other words, any negative week shows much better performance the next week than any random week.

Weekly gains following a positive week

The table below shows the return the following week after weeks with positive returns:

>0	>1	>2	>3	>4	>5
0.05	-0.04	-0.11	-0.08	-0.36	-0.40

If this week was positive, we can expect a negative return next week.

We can conclude the S&P 500 has over the period shown strong mean reversion.

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