# Bean Counting

Yesterday I noted that daily S&P 500 returns are 50% mean reverting (sign of returns differ day over day) and 50% momentum (same sign).

Turns out I was wrong.

I did a quick totting up and found that over 65 years of returns, there are 10% more momentum returns than mean reverting ones.

Probably why this super simple momentum strategy works.

In any case the cumulative occurrences of both types of returns since year dot look like this.

So, even though on average there are more momentum returns than mean reversion, the trend has been downward since 1975.

This chart says nothing about return magnitudes.

If mean reversion returns were 10% *larger* in magnitude you could imagine that balancing out 10% *more* momentum occurrences, right?

The Lazy PCA site fits an almost exact circle to the returns, meaning momentum and mean reversion cancel each other out over the fullness of time.

[The 'momentum' radius length of the ellipse is 0.98% and mean reversion is 0.96%; volatility should be about 0.97%]

Another point to ponder is whether markets were woefully inefficient decades ago?

Maybe, but a string of small momentum returns might have often been followed by a steam roller of a mean reversion return.

Luckily you can investigate these questions out for yourself with the Lazy PCA site.