A pal was working through some momentum and mean reversion ideas, and he came up with some really nice ways to understand what might be going on.

Here's my take.

Graph '0' is a daily price time series.

Daily returns are approximately followed by the same sign 50% of the time (momentum) and another sign another 50% of the time (mean reverting).

Daily stock returns usually have equal proportions of both types of returns over time and are hard to predict.

'1' shows pure momentum both positive and negative.

Pretty easy to predict what'll happen in the next period, eh?

Graph '2' has mostly momentum returns, with a single kink.

Graph '3' perhaps shows monthly stock returns over a long time period.

While there are fewer mean reverting returns, you shouldn't just count the number but also the magnitude of each type of returns.

Maybe only a portion of mean reverting returns will equal double the number of momentum returns in magnitude (that would make for a nice little investigation on the S&P 500).

Finally in graph '4' we see pure mean reversion. The return period coincides with a quarter of the wavelength.

If you could find the average return period which maximises mean reversion over time, perhaps you could come up with an approximation of economist's mythical business cycle. Perhaps.

With the same wave, now you can see how momentum can morph into mean reversion by just increasing your time horizon from daily to quarterly for example.

Real-life returns are a lot more complicated, but it's good to have some intuition into what's happening.