My Lazy PCA analysis tool plots returns against lagged returns and then fits principal components to the data.

('SP5HBI' S&P 500 High Beta index weekly)

The surprising thing is that the fitted components almost always have a slope of plus or minus one (except when there's a lack of data).

It's as if every single food stuff you analysed was only ever made up of a combination of two nutrients.

('INDEX_HSI' Hang Seng index quarterly)

When lagged returns are followed by their mirror image (e.g. a 10% return is followed by a -10% return or vice versa) they are bucketed as pure 'mean reversion' returns/

The more mean reversion returns the longer the fitted principal component becomes relative to the momentum component.

('LNKD' Linked In weekly)

Momentum works in the same way.

The more returns further away from the mean increases the vectors and ellipse area.

('XOM' Exxon Mobil quarterly)

The rounder the ellipse the closer the length of the momentum and mean reversion radii become, eventually they converge to the volatility of the return time series.

('TWTR' Twitter daily)

A circle implies 'invariance' which means the returns are close to the idealised return academics assume and we can safely scale returns by the square root of time etc.

The puzzling thing is, why the components of *every* return time series breaks down along only those two -1 and +1 slopes.

Previously I have likened components to 'ideas'.

If you apply this sort of analysis to a portfolio for example, you can extract the main return drivers over time and then understand how many 'ideas' are generating profits. The more ideas and the more diversification the better.

The upshot is that every return time series plotted against its own lagged returns can be explained by two 'ideas' - momentum and mean reversion.

Principal components analysis is notorious for having undecipherable results and yet in this case it gives us intuitive results *every* single time.

I must be missing something obvious, but I can't put my finger on why this *has* to be the case.

Perhaps it doesn't, perhaps it just a matter of finding the right type of returns which buck the trend.

This has been puzzling me for months, if anyone has any ideas let me know!