Always outnumbered but never outgunned.

That's how the saying goes.

But this time you are outgunned and staring death squarely in the face.

In the moments before your final reckoning, you think about your children, husband - and the impending invasion.

This is it.

And that is precisely what economists face every day when forecasting markets.

They're intellectually overwhelmed, backs against the wall.

So in a move worthy of any blockbuster, economists claimed that markets should be unpredictable.

The defining feature of markets is that economists are ignorant of how they will move in the future.


Let's unpack what unpredictable means.

Usually in statistics it means that returns are IID (independent and identically distributed).

Volatility is ghost-like, always viewed indirectly - but everyone understands how it can fluctuate.

So with fluctuating volatility returns cannot be identically distributed.

Let's scratch that off, we may not need it, as time varying distributions can converge to IID-like results over time.

So, how about independent returns?

This is a strong statement, as we are saying that we cannot find any relationship. How do you test that? Brute force check against an infinite number of marginal distributions? Unlikely.

(This is also an excellent reason why you should never introduce any sniff of dependency into your statistics, no matter how little data is available - independence tests afterwards are insufficient.)

A testable tweak to independence is to check whether returns are autocorrelated.

Lo and McKinlay do this with their 'Variance Ratio' test, who note that the variance of a sum of returns should be equal to the sum of variances.

(The basis of a popular trick to scale up or down volatilities by the square root of time.)

If the variance ratio is well above one, we have positive autocorrelation or momentum, and below one we see mean reversion.

When mean reversion and momentum balance each other out the variance ratio is around one.

This is illustrated graphically on my Lazy PCA site.

One more technical point to be aware of is that typical statistical analysis goes out the window when the underlying return generating process has 'infinite volatility', as with er, equity distributions.

So the advice given here about hedging out extremes is very much still applicable.

It's interesting that even a simple trick, like assuming ignorance has led to decades of research into trying to understand the exact nature of the ignorance we are pleading.

And of course, what were Lo & McKinlay's findings in the end?

Markets aren't all that random.

Looks like we weren't outgunned after all!