Dead Air

You can count dead air on the radio by the millisecond, when you expect to hear something but don't, your ears become acutely aware of not hearing anything at all.

This doesn't happen with white space on a page. Look at a well designed website; your eyes will happily swim around it; luxuriate in the emptiness.

Most of the time dead air is a blatant mistake, but there are moments when it's used to devastating effect.

For example,

Dan Carlin is another dead air guru. A second of dead air in Carlin's mouth is worth a thousand words.

Sitting on a lot of cash is a trader's dead air, and shows a lack of ideas.

So, let's naively assume that more often than not one S&P daily return is followed by another of the same sign (Simple Momentum). Let's also restrict ourselves to long positions - our rule is to jump into the market when the previous day's return was positive and autocorrelation is positive.

r > 0 && ac > 0 ? INDEX_GSPC = 1 : INDEX_GSPC = 0

Here's a picture of the S&P 500 and newly christened 'Selective Momentum' Sharpe trajectories.

Sharpe Trajectories are demeaned so that we can compare returns across time periods. This means a stretch of non-trading looks like a straight downward sloping line, as the mean return is subtracted away from zero returns each period.

Obviously, it looks like our strategy took early retirement around 2000, which means positive autocorrelation (calculated with 2 years of daily returns) more or less died.

Jake shows something similar in a lovely picture here.

As the S&P 500 faffs around, Selective Momentum spans the years with a beautiful arc and a Sharpe ratio of 1.5.

Of course, by not trading at all Selective Momentum dodges the busts around 2000 and 2008. It stops trading more or less at its peak.

20/20 hindsight is a wonderful thing, but as Jake and Mike point out something fundamentally changed around 2000.

Auto correlation with a daily lag has been sub zero since around 2000.

We can also clearly see in 8 short years that the demeaned S&P 500 time series went from peak to trough.

What happens if we add a mean reversion component to deal with the post millennial situation? Even though we would make money, we bring the average return down considerably and therefore our Sharpe ratio too (1.25).

Don't know about you, but I'd rather money in my pocket than good looking statistics!

(It's really hard to be more 'efficient' than a straight line!)

Once you achieve a decent return, not trading and dead air can make for good looking (often overfitted) statistics.

Taken to an absurd extreme, just quitting after a handful of positive returns would let the dead air inflate your Sharpe ratios substantially.

The more dead air and less trading the less the strategy is really being tested and the more susceptible to overfitting it becomes.

The momentum strategy presented here doesn't trade for the best part of 15 years (an extreme example) and has a Max Wait to profitability of 19 years which is a tell tale sign of problems; but there are less extreme scenarios where dead air bloats statistics.

[Code for the Lazy Backtesting IDE is here]