# Timing Strategy Comparison

Way back when I got interested in testing market efficiency, which led me to build the Lazy PCA site; and then I noticed that the principal components / drivers / ideas of *almost* every return time series are momentum and mean reversion.

I never expected that returns could be sliced up so neatly.

Well, as part of my testing of the Lazy Backtesting IDE, I began exploring momentum and mean reversion strategies and came up with a few interesting ideas.

Simplest Momentum. Mainly a teaching tool, but also it uncovered how much momentum there was back in the day!

Correlation strategy. Using auto-correlation to look for indications of momentum and mean reversion

Fractal strategy. Similar to the autocorrelation strategy, but using Hurst exponent estimations instead of auto-correlation

Their Sharpe ratios are 1, 1.6 and 1.25 respectively.

(Many readers have shared better performing other variants now, thanks for sharing!)

But they all do similar things, especially the last two.

Here's how they look graphically.

Each is normalised to have zero return on average, more here.

The Correlation strategy takes the most efficient path, and therefore also has the highest Sharpe ratio (or vice versa!).

The correlations between all 3 are:

- Correlation vs Simplest: 0.2
- Correlation vs Hurst: 0.4
- Hurst vs Simplest: 0.9

Combining the Correlation and Simplest Strategies (the two with the lowest correlations) results in this.

The combined strategy avoids cumulative negative territory early on unlike the plain Correlation strategy and likewise has a much smoother landing than the Simplest strategy; leading to a Sharpe ratio of 1.7.

Nevertheless it's obvious that these strategies make the bulk of their money during the 70s (like Casino the movie) ideally that rump would be spread out more evenly over time, which would not only lead to more consistent returns but also a higher Sharpe ratio.

The takeaway is that improving Sharpe ratios can and should be thought of being the same as improving performance *consistency* over time.