A simple post on position sizing, comparing three similar volatility-based approaches. In order test the different sizing techniques I’ve set up a long-only strategy applied to SPY, with 4 different signals:

• UDIDSRI.
• 2-day candlestick KNN search, going long if the expected return is > 0.125%.
• Cutler’s RSI(3): long if RSI <= 10, exit if > 50.
• Long at every 15 day low close.

On top of that sits an IBS filter, allowing long positions only when IBS is below 50%. A position is taken if any of the signals is triggered. Entries and exits at the close of the day, no stops or targets. Results include commissions of 1 cent per share.

Sizing based on realized volatility uses the 10-day realized volatility, and then adjusts the size of the position such that, if volatility remains unchanged, the portfolio would have an annualized standard deviation of 17%. The fact that the strategy is not always in the market decreases volatility, which is why to get close to the ~11.5% standard deviation of the fixed fraction sizing we need to “overshoot” by a fair bit.

The same idea is used with the GARCH model, which is used to forecast volatility 3 days ahead. That value is then used to adjust size. And again the same concept is used with VIX, but of course option implied volatility tends to be greater than realized volatility, so we need to overshoot by even more, in this case to 23%.

Let’s take a look at the strategy results with the simplest sizing approach (allocating all available capital):

Top panel: equity curve. Middle panel: drawdown. Bottom panel: leverage.

Returns are the highest during volatile periods, and so are drawdowns. This results in an uneven equity curve, and highly uneven risk exposure. There is, of course, no reason to let the market decide these things for us. Let’s compare the fixed fraction approach to the realized volatility- and VIX-based sizing approaches:

These results are obviously unrealistic: nobody in their right mind would use 600% leverage in this type of trade. A Black Monday would very simply wipe you out. These extremes are rather infrequent, however, and leverage can be capped to a lower value without much effect.

With the increased leverage comes an increase in average drawdown, with >5% drawdowns becoming far more frequent. The average time to recovery is also slightly increased. Given the benefits, I don’t see this as a significant drawback. If you’re willing to tolerate  a 20% drawdown, the frequency of 5% drawdowns is not that important.

On the other hand, the deepest drawdowns naturally tend to come during volatile periods, and the decrease of leverage also results in a slight decrease of the max drawdown. Returns are also improved, leading to better risk-adjusted returns across the board for the volatility-based sizing approaches.

The VIX approach underperforms, and the main reason is obviously that it’s not a good measure of expected future volatility. There is also the mismatch between the VIX’s 30-day horizon and the much shorter horizon of the trades. GARCH and realized volatility result in very similar sizing, so the realized volatility approach is preferable due to its simplicity.