I’ve never quite understood the rational for scaling in for mean-reversion type trading systems. Scaling in for trend-following trades is simple and intuitive. By trading only a portion of your allocated capital at first, you can wait for further confirmation of the trend until you trade the rest of your capital. The trade off is that you will receive a worse entry price. However, for mean-reversion trading strategies you receive a better entry price at the cost of less trading opportunities. This may seem obvious, but my question is why scale in at all? Why not just place 100% of the order on the first or the second scaled-in purchase signal? Intuitively, it seems like either purchasing 100% of the position at the initial buy signal, or purchasing 100% of the position at the first dip after the buy signal, would produce the best results, and scaling in would only produce a return somewhere in between the other two results. To test this out, I backtested three frictionless versions of a simple long-only DV2 system on SPY from 1/1/2000 – 2/5/2013.

Default(Buy 100% of equity when DV2 < 50, Sell 100% of position when DV2 > 50):

- Number of trades: 573
- Avg. Profit/Loss %: 0.30%

Purchase at first Dip(Buy 100% of equity the first day the close is less than the close of the day DV2 < 50, Sell 100% of position when DV2 > 50):

- Number of trades: 292
- Avg. Profit/Loss %: 0.43%

Scale In(Buy 50% of equity when DV2 < 50, Buy 50% of equity more the first day the close is less than the close of the day DV2 < 50, Sell 100% of position when DV2 > 50):

- Number of trades: 575
- Avg. Profit/Loss%: 0.55%

I tested a similar system on all Nasdaq-100 stocks (that are currently listed as of 2/15/2013. Does contain survivorship bias).

Default(Buy 2% of equity when DV2 < 50, Sell 100% of position when DV2 > 50):

- Number of trades: 38998
- Avg. Profit/Loss%: 0.52%

Purchase at a Dip(Buy 6% of equity the first day the close is less than the close of the day DV2 < 50, Sell 100% of position when DV2 > 50):

- Number of trades: 13056
- Avg. Profit/Loss%: 0.59%

Scale In(Buy 1% of equity when DV2 < 50, Buy 1% of equity more on each subsequent day the close is less than the close of the first day DV2 < 50, Sell 100% of position when DV2 > 50):

- Number of trades: 37342
- Avg. Profit/Loss%: 1.48%

Lastly, I tested a system individually on each Nasdaq-100 stock.

Default(Buy 100% of equity when DV2 < 50, Sell 100% of position when DV2 > 50):

- Average of Avg. Profit/Loss%: 0.50%
- Standard Deviation of Avg. Profit/Loss%: 0.22%

Purchase at first Dip(Buy 100% of equity the first day the close is less than the close of the day DV2 < 50, Sell 100% of position when DV2 > 50):

- Average of Avg. Profit/Loss%: 0.57%
- Standard Deviation of Avg. Profit/Loss%: 0.34%

Scale In(Buy 50% of equity when DV2 < 50, Buy 50% of equity more the first day the close is less than the close of the first day DV2 < 50, Sell 100% when DV2 > 50):

- Average of Avg. Profit/Loss%: 1.07%
- Standard Deviation of Avg. Profit/Loss%: 0.26%

The results produce a unanimous conclusion across all three tests: scaling in produces the best average profit/loss. The only possible explanation I can think of is this: Avg. Profit/Loss % is independent of position sizing (meaning that a 2% gain on 50% of equity is the same as a 2% gain on 100% of equity) so scaling in would produce an outsized Avg. Profit/Loss% because the system contains the trades that never face a loss throughout its life, while being able to average down on trades that do contain a loss. Since these two types of trades will be weighted equally in the calculation of Avg. Profit/Loss% (because of the fact that the metric is independent of position sizing) it substantially boosts Avg. Profit/Loss%. In essence, I picked a subpar performance metric (Scaling In (Part Two) is a posts that run the same tests with a different performance metric). If anyone has any other insights as to why this occurs, please comment below!

One of the Sinclear option books has discussion on position sizing vs. mean reverting time series, sorry I can’t remember which one (both are worth reading), but he derives the optimal position size vs. distance from the mean and as it turns out it’s optimal to scale in to a point.

Interesting series of tests. This comment made me laugh: “In essence, I picked a subpar performance metric.” Don’t you hate after putting a lot of time into testing when you discover the performance metric sucked? I’ve been there. Anyway, any ideas on what the appropriate performance metric might be? What about something as simple as the CAGR / Max System Drawdown? Using CAGR will address the issue of having the average trade % not reflect the fact that sometimes the system was only 50% invested. Using Max System Drawdown will incorporate the losses that come when buying in 100% and then having the market continue down for a bit before reversing.

Thanks for the suggestion. Haha yeah it was pretty annoying having to go back through everything just to use a different performance metric.

I usually use CAGR and MDD as performance metrics (not CAGR/MDD though because often times I find myself having inflated results even though I have a low CAGR because of an even lower MDD), but unfortunately I used Average Profit/Loss% this time in attempt to compare the systems to each other despite their difference in exposure.

Can you provide results with a better performance metric? As mentioned, CAGR would work. So too would % gain as a percent of total equity at risk.

Thank you for your suggestion. I just finished another article using the same tests with difference performance metrics (CAGR/MDD/Exposure):

https://adaptivetrader.wordpress.com/2013/02/17/scaling-in-part-two/