**For an ETF asset class rotational system which uses weekly data, what is the optimum number of weeks to look-back in order to calculate the relative strength score?**

Previous posts on the development of this system.

For this area of development, I set out to determine how robust the weekly look-back periods were. Also, I wanted to determine if there were any benefit to using more than one relative strength calculation. For example, would there be any benefit to ranking the ETFs based on the last ((X weeks + Y weeks)/2) average? Many rotational systems seem to use more than one calculation for relative strength. My gut feeling was that it may be unnecessary to do so.

Based on the results of the last post, the system will only trade on Thursdays. Because the ETFs are ranked using a weekly calculation, there is a delay between the ranking (which occurs at the close of the previous Friday) and the actual trade. I am not sure whether this factor hurts or helps performance. In future tests, I will remove the trade on Thursday only requirement so that the rotations are taking place on the same day as the ranking. In real life, it will be almost impossible for me to trade the system when it ranks and rotates on the same day.

**The Rules:**

- Buy 1 of 5 ETF asset classes at Thursday’s close based on its X week relative strength rank. Simply put, but the ETF that has gained the most over the last X weeks compared to the other ETFs.
- Re-rank at Friday’s close and rotate or not into the top ranked ETF next Thursday

No commissions or slippage included. Tests run from 1.1.2003 – 3.23.2012.

**The Results:**

These results show a large area of returns > 10% and drawdowns averaging -25%. I like a period of anywhere between 14 and 20 weeks. Keep in mind that in these tests there is no moving average filter applied to reduce drawdowns.

I chose 17 weeks as the optimum look-back.

Now, lets add a second relative strength rank. Since the first rank used 1-24 weeks, the 2nd one will use 25-52 weeks. This test will rank the ETFs this way: (17_week_change + Y_week_change)/2.

After adding a 2nd calculation and averaging it with the 1st in order to rank the ETFs, we see performance has decreased slightly while drawdowns have increased significantly.

Based on this simple test, there does not appear to be any benefit to adding more than one ranking routine.

**Thoughts and Caveats:**

Perhaps adding multiple ranking routines makes the system more robust. My results, using only 1 ranking routine, appear robust. There have been many studies which show that a relative strength calculation between 3 to 12 months is robust. 17 weeks works out to be near 4 months. Based on my review of many other studies and the results above, I do not believe it is necessary to use more than one ranking routine.

The ETFs used do not have much history. DBC and VEU did not start trading until 2006 and 2007, respectively. Results previous to 2006 were generated only from trading VTI, IYR, and IEF. This is a rather severe limitation.

These tests are very simple. The idea is to control for each variable, studying the effects, in order to develop a deep and thorough understanding of what makes the system tick.

The next factor to study will be the addition of a moving average filter in an attempt to reduce drawdowns.

Below is the equity curve using a 17 week ranking, holding the top ETF, with all trades taking place on Thursdays.

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