Rotational Momentum Investing: Normalizing the Data

I’ve been looking into trading a rotational model using momentum lately. This post covers a few good reason for why one should trade momentum. My personal reasons are:

• It provides diversification
  • I plan to trade a mean-reversion system soon, so adding a trend-following trading system will smooth my equity curve.
• It is proven within academia
  • There are multitudes of research papers written over the momentum effect, and it is well-established anomaly within academia. You can find some of these for free over at QuantPedia.
• Easy to trade
  • Trading a momentum system will only require to monitor it weekly, or monthly, leaving time for research into other efforts.

The momentum system being tested:

• Invests 100% of equity in the top four stocks using equal weights.
• The stock universe is all NASDAQ-100 stocks according to the NASDAQ website on 01/01/2013 (ticker list: NASDAQ Ticker List)
  • Not free from survivor-ship bias – results will be inflated
• Test will be frictionless, from 01/01/1998 – 01/13/2013
• Re-ranks and trades monthly. Does NOT re-balance monthly.
  • I used AmiBroker to test this. I re-rank at the first, second, and third day of every month. I also set an option where I am forced to hold onto a position for at least 5 days before selling. There are some occurrences where this may not perfectly replicate a monthly re-rank.

For this test, I will be using four different indicators:

• TSI()
  • CAGR: 31.52%
  • MDD: -69.06%
• Close relative to the 250-day high of the high
  • CAGR: 13.38%
  • MDD: -50.84%
• 250-day ROC of Close
  • CAGR: 35.25%
  • MDD: -73.00%
• Close relative to the all-time high of the high
  • CAGR: 15.17%
    MDD: -49.86%

For the purposes of creating a better performing ranking criterion, I will aggregated all four indicators into one. There are two obstacles I must first overcome:

1. Normalizing the criterion
   1. The four indicators each have different scalings and different distributions. To create an aggregate indicator, we should normalize the indicators so they have similar sensitivies.
2. Weighting the criterion
   1. The four indicators will most likely not contribute equal amounts to increasing performance. TSI() may have twice as much predictive power as the 250-day ROC, or it may be the other way around. Designing a weighting scheme will assign relative importance to the contribution of an indicator to ranking criterion

Normalizing the data:

There are two methods of normalizing the data which I will be testing for individual performance. The perfect rank function, and the z-score function.

Z-Score:

• TSI()
  • CAGR: 18.48%
  • MDD: -68.04%
• Close relative to the 250-day high of the high
  • CAGR: 17.33%
  • MDD: -49.88%
• 250-day ROC of Close
  • CAGR: 25.55%
  • MDD: -46.69%
• Close relative to the all-time high of the high
  • CAGR: 19.29%
  • MDD: -42.78%

Percent Rank:

• TSI()
  • CAGR: 20.21%
  • MDD: -65.30%
• Close relative to the 250-day high of the high
  • CAGR: 14.45%
  • MDD: -54.53%
• 250-day ROC of Close
  • CAGR: 22.48%
  • MDD: – 45.45%
• Close relative to the all-time high of the high
  • CAGR: 16.07%
  • MDD: -50.51%

Conclusion:

Z-score turned out to be better at normalizing indicator sensitivities while maintaining (or in the case of close relative to the all-time high of the high/250-day high of the high, increasing) performance.  From this test, we can also form a tentative conclusion that TSI and 250-day ROC are indicators that perform better as a ranking indicator on an absolute basis (it doesn’t matter historically where the indicator resided), whereas for indicators such as the close relative to a variable, they perform better on a relative basis (where the indicator has resided historically positively impacts performance).