DRAFT Data Dredging Momentum Strategies

In July of 2020 I presented momentum results from Momentum202007. Momentum202007 ran a modified version of the Jegadeesh/Titman/Rowenhorst momentum algorithm.

Momentum202007 computes btmN, topN, topNx (topN - ^IRX), and timedTopNx on portfolios containing 1-6 members on the NASDAQ, DOW, DAX, S&P 100 and Russell 1000 indices. Critically, Momentum202007 used months instead of days and limits K to 1 month (as per Don Maurer). Momentum202007's price database comes from 22 years of Yahoo's price adjusted data. Momentum202007 did not take into account the evolution of index composition through time and so was subject to survivorship bias. Momentum202007 determined that the result of a strategy was significant if, when compared to its benchmark, it had an independent t-test > 3.64. Among other results, Momentum202007 showed significant results over 20 years for momentum portfolios utilizing lags of 01_03_06_12mos containing 6 members (Fundx) and a lag of 11mos containing 3 members.

Momentum202104 is similar to Momentum202007, but accounts for the evolution of index composition for the universes shown below (Thanks to Don Maurer fo allowing me to run Momentum202104 on his Norgate Machine). This limits survivorship bias.

Momentum202104 runs the cross product of

• The above 5 universes: SPx500, DOW30, SPx100, RUx1000, NDx100.
• 1351 lag strategies formed by taking Harris (1,3,6,6) plus all 1,2 and 3 length combinations of the Portfolio Visualizer months.
  • months=[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 18, 21, 24, 27, 30, 33, 36]
• 6 different portfolio lengths of 1,2,3,4,5 and 6 members.
• 4 methods
  • topN is the top N tickers sorted by the above equally weighted lags
  • timedTopN is topN except when an absmom5 calculation says turn to cash.
  • btmN is the btm N tickers sorted by the above equally weighted lags
  • btmNS which sells short the btmN selected stocks.
• 14 timeframes (5,10,15,20...70 years)

• None of the 1350 lag strategies produced significant results for the Dow, SPX100 and RUx1000.
• Only 394 of the 1,108,728 rows have a paired t-test > 3.64.
• Lag strategies cluster as shown in the Figures Section, showing significant and clear separation between NDx100 and SPx500 groups and significant and clear separation between portfolios with 1 member and > 1 member.
• The top left cluster consists entirely of portfolios with 35 year timeframes.
              4 3 2     1  <- NDX
  
    6  5  4  3    2      1    <- SPx500
• Although neither FundX nor Harris (1,3,6,6) nor 11mos made the cut, 03_06_12mos with 3 members and 03_11mos with 4 members did.

• 20210430 - You compared the monthly returns of the strategy against the monthly returns of the index. Why did you use a t-test value of 3.64? That is a very extreme value which tests for significance at above the 99.95% level.
  • I find it instructive to see how the risk/return plot populates as I vary the t-test from most to least restrictive. E.g. consider the figures below
• 20201117 - If your algorithm is good, it should be able to pick out the better stocks independent of the options that it is fed so long as the choices are broad.
  • Given the clean cluster separations in the Risk/return plot, apparently the algorithm is not "good". It is (clearly) dependent on timeframe, universe and membersize choice. Particularly instructive is the strategy that produces the best return overall: NDx100 with 1 member and 11 month lag (t = 3.873891). SPx500 with 1 member and 11 month lag is also statistically significant (t = 3.434263). We compare them in the Table "A Comparison of 11mos 1 member TopN strategies for NDx100 and SPx500 from 2018 to 2021". The table is subject to A LOT of interpretation, but apparently one danger of a large universe (e.g. S&P 500) is that it has a larger collection of tickers (e.g. NKTR) that look good over an 11 month period, but are unable to sustain performance. As such, it might be worthwhile to return to the Rowenhorst approach and vary K (holding period) to see if results improve.

This document is a DRAFT. These strategies were discovered, not proposed and then checked post hoc. This is the very definition of p-hacking or (Data Dredging). As an aside, that is why I trust 11 month lookback more than FundX or any of the other 2, 3 and 4 month lookback stratgies (e.g. FundX and Harris). Adding more dependent variables increases the False positive rate of any theory (Is Most Published Research Wrong?). In order to validate the results, I need to add topNx and timedTopNx methods and compare a run of Momentum202104 with Yahoo data to a Momentum202007 with the same data

• Momentum References
  • [19930300] Jegadeesh and Titman - "Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency"
  • [19980200] Rouwenhorst, K.G. - "International Momentum Strategies"
  • [20150415] JP Morgan e-book, "Momentum Strategies Across Asset Classes, April 2015"
  • [20170816] Lingane, Peter J. - Momentum Strategies to Increase Return and Reduce Risk.
• [20161218] Rouwenhorst Sensitivity To js[25,35,45,65,130]/ks[25,35,41,65,130] here
• [20141204] Scholtz, H.D. - "Is Systematic Risk Diversifiable? Presentation of a Portfolio Model that Eliminates Systematic Risk" - SSRN

A Comparison of 11mos 1 member TopN strategies for NDx100 and SPx500 from 2018 to 2021

Appendix: 11154 Strategies/ 5085096 Total t>3.650 significance