A Value or Momentum portfolio is selected each month, based on the highest previous 12 month return (R). Data are from Ken French’s library from 1950 to 2015. I use the large momentum portfolio and small value portfolio (the HML anomaly does not exist in large cap stocks).

I found two surprises:

1) Ranking on squared returns (n=2) consistently outperforms ranking by return alone (n=1). In other words, the magnitude of return is important, positive or negative. Mean reversion probably accounts for the improvement but this needs more detailed investigation. Annual returns exceed 20% over the last 4 decades.

The table shows that the n=2 strategy performs much better than the component portfolios, particularly this century: 17% compared to 13% and 8% for Value (V) and Momentum (M) respectively.

2) Overlaying an absolute momentum filter (hold cash when return < 0) degrades returns. The margin widens with recency: to 3.6% annually since 1999! Sharpe ratio is not materially reduced as deviation shrinks proportionally.

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Have you tried N squared for a 3 factor portfolio?

Not yet! I guess the next step is to compute a kxN matrix: k factors versus exponent N.

Are you squaring negative returns or how can you get different ranking otherwise?

Exactly, for n=2 all returns are squared.

Got lost… Do you square the continuous returns (i.e. +5% written as 1.05, with 1.05^2=1.1025; while -5% written as 0.95, with 0.95^2=0.9025) or the discrete/percentage returns (+5%^2 = +25%; while -5%^2=+25%)? I assume you use the second, to be able to capture mean reversion effects… Am I right or simply lost?!

Yes you are right. Sorry for the delay in response (and new posting!).