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Many momentum studies skip the most recent month when calculating momentum to account for "reversal effects." On the other hand, I've read online that some people get better results from not skipping the most recent month. And some papers seem to skip two months.

What was the first paper to propose the skip-month? Does the momentum effect generally appear stronger across time and across different countries when skipping a month?

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The idea of skipping a month was already in Jegadeesh and Titman 1993. The key academic paper in this area.

Jegadeesh himself (without Titman) discovered a 1-month return REVERSAL effect in 1990, so it makes sense that he would take out 1 month in calculating returns in his later (1993) study. He already knew what happens to stocks that are up a lot over previous month; and wanted to investigate the effect of longer term (3mo, 6mo, 9mo, 12 mo) returns.

Academic researchers coming after have usually reproduced the Jegadeesh Titman procedure. IMHO that is the way careful research should be done. Of course you can also try minor variants "to see if you can do better" but that adds very little value statistically speaking (i.e. non significant, random variations).

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