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Why Momentum Tests Use Overlapping Holding Periods

Article Quant Q&A · Author: zsljulius
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Summary

The document asks why Jegadeesh and Titman used overlapping portfolio holding periods when testing momentum strategies. The replies give two intuitions: overlapping periods can create a larger sample than non-overlapping periods, and examining portfolios across varied formation or holding inputs may show that a result is not confined to one particular setup. A larger sample can improve a test’s ability to detect an effect, all else equal.

The replies do not provide a formal power calculation or empirical comparison. Overlap also makes portfolio returns dependent across adjacent periods, so standard errors must account for that dependence; a cited discussion points to this estimation issue but does not answer the power question. Thus overlap can increase observations and test power, but observations are not equivalent to independent evidence, and the claimed robustness from parameter variation is a separate consideration from statistical power.

Key ideas

  • Overlapping holding periods produce more portfolio observations than non-overlapping periods.
  • A larger sample can improve a statistical test’s ability to detect a genuine momentum effect.
  • Adjacent overlapping returns are dependent, so inference must use appropriate standard errors.
  • Testing varied parameters can probe robustness, but it is distinct from the effect of sample size on power.

Tags

MomentumEquitiesBacktestingStatistics
Full text
# Jegadeesh and Titman 1993 Power of their test


# Jegadeesh and Titman 1993 Power of their test












I am reading this classic paper(http://www.business.unr.edu/faculty/liuc/files/BADM742/Jegadeesh_Titman_1993.pdf) and got confused by one of their arguments on their overlapping portfolio strategy to test momentum. They claimed on page 68:

> To increase the power of our tests, the strategies we examine include portfolios with overlapping holding periods.

I don't quite sure why overlapping holding periods increase the power of their statistical test. Can someone please give an intuitive explanation?

## Answer by BAR (score 1, accepted)

https://quant.stackexchange.com/a/20857

It is due to parameter variation.

By overlapping portfolios they can better show that their results are not a one-off result that only works given this very specific set of inputs.

Without testing with different parameters (stocks, timeframe, etc), results are liable to blow up given a different input.

That is not to say using parameter variation always guarantees future results, only that it increases the probability.

## Answer by user3264325 (score 4)

https://quant.stackexchange.com/a/20844

Non overlapping periods would make for a far smaller sample

## Answer by zsljulius (score 0)

https://quant.stackexchange.com/a/20854

I have found a great post here explaining the estimation errors with overlapping portfolio construction. http://www.alexchinco.com/standard-error-estimation-with-overlapping-samples/.

I have not finished reading yet, but it doesn't seem to address the problem of power of statistical test.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.