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What fifty years of research have made of it

By 1970, Levy's measure had been refuted. That it is still calculated today is not thanks to him — but to what came afterwards.

In 1993 the effect was independently confirmed, on data that lay mostly after Levy's period. In 1997 it became a factor alongside market, size and value; anyone explaining a fund's performance today accounts for it. By 2013 it had been demonstrated across countries and asset classes.

This page follows that path — including the points where the strategy was expensive. At the end you will find what of it appears in this list as a separate column, and what follows from that. Where the measure comes from and how it is calculated is covered in the first part: RSL: Method & Origins.

since 1967 studied — from Levy's paper to today's literature Robert A. Levy 1967, Journal of Finance 22(4), p. 595
8 markets individual stocks in four regions, country indices, government bonds, currencies and commodities Clifford S. Asness 2013, Introduction
1927–2013 length of the data series analyzed — 87 years Kent Daniel 2016, Table 1

The path through the research

Nine milestones at which the assessment changed. The first two are covered in the first part, the other seven each get their own section further down; each is listed in full in the references at the end.

1993

The evidence

12.01% p.a. compounded excess return, six months formation and six months holding, winners minus losers Narasimhan Jegadeesh 1993, Conclusions
1965–1989 study period, mostly after Levy's period Narasimhan Jegadeesh 1993, Conclusions
half of the first year's excess return disappears over the two following years Narasimhan Jegadeesh 1993, Conclusions

Not Levy's rule, but the same idea, set up properly: Narasimhan Jegadeesh and Sheridan Titman sort stocks by their return over the past three to twelve months, buy the winners, sell the losers short and hold for three to twelve months. The strategy they examine most closely — six months of formation, six months of holding — earns a compounded excess return of 12.01 percent per year from 1965 to 1989, which cannot be explained by systematic risk.

What matters is not the size of the number but where it comes from: the data lie mostly after Levy's period, and it is not his sample. That was exactly the objection in 1970.

The number comes with a second finding that is cited less often: half of the first year's excess return disappears again over the two following years. The effect has a horizon, and anyone who extends it beyond that is counting on something the source does not support.

Source: Narasimhan Jegadeesh 1993, Conclusions

Does the finding hold?

After 1970, this is the fair question of a skeptical reader: why should I believe it this time?

Because the effect has since been found outside the original data, in other countries and in other asset classes — and because it has made its way into the models the industry uses to evaluate fund performance.

1997 — Adopted into the standard models

In 1997, Mark M. Carhart adds momentum as a fourth factor alongside market, size and value. Since then, anyone who wants to explain a fund's performance accounts for it: a fund that is ahead only because it bet on rising stocks no longer counts as above-average management in this model.

In the literature the factor is usually called UMD — “up minus down” — and it is freely available in Kenneth French's data library with monthly values from 1927. The header of the file states how it is measured: “Prior return is measured from month −12 to −2” — that is, with exactly the gap from the section further down.

Source: Mark M. Carhart 1997, Abstract, French Data Library

2013 — Across countries and asset classes

Clifford Asness, Tobias Moskowitz and Lasse Heje Pedersen find value and momentum premiums in eight markets and asset classes: individual stocks in the US, the UK, continental Europe and Japan, plus country equity index futures, government bonds, currencies and commodity futures. The returns of value and of momentum are more closely related across these classes than the asset classes themselves — a sign of a common cause, not of eight chance findings.

In practice, however, the most important statement of the paper is a different one: value and momentum are negatively correlated with each other, within each asset class as well as across classes. A strategy based on relative strength therefore tends to do poorly when a value strategy does well. Holding both is not holding the same thing twice.

Source: Clifford S. Asness 2013, Abstract, Introduction

2016

The downside

The average is good. The bad case is very bad.

Kent Daniel and Tobias Moskowitz analyze the months from January 1927 to March 2013, 87 years, and show what the average conceals: the big losses come in clusters. The strategy's two worst months are July and August 1932, back to back, after a market decline of around 90 percent from the 1929 peak. March and April 2009 rank 7th and 4th; three of the ten worst months fall in 2009, within a three-month period in which the market rose strongly and volatility declined.

What matters is where the crash comes from: the short side. In both episodes the market rose strongly — and the losers rose several times as much. A momentum strategy has sold exactly these losers short. It does not crash because its winners fall, but because its losers rise.

Source: Kent Daniel 2016, Table 1 and the accompanying text

July and August 1932

  • Market +82%
  • Winner decile +32%
  • Loser decile +232%

Kent Daniel 2016, text on Table 1

March to May 2009

  • Market +26%
  • Loser decile +163%

Kent Daniel 2016, text on Table 1

This leads to the point that matters for this list: anyone who bought only the top of the ranking did not crash in 1932 — they were 50 percentage points behind the market. The strategy's crash is the crash of its short positions.

The momentum factor, recalculated

How often this happens can be counted in the raw data. Kenneth French's data library lists the factor with monthly values from 1927. We calculated the values below ourselves from that data rather than copying them. They belong to a long-short portfolio with short selling — not to what this list shows; the underlying signal, however, is the same.

8.6% UMD factor (long-short): average of the annual values 1927–2025 French Data Library, annual values, CRSP data as of 202607
21 of 99 UMD factor (long-short): calendar years with a loss French Data Library, annual values, CRSP data as of 202607
−83.5% UMD factor (long-short): worst year, 2009 French Data Library, annual values, CRSP data as of 202607
−52.6% UMD factor (long-short): worst month, August 1932 French Data Library, monthly values, CRSP data as of 202607
−73.7% UMD factor (long-short): June to August 1932, compounded French Data Library, monthly values, CRSP data as of 202607
−49.4% UMD factor (long-short): March to May 2009, compounded French Data Library, monthly values, CRSP data as of 202607

What research has learned about measuring

Having the idea is one thing. Measuring it correctly kept research busy for another fifty years.

Three refinements came out of it. The first concerns the measurement window, the second the reference point, and the third is not about the signal at all, but about exposure. All three appear in our list in the next section — as separate columns next to the RSL, not in its place.

1990 — The most recent period should be skipped

Over horizons from one week to one month, prices do not continue but reverse — Narasimhan Jegadeesh shows this in 1990, and Bruce Lehmann independently in the same year. That is why the academic standard measures over months t−12 to t−2 and deliberately leaves out the most recent month.

Including it mixes into the signal exactly the effect that works against it. Our own formula does this in a stronger form: in it, the latest price is not just inside the measurement window, it is the numerator.

It also shows in Jegadeesh and Titman 1993, on their own data: their portfolio of winners minus losers makes a profit month after month after formation — with exactly one exception:

With the exception of the first month, this portfolio realizes positive returns in each of the 12 months after the formation date.

Narasimhan Jegadeesh 1993, Conclusions

Source: Narasimhan Jegadeesh 1990, Abstract, Bruce N. Lehmann 1990, Narasimhan Jegadeesh 1993

2004 — The best single measure is again a price ratio

Thomas J. George and Chuan-Yang Hwang put the nearness of a price to its 52-week high in direct comparison — against the classic momentum of Jegadeesh and Titman and against the industry momentum of Moskowitz and Grinblatt. The price ratio dominates both, and the returns it predicts do not reverse in the long run.

For Levy's basic idea, this is a late confirmation: relating a price to a reference of its own is not the weaker approach. It is just that the best-documented reference is not the moving average, but the high.

Source: Thomas J. George 2004, Abstract, Tobias J. Moskowitz 1999

2015 — The biggest lever is not the signal, but the risk

Pedro Barroso and Pedro Santa-Clara scale the strategy by the inverse of its own realized volatility over the past six months — so they put less to work when things get turbulent. The crashes from the next section practically disappear.

What is remarkable is where the improvement comes from: not from a better forecast, but from managing exposure. Someone reading a ranking cannot scale anything. What a list can do is show each stock's volatility openly — as risk information, not as a verdict. What they measure is the volatility of the whole portfolio, not that of a single stock.

Source: Pedro Barroso 2015, Abstract

t−12 to t−2 measurement window of the academic standard — the most recent month is left out French Data Library, file header
month 1 negative winners minus losers: a loss in the first month after formation, a profit in the eleven that follow Narasimhan Jegadeesh 1993, Conclusions
52-week high beats classic momentum in a direct comparison Thomas J. George 2004, Abstract

What of this is in this list

We do not replace the RSL. We place next to it what research shows to be stronger — and show the difference.

ColumnWhat it measuresSource
RSL_26W Levy's measure C/A26: price divided by the average of the current price and the 26 weekly closing prices before it. Robert A. Levy 1967
RSL_26W_o The same value, shifted back by one week — numerator and denominator together. If it is far from the RSL, the latest price is driving the ranking. Narasimhan Jegadeesh 1990
Mom_12_2 Price return from 12 months ago to 2 months ago — the momentum factor as research measures it. Mark M. Carhart 1997
Hoch52W Price divided by the highest closing price of the last 52 weeks. 1.00 means the stock is at its high for the year. Thomas J. George 2004
Vola6M Volatility of daily returns over the last 6 months, annualized. Risk information without a rating: for deciding how much to put to work, calm is better; when choosing stocks, Levy found that those that were both strong and volatile did best. Pedro Barroso 2015

Why the RSL stays what it is

It is a defined indicator, not a suggestion. Anyone who recalculates it elsewhere must get the same number — otherwise this list cannot be verified, and being verifiable is its only claim. “An improved RSL” would no longer be an RSL: anyone looking up a stock's relative strength who finds a different number here than everywhere else will not conclude that we are the ones who are right.

The second column is the most interesting. It shows the same RSL, just calculated one week earlier. If the two values are regularly far apart, that is evidence that the latest price dominates the ranking — measured on our own numbers rather than claimed from the literature.

And the point that matters

We have not tuned any of these parameters. No trying out whether eleven or thirteen months work better, whether forty-eight or fifty-two weeks, whether the gap should be two weeks instead of one. The specifications are as they appear in the literature, and they are exactly the same here. The reason for choosing them is the evidence behind them — not how they perform on our data.

That refers back to 1970 and closes the circle of this page: Levy's mistake was not his idea. It was publishing the best of sixty-eight attempts.

Conclusion

The effect is documented. The measure this list uses for it is the simplest of all — and deliberately left unchanged.

Three things remain after fifty years of research. First: Levy's own figures — 9.6% for the strongest versus 2.9% for the weakest ten percent — showed a pattern; as a trading rule it did not survive the re-examination of 1970: after costs and at equal risk, nothing was left. The effect itself, however — that price strength persists for a while — has since survived changes of data, decade, country and asset class. An anomaly that withstands that is not a chance finding. Second: it comes at a price, and the price is not small. The momentum factor returned 8.6% a year on average and lost money in 21 of 99 years, −83.5% in the worst one. These crashes are not a footnote but the property that makes a strategy unusable if you cannot sit through them — and they come from the short positions, not from the winners. Third: measurement has improved on Levy's original rule — skipping the most recent month, the distance to the 52-week high, managing exposure through volatility.

What does this mean for this list? It continues to calculate Levy's RSL, unchanged, and places the three refinements next to it as separate columns. The reason is the same as in 1970: anyone who tunes parameters until the result looks good gets a good result and no insight. The numbers here can be recalculated because nobody optimized them.

And what does it not mean? That any single row of this table says something about tomorrow. Research measures broadly diversified portfolios over months; this list shows individual stocks on a single day. The difference is explained in detail in the first part — it is the reason why this is a ranking and not advice.

References

Every figure on this page is shown with its exact location in the source — section, table or page. The links lead to the paper via its DOI; the full texts are mostly behind publishers' paywalls, but the bibliographic details are enough for any library.

  • Robert A. Levy (1967): Relative Strength as a Criterion for Investment Selection. The Journal of Finance 22(4), pp. 595–610. doi:10.1111/j.1540-6261.1967.tb00295.x
  • Michael C. Jensen, George A. Benington (1970): Random Walks and Technical Theories: Some Additional Evidence. The Journal of Finance 25(2), pp. 469–482. doi:10.1111/j.1540-6261.1970.tb00671.x
  • Narasimhan Jegadeesh (1990): Evidence of Predictable Behavior of Security Returns. The Journal of Finance 45(3), pp. 881–898. doi:10.1111/j.1540-6261.1990.tb05110.x
  • Bruce N. Lehmann (1990): Fads, Martingales, and Market Efficiency. The Quarterly Journal of Economics 105(1), pp. 1–28. doi:10.2307/2937816
  • Narasimhan Jegadeesh, Sheridan Titman (1993): Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency. The Journal of Finance 48(1), pp. 65–91. doi:10.1111/j.1540-6261.1993.tb04702.x
  • Mark M. Carhart (1997): On Persistence in Mutual Fund Performance. The Journal of Finance 52(1), pp. 57–82. doi:10.1111/j.1540-6261.1997.tb03808.x
  • Tobias J. Moskowitz, Mark Grinblatt (1999): Do Industries Explain Momentum?. The Journal of Finance 54(4), pp. 1249–1290. doi:10.1111/0022-1082.00146
  • Thomas J. George, Chuan-Yang Hwang (2004): The 52-Week High and Momentum Investing. The Journal of Finance 59(5), pp. 2145–2176. doi:10.1111/j.1540-6261.2004.00695.x
  • Clifford S. Asness, Tobias J. Moskowitz, Lasse Heje Pedersen (2013): Value and Momentum Everywhere. The Journal of Finance 68(3), pp. 929–985. doi:10.1111/jofi.12021
  • Pedro Barroso, Pedro Santa-Clara (2015): Momentum has its moments. Journal of Financial Economics 116(1), pp. 111–120. doi:10.1016/j.jfineco.2014.11.010
  • Kent Daniel, Tobias J. Moskowitz (2016): Momentum Crashes. Journal of Financial Economics 122(2), pp. 221–247. doi:10.1016/j.jfineco.2015.12.002
  • Kenneth R. French (2026): Data Library: Momentum Factor (Mom), monthly and annual. Tuck School of Business, Dartmouth College, dataset, CRSP data as of 202607. Data library

The values of the momentum factor are the only figures on this page that we calculate ourselves: from the raw data of the data library, CRSP data as of 202607, monthly values from 1927 to 2026. They belong to a long-short portfolio with short selling and are not a return of this list.