RSL without the latest week

The weakness: the latest price in the numerator

In the RSL, the latest price does not count as one among many. It is half of the formula.

Levy divides the current price by the average of this price and the 26 weekly closing prices before it. In the denominator the latest price is one of 27 and hardly carries any weight. In the numerator it stands alone. If a stock rises ten percent in the last week, its RSL rises by almost the same amount — whatever happened in the months before.

That would not matter if price movements behaved the same over every horizon. They do not. Narasimhan Jegadeesh and Bruce Lehmann showed independently in 1990: over horizons from one week to one month, prices do not continue but reverse. What has risen sharply in the short term tends to give some of it back; what has fallen tends to recover. Over several months, by contrast, movements tend to continue — that is the effect the RSL sets out to measure.

The RSL thus takes in at full force exactly the week in which the opposite of the effect it is built for tends to show. Momentum research drew the consequence and leaves out the most recent month altogether; what that looks like is shown on the page on Mom 12−2.

Source: Robert A. Levy 1967, Section II (“Price Ratios”), Narasimhan Jegadeesh 1990, Abstract, Bruce N. Lehmann 1990, Narasimhan Jegadeesh 1993, Conclusions

What “shifted back by one week” means exactly

Numerator and denominator move back together by one weekly closing price. It is the same RSL, just at an earlier point in time.

Take the series of weekly closing prices, drop the latest one, and on the rest calculate exactly the RSL the list calculates anyway: again 27 prices in the denominator, again the last of them in the numerator. The column therefore shows the RSL the stock would have had one week ago.

What it does not mean is today's price divided by an older average. That would be a new measure, and the latest price would still sit in the numerator — exactly what the column is meant to avoid.

“One week” means precisely: one weekly closing price. A week's price is that of the last trading day up to Friday; the current week counts with its latest price. On a Friday, the two numerators are therefore exactly five trading days apart, on a Tuesday only the two days since the previous Friday. If a stock has fewer than 27 weekly closing prices before the latest week, the field stays empty.

The column is always calculated from weekly closing prices — hence the “26W” in its name.

A worked example you can check

Two made-up stocks, 28 weekly closing prices each. By the RSL, A is ahead; one week earlier, B.

A has not moved for months and jumped in the last week. Its RSL of 1.14 comes from that week alone: one week earlier it stood at 1.00, exactly at its average.

B rose in the middle of the window and has held that level since. Nothing happened in the last week; the shift barely changes its value, from 1.11 to 1.12. That it is even a little higher one week earlier has a simple reason: with a price moving sideways, the average slowly catches up.

By the RSL, A ranks ahead of B; one week earlier, B ahead of A. Neither number says which of the two stocks is the better one. They only show where the lead comes from.

How to read the two columns side by side

If they are close together, the last week hardly matters. If they are far apart, the last week is driving the ranking.

• Both about the same: the value rests on the course of the past months. Whether the latest week is included or not changes little.
• RSL clearly above RSL 26W −1W: the stock rose in the last week, and a good part of its rank comes from that. According to the finding on short-term reversal, this is the part that, on average across many stocks, tends to fade again.
• RSL clearly below RSL 26W −1W: the stock fell in the last week. The RSL shows it as weaker than its course before that was.

For an individual stock, this predicts nothing. Short-term reversal is a finding about many stocks over many years, not a rule every price follows. The second column is a reading aid: it shows how much a rank depends on a single week.

Nor does it remove the whole reversal. Research finds it over horizons of up to one month; the column leaves out only one week, the smallest step a series of weekly closing prices allows. A longer gap would be conceivable. We have deliberately not tried one — the next section explains why.

Why the list is still ranked by the RSL

The RSL is a defined indicator. Anyone who recalculates it elsewhere must get the same number.

An “improved RSL” that leaves out the latest week would no longer be an RSL. Anyone looking up a stock's relative strength who finds a different number here than everywhere else cannot verify the list. That is why the RSL in this list is still calculated unchanged following Levy and decides the ranking. The shifted column stands next to it, not in its place. This is covered in detail under Why the RSL stays what it is.

For the same reason, nothing about the column has been tuned. One week is not a value that proved best on our data, but the smallest shift the series allows. Anyone who turns such dials until a curve looks good repeats Levy's actual mistake: publishing the best of many attempts.

What our own numbers show

Whether the latest price often shifts the ranking in this list's numbers cannot be claimed, only measured. Every run therefore records, for each index, how well the two rankings agree and how far apart the positions are. An evaluation over enough weeks is not available yet, and so there is no number here. It too will only show how much the two columns differ — not which of them picks the better stocks.

Where the RSL comes from is covered in RSL: Method & Origins.

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
• 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