How an RSL strategy is built

Before the first purchase

Before the first purchase, the index and the measure used for sorting are fixed. A rank is only comparable within one index, because it gives a stock's position among all stocks in the same index. Switching index or measure whenever another choice would have done better in hindsight means selecting a rule after the fact. That was precisely the objection Jensen and Benington (1970) raised against Levy's results.

The portfolio holds the five top-ranked stocks in the ranking. There is no evidence for this number. The studies on the momentum effect form portfolios of dozens or hundreds of stocks, and according to Statman (1987) a portfolio counts as broadly diversified only from 30 to 40 stocks. Five positions are considerably more concentrated: the price of a single stock moves one fifth of the portfolio.

All five positions are bought with the same amount, regardless of the company's share price or market value. Jegadeesh and Titman (1993) weight their portfolios the same way in their confirmation of the momentum effect. With $5,000 to invest, each stock receives $5,000 ÷ 5 = $1,000.

Equal amounts usually require a broker that offers fractional shares, that is, the purchase of fractions of a share. If a share costs $1,800, $1,000 is not enough for a whole share; with fractions it buys $1,000 ÷ $1,800 = 0.556 shares. Without fractions, the smaller the amount invested, the more the positions differ from one another.

The purchase

The five stocks with the highest RSL enter the portfolio. The approach goes back to Levy (1967), who assembled his portfolios from the stocks with the highest values. Two optional checks, described further below, can skip a stock at the top.

A market filter delays new purchases as long as the overall market is below its trend. Cooper, Gutierrez and Hameed (2004) show that relative momentum earns its profits mainly after rising markets. Daniel and Moskowitz (2016) find the momentum strategy's heaviest losses in the recovery after a market crash. Faber (2007) tests a trend rule based on the moving average for entire asset classes; it has not been studied for individual stocks. The short summary of the market trend shows where the overall market currently stands.

In a takeover, a company is sold as a whole: a buyer offers all shareholders a fixed price per share. The offer drives the price up abruptly and thus to the top of the ranking; it can hardly rise further, because the buyer pays no more than offered. When Elon Musk bought Twitter in 2022, the offer was $54.20, and the stock traded at $49.11 on April 28. If the deal succeeded, ($54.20 − $49.11) ÷ $49.11 = 10.4% remained. When Musk sought to withdraw from the purchase in July, the price fell to $32.65 by July 11, that is ($32.65 − $49.11) ÷ $49.11 = −33.5%. Mitchell and Pulvino (2001) describe this pattern of a small gain and a large risk of loss for takeover bets in general. An optional rule therefore skips stocks whose company is to be sold as a whole.

A sector is a group of companies in the same industry, such as technology or energy. According to Moskowitz and Grinblatt (1999), momentum often appears across entire industries at once, so the five top-ranked stocks frequently come from the same sector. An optional rule therefore limits the number of positions per sector, for example to two. The limit reduces concentration risk, that is, the portfolio's dependence on a single industry. At the same time it gives up part of the effect, because Moskowitz and Grinblatt attribute a large part of momentum to industries.

The weekly check

The portfolio is compared with the current ranking once a week, on a fixed weekday. The RSL is based on weekly closing prices, as it already was for Levy (1967); a daily check changes little in the ranking but creates more occasions to trade. The list on this site is recalculated every day; the strategy uses one day of it per week.

A holding band separates the threshold for buying from the threshold for selling. Stocks are bought only in places 1 to 5; they are held as long as they rank in the top quarter of the ranking. With 500 stocks, the top quarter ends at rank 500 ÷ 4 = 125. Without a holding band, every position would be sold as soon as it slipped from place 5 to place 6, and every switch costs fees. Novy-Marx and Velikov (2016) show that such a gap substantially reduces the trading costs of momentum strategies. The list gives places 1 to 5 and all rows below the top quarter their own background color.

Rotating the stocks in the portfolio

A position is sold as soon as one of two conditions occurs: it leaves the top quarter of the ranking, or its RSL falls below 1.00. The first condition is the holding band from the previous section. The second applies when the price falls below its own average, even if the rank is still good enough. This happens in weak markets because the ranking is always filled: if fewer than a quarter of the stocks are above 1.00, the top quarter also contains stocks below it. On October 16, 2026, 254 of 500 S&P 500 stocks were above 1.00. The evidence for the threshold of 1.00 is weak, because Faber (2007) tested it only on asset classes.

The vacated slot goes to the highest-ranked stock that is not yet in the portfolio; the same checks apply to it as for the first purchase. If the overall market is below its trend, the money stays uninvested until a later check. Only one fifth of a sale's gain goes into the stake: with a stake of $1,000 and a sale for $1,500, that is $500 ÷ 5 = $100, so $1,100 for the new stock and for every further switch. The remaining $400 stay as a reserve and cover later sales that bring in less than the stake. A loss lowers the stake in the same way. The positions thus stay close to equal amounts, with one order for the sale and one for the purchase. There is no study of this rule.

What each switch costs

Each rotation consists of two orders, a sale and a purchase. Each order costs a broker fee and the spread, that is, the gap between the price for buyers and the price for sellers. With an assumed 20 rotations a year, that makes 20 × 2 = 40 orders; at $1 per order this costs $40 a year, or $40 ÷ $5,000 = 0.8% of a $5,000 investment, not counting the spread. Costs already ate up Levy's results: Jensen and Benington (1970) found no advantage over buying and holding after costs. Lesmond, Schill and Zhou (2004) show that momentum profits arise mainly in stocks that are expensive to trade. Taxes come on top of these costs: depending on the country, a sale at a profit can be taxable, and the replacement rule then works with the gain after tax.

What is supported and what is not

Each component of this strategy rests individually on a study, with two exceptions: the number of five positions and the rule for the stake at rotation. The combination of the components has not been scientifically tested, and this site has no backtest of its own. A backtest is a calculation that applies a strategy to past prices and shows how it would have performed at the time.

• Index and measure: They are fixed in advance, based on the objection Jensen and Benington (1970) raised against Levy.
• Five positions: There is no evidence for this number; Levy compared the strongest 10% of his 200 stocks, that is 200 × 10% = 20 stocks, and in the S&P 500 it would be 500 × 10% = 50.
• Equal amounts: supported by Jegadeesh and Titman (1993).
• Buying at the top: supported by Levy (1967).
• Market filter: Cooper, Gutierrez and Hameed (2004) and Daniel and Moskowitz (2016) show the dependence on market conditions; the trend rule itself has not been tested on individual stocks.
• Takeovers: Mitchell and Pulvino (2001) study takeover bets; they say nothing about momentum strategies.
• Sector limit: Moskowitz and Grinblatt (1999) give the reason for it but do not measure its effect.
• Weekly check: It adopts the rhythm of Levy's weekly prices (Levy (1967)).
• Holding band: supported by Novy-Marx and Velikov (2016).
• Sale below 1.00: The evidence is weak, because Faber (2007) tested the rule only on asset classes.
• Stake at rotation: There is no evidence for this rule; it only serves to keep the number of orders low.

Frequently asked questions

How much money does this strategy need?

There is no fixed minimum; with fractional shares, each position can be bought even with a small amount. Costs weigh more heavily, however, the smaller the amount invested. With $40 in fees a year, that is $40 ÷ $5,000 = 0.8% of a $5,000 investment, and already $40 ÷ $2,000 = 2% of $2,000.

Why only five stocks?

Five positions are a choice made by this page without supporting evidence. More positions spread the risk more widely: Levy compared 20 stocks, and according to Statman (1987) a portfolio counts as broadly diversified only from 30 to 40 stocks. Each additional position, however, brings more rotations and thus more orders. The number is a trade-off between diversification and costs.

What happens when the market trend is red?

The market filter applies as soon as the index RSL of the S&P 500 is at 1.00 or below, that is, at red and at yellow with a weak index. Positions in the portfolio are not affected; the sale rule continues to apply to them. Money from sales stays uninvested until the index rises above its average again. In a long downturn, the portfolio thus gradually turns into cash.

Does this also work with another index?

Yes. The list calculates a separate ranking for each index, and the rules on this page can be applied to any of them. The index is fixed before the first purchase and not changed afterwards. In a smaller index the top quarter ends earlier, with 100 stocks at rank 100 ÷ 4 = 25. The market trend on this site shows only the S&P 500.

Why is the check only once a week?

The RSL is based on weekly closing prices: within a week, only the current price in the numerator changes, while the average in the denominator stays the same. A daily check creates more occasions to trade without changing the basis of the measure. Every additional switch costs two orders. A fixed weekday also prevents the timing of the check from being chosen according to the price movement.

Does the list give buy signals?

No. The list ranks the stocks of an index by a measure and recommends none of them. A place at the top means that the price is further above its average than for the other stocks; it says nothing about future performance. This page explains how such a ranking can be put into rules. Whether and how someone applies them is their own decision.

Further reading

References

The section “What is supported and what is not” shows which study supports which rule. The links lead to the paper via its DOI.

• 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
• Meir Statman (1987): How Many Stocks Make a Diversified Portfolio?. Journal of Financial and Quantitative Analysis 22(3), pp. 353–363. doi:10.2307/2330969
• 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
• 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
• Mark Mitchell, Todd Pulvino (2001): Characteristics of Risk and Return in Risk Arbitrage. The Journal of Finance 56(6), pp. 2135–2175. doi:10.1111/0022-1082.00401
• Michael J. Cooper, Roberto C. Gutierrez Jr., Allaudeen Hameed (2004): Market States and Momentum. The Journal of Finance 59(3), pp. 1345–1365. doi:10.1111/j.1540-6261.2004.00665.x
• David A. Lesmond, Michael J. Schill, Chunsheng Zhou (2004): The Illusory Nature of Momentum Profits. Journal of Financial Economics 71(2), pp. 349–380. doi:10.1016/S0304-405X(03)00206-X
• Mebane T. Faber (2007): A Quantitative Approach to Tactical Asset Allocation. The Journal of Wealth Management 9(4), pp. 69–79. doi:10.3905/jwm.2007.674809
• 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
• Robert Novy-Marx, Mihail Velikov (2016): A Taxonomy of Anomalies and Their Trading Costs. The Review of Financial Studies 29(1), pp. 104–147. doi:10.1093/rfs/hhv063