Lesson T7.4 · 4 of 6 · Oscillators and momentum
Rate of change and momentum: formula, zero line and the research
ROC shows the percentage change in price compared with N periods ago; momentum shows the same change in money terms. Research has found that shares which rose most over the past 3-12 months went on, on average, to beat the weakest ones. The effect also suffers sudden crashes, as in 2009.
Terms in this lesson
- Price momentum
- How much the stock has risen or fallen in recent months: the force of the move.
- RSI
- Shows whether the price rose or fell too fast over the last two weeks.
- Stop-loss
- An order that sells automatically if the price falls to a level you choose.
What ROC and momentum are: the formula and the zero line
Definition
ROC and momentum
Two ways of measuring how far the price has moved over the last N periods.
ROC = (today’s price - price N periods ago) ÷ price N periods ago × 100, in per cent; StockCharts uses 12 periods by default. Momentum = today’s price - price N periods ago, in money terms. Both swing around a zero line: above zero, the price is higher than N periods ago; below zero, it is lower.
The price climbs quickly from about 91 to 105, then ever more slowly to about 107.5, and falls back to 100 at the end. The 12-day ROC peaks at 15% on candle 16 and slides gradually towards 2% before the price falls. The 10-day momentum, in money terms, has the same shape.
The chart shows what ROC really measures: speed. The price kept rising until candle 29, but more and more slowly, so ROC slid from 15% towards zero before the price turned. StockCharts warns, though, that zero-line crossings throw up many false signals in the short term.
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Create a free accountWhat the research says about momentum: Jegadeesh and Titman, 1993
Narasimhan Jegadeesh and Sheridan Titman published “Returns to Buying Winners and Selling Losers” in the Journal of Finance in 1993. They took NYSE and AMEX shares from 1965 to 1989, ranked them on their returns over the previous 3, 6, 9 or 12 months and split them into ten groups. The strategy: buy the group of best performers, short-sell the group of worst, then hold the positions for 3-12 months.
The authors also found that part of the extra return earned in the first year disappears over the following two years. In 2012, Tobias Moskowitz, Yao Hua Ooi and Lasse Pedersen showed a related effect in the Journal of Financial Economics, time series momentum: for every one of the 58 futures contracts they studied (equity indices, currencies, commodities and bonds), returns over the past 1-12 months tended to persist, and partly reversed over longer horizons.
Momentum crashes: 1932 and 2009
Three columns showing US share returns from March to May 2009: the bottom 10% of the previous year, +163%; the top 10%, +8%; the market, +26%. Source: Daniel and Moskowitz (2016).
Kent Daniel and Tobias Moskowitz studied US shares from 1927 to 2013 in “Momentum Crashes” (Journal of Financial Economics, 2016). Their strategy buys the top 10% on returns over the previous 12 months, skipping the latest month, and short-sells the bottom 10%. The conclusion: crashes are rare but large, and they come in panic periods, after market falls and when volatility is high, just as the market rebounds sharply. In July and August 1932, the past losers rose 232%, the past winners 32% and the market 82%.
The momentum indicator on a chart and the momentum factor in research
| ROC or momentum on a chart | The momentum factor in research | |
|---|---|---|
| What it compares | A share’s price with its own price N days ago | A share’s return with the returns of hundreds of others |
| Time frame | Usually 10-14 days | 3-12 months, sometimes skipping the latest month |
| How it is used | Signals on a single share | A portfolio: buy the leaders, sell the laggards |
| The evidence | StockCharts: many false signals at the zero line | Positive average returns in studies, with rare, large crashes |
The returns in these studies come from theoretical portfolios; tax and real-world trading costs reduce them.
Lessons are educational. They are not a recommendation to buy or sell. Investing involves risk and you can lose money. Sources: StockCharts ChartSchool, “Rate of Change (ROC) and Momentum”, accessed 29 October 2026; Technical Analysis of Stocks & Commodities (traders.com), “Momentum”; N. Jegadeesh and S. Titman, “Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency”, Journal of Finance 48(1), 1993; N. Jegadeesh and S. Titman, “Profitability of Momentum Strategies: An Evaluation of Alternative Explanations”, NBER Working Paper 7159 (1999), published in the Journal of Finance 56(2), 2001 (summary of the 1993 results: about 1% a month, winners ahead of losers in every month except January); T. Moskowitz, Y. H. Ooi and L. H. Pedersen, “Time Series Momentum”, Journal of Financial Economics 104(2), 2012; K. Daniel and T. Moskowitz, “Momentum Crashes”, Journal of Financial Economics 122(2), 2016 (NBER Working Paper 20439). The candlestick charts are teaching diagrams, not real prices.