See why different lookback windows can tell different price stories.
Analyse a CompanyIntermediate4 min
Plain English
Describe the move before explaining it
Price momentum concerns the pattern of past price changes over a chosen period. A simple measurement asks how much a price has risen or fallen between two dates. That observation is different from a claim about company fundamentals, a valuation estimate or a prediction of the next move.
The lookback is part of the definition. A six-month change and a one-month change can point in opposite directions without either calculation being wrong. One includes more history than the other. Naming the start date, end date and type of price series is therefore as important as reporting the resulting percentage.
The word momentum also appears in academic research and investment methods with specific construction rules. Those rules can include ranking many securities, excluding a recent period or forming portfolios. A simple historical price change is useful for introducing the idea, but it should not be presented as a replication of every momentum measure.
Worked Example
Up over six months, down in the final month
Consider a synthetic price index beginning at 100. It reaches 110 at the end of month five, then ends month six at 104.5. These are invented index levels, not currency amounts or observations from a traded investment. Assume the levels are comparable throughout, with no dividends or corporate actions to adjust.
Across the full six months, divide 104.5 by 100 and subtract one. The result is 4.5%. Across the final month, divide 104.5 by 110 and subtract one. The result is −5%. Both measurements end at the same level but begin from different reference points.
The final month’s 5% fall removes 5.5 index points, because its starting level is 110. It does not remove five points from the original 100. Linking the first five months’ 10% increase with the final month’s 5% decline gives 1.10 times 0.95, or 1.045. That reconciles the six-month change.
Formula
Six month change equals one hundred four point five divided by one hundred, minus one
The final-month change uses 110 as its denominator and is −5%.
Starting index
100
End of month five
110
End of month six
104.5
Six-month change
+4.5%
Final-month change
−5%
Reading the result
The window changes the description
The six-month result says the endpoint remains above the initial level. The final-month result says the most recent interval reversed part of the earlier rise. Neither result explains why that happened. Earnings news, changing expectations or broader market conditions could matter, but the three levels alone cannot identify a cause.
The illustration joins the stated observations to make the two measurement windows visible. It does not show what happened on every intervening day, and its line stops at the final observation. Extending it into the future would add an assumption that the example does not support.
Kenneth French’s daily momentum-factor description uses a specified trading-day window, from t−250 through t−21, described as prior months two to twelve, alongside portfolio construction rules. That convention differs from our six-month endpoint comparison and excludes the most recent month from its formation signal. The source demonstrates why a named research definition needs to be read before borrowing its label.
Limits and assumptions
Check what the series includes
For a real share, a cash dividend can affect the quoted price without representing an equivalent loss of total shareholder value. A split changes the number of shares and the price per share. Historical series therefore need consistent adjustment conventions; comparing an adjusted observation with an unadjusted one can create a misleading return.
Different providers can also use different dates, closing prices or distribution treatments. State whether a figure is a price return or a total return, and whether it is cumulative or annualised. Our example reports cumulative changes over the named windows and does not annualise them. Observed price persistence can reverse, and a historical measurement alone supplies neither a trading rule nor a reliable future outcome.
Common Mistake
Choosing the window after choosing the story
Selecting only the interval that makes a price look strongest can conceal a recent reversal or a longer decline. Showing both predefined windows makes the description more transparent. The aim is to understand what was measured and what was omitted, rather than turn a favourable percentage into evidence that a business is cheap or improving.
Self-check
Check your understanding
How can +4.5% and −5% both be correct?
They use different starting levels: 100 for six months and 110 for the final month.
Why not add 10% and −5% to obtain 5%?
Successive percentage changes apply to changing bases. Multiplying 1.10 by 0.95 produces a cumulative 4.5% gain.
Does this reproduce French’s momentum factor?
No. That factor uses a specified prior-return window and portfolio construction. This is a simple synthetic price comparison.
Continue learning
Connect the ideas
Follow the related articles below to explore the assumptions behind this example.
Disclaimer
Educational Use Only
This article is for informational and educational purposes only. It does not provide personalised investment advice.
