Charts · Comparison
Compare Stocks on One Chart, and What the Ranking Depends On
Put two instruments on one price axis and the expensive one dominates whatever it does. Index both to 100 and the answer can reverse, same data, same period, opposite conclusion.
The problem in one sentence
A price axis measures points, and a point is not a comparable unit between instruments. Twelve dollars and three hundred and forty dollars share a chart badly: the expensive series occupies the axis, its ordinary moves look large, and the cheap series is a flat line at the bottom whatever it does.
The fix, and the decision it hides
Indexing is arithmetic: divide each series by its own first value and multiply by a hundred. Both start at 100 and every later number is a percentage of the start, so the vertical gap between the lines is a difference in return.
indexed = (price ÷ price on the base date) × 100
The decision it hides is the base date, and it is where most misleading comparison charts come from. A chart indexed from one instrument’s low will show that instrument outperforming for years, and every number on it will be correct. The habit that fixes it is cheap: state the base date, and before believing any claim from an indexed chart, redraw it from two or three other start dates and see whether the conclusion survives.
Three more things that belong in a comparison
| Factor | What it does | The fix |
|---|---|---|
| Dividends | A price series omits cash paid out, so a high-yielding instrument looks permanently worse than it was, and the gap compounds over a decade. | Use total-return series for both, or state that neither includes distributions. |
| Currency | A cross-border comparison contains an exchange-rate move as well as two performances. | Convert both to one currency and say which, the Toronto page works through a case where this is most of the apparent divergence. |
| Corporate actions | A split in an unadjusted series looks like a collapse, and an indexed chart propagates it through every subsequent value. | Use adjusted prices. The biggest-losers page shows what unadjusted data does to a ranking. |
| The scale | On a linear axis, later moves in a strongly rising indexed series visually dominate earlier ones of the same percentage size. | Logarithmic, for any comparison spanning a large change. |
The relative-strength line, and what it discards
A third form divides one instrument by the other and plots a single series. On the pair above that ratio rose 31 per cent over the period, which states the answer directly and compactly.
What it discards is the level of either instrument. A rising ratio line is entirely compatible with both instruments losing money, as long as the numerator loses less, so "it is outperforming" and "it is going up" become impossible to tell apart. That is the standard way a relative-strength chart misleads, and the remedy is to keep it beside the indexed chart rather than instead of it.
Comparing an instrument against an index
The most common version of this chart is not two instruments but one instrument against a benchmark, and it carries one extra trap on top of everything above: the two series are not the same kind of thing.
An index level is a construction, a value-weighted number scaled by a divisor, as the S&P 500 page sets out, while an instrument's price is a price. Indexing both to 100 makes them comparable as returns, which is fine, and it quietly invites two further mistakes. The index return excludes dividends in most published forms while the instrument's may not, so the comparison is between a price return and a total return. And a capitalisation-weighted benchmark is dominated by its largest members, so "beating the index" over a period when a handful of enormous companies drove it is a much narrower achievement than it looks.
The second point is where the breadth measures earn their place beside a comparison chart. If most constituents fell while the index rose, then an instrument that underperformed the index may still have outperformed most of the market, and the comparison chart cannot show that, because no weighted index carries the information about how many members took part.
Volume between instruments is a separate problem
Everything above concerns price. Volume cannot be compared between instruments at all in the form it is published: a share count depends on the price level and on how many shares each company divided itself into, so the larger number is frequently just the cheaper stock.
The most-traded page computes what that does to a ranking, seven of eight instruments change position when the same universe is ordered by money instead of by shares. For a comparison, use dollar volume if the question is about money, turnover against free float if it is about how much of the company traded, or each instrument against its own recent average if the question is which one is unusually busy. Those three answer different questions and none of them is the raw share count.
Frequently asked questions
Why can two instruments not be compared on a raw price chart?
Because the vertical axis then measures points, and a point means something different at twelve dollars than at three hundred and forty. The expensive instrument dominates the chart whatever it does, and a modest percentage move in it looks larger than a substantial one in the cheap one. The figure on this page computes a case where the raw chart and the indexed chart name different winners over the same period.
What does indexing to 100 do?
It divides every value in each series by that series’ first value and multiplies by a hundred, so both start at the same place and every subsequent number is a percentage of the start. After that the vertical distance between the two lines is a difference in percentage return, which is the quantity people mean when they say one instrument outperformed another.
Does the start date matter?
Enormously, and it is the most common way a comparison chart misleads without containing an error. Indexing sets both series to 100 on a date you choose, and moving that date changes the whole picture, a comparison beginning at one instrument’s low will show it outperforming for years. Any indexed chart should state its base date, and a claim built on one should be checked against two or three other start dates before it is believed.
Should the comparison use price or total return?
Total return, if either instrument pays a meaningful dividend, and the difference compounds. A price series omits the cash paid out, so a high-yielding instrument looks permanently worse than it was, over a decade that gap becomes large enough to reverse a ranking on its own. Most charting tools default to price. Establishing which series you have is a one-time check worth making.
What about currency?
A cross-border comparison contains an exchange rate whether you wanted one or not. Two instruments quoted in different currencies, both indexed to 100, differ by the currency move as well as by their own performance, which is a real effect for a holder and a distortion if the question was about the companies. Convert both to one currency and state which, or compare each in its own and treat the difference as unresolved.
What is a relative-strength line?
One instrument divided by the other, plotted as a single series. It answers "which is winning" directly and it discards the fact that both may be falling, a rising ratio line is compatible with both instruments losing value, as long as the numerator loses less. It is a compact and easily misread form, and it is worth having beside the indexed chart rather than instead of it.
How should volume be compared between instruments?
Never in share counts. A share count is not comparable between instruments at all: it depends on the price level and on how many shares each company divided itself into. Compare dollar volume if the question is about money, turnover against free float if it is about how much of the company traded, or each instrument’s volume against its own recent average if the question is which one is unusually busy. The most-traded page works through all three.
Does the log scale matter here too?
Yes, and after indexing it matters more rather than less. On a log scale equal vertical distances are equal percentage moves, so two indexed series can be compared by eye at any point in the chart; on a linear scale the later part of a strongly rising series visually dominates its own earlier moves. For a comparison spanning a large change, indexed plus logarithmic is the combination that supports the reading people take from it.