Ratio analysis and relative strength

The answer

A ratio chart divides one price series by another and plots the result. It removes what the 2 have in common and shows only which one is winning. Its direction is the whole message and its level means nothing. A relative rotation graph is a way of showing many of these ratios at once, and it adds convenience, not information.

Why this costs you money

Here is the specific and very common loss.

You own a company in a sector that has been strong. The share is up. You feel good about the decision. What you have not checked is whether the share is up as much as its own sector, and it usually is not, because the sector's rise came from 2 or 3 constituents and you own a fourth one.

So you hold a stock that beat the market, lagged its own sector, and gave you single-company risk in exchange for less than the group return. Your app shows a profit. Nothing in your account tells you that a cheaper, more diversified version of the same idea did better.

This mistake survives for years because it is invisible to every measurement most people use. Absolute return says you made money. Return against your purchase price says you were right. Only a ratio says you were right about the sector and wrong about the company, and that is exactly the distinction that decides whether you should be picking companies at all.

The second cost is subtler. People use ratio charts to justify holding losers. A ratio line that has stopped falling is read as improving, which becomes a reason to keep a position. A line that has stopped falling is a line that is flat, and flat means the holding is now tracking the thing you could have owned for free. That is not improvement.

How it works

Building a ratio

Divide series A by series B on each day and plot the result. That is the whole construction. Every chart platform can do it, usually by typing 2 symbols with a division sign, or by adding a comparison series.

Three rules govern how to read it.

The direction is the message. Rising means A is beating B. Falling means B is beating A. Flat means they are moving together.

The level means nothing. The number depends on the units of both series. A ratio of 0.004 is not smaller or weaker than a ratio of 240. Never compare the level of one ratio to the level of another.

Flat is a result, not a pause. A flat ratio between your holding and the index means you are taking single-company risk and receiving index returns. That is a finding, and most people read it as neutral.

The ratios worth building

Different ratios answer different questions. Six are worth knowing.

The last 3 are the ones most readers never build, and they are the most useful, because they are about the market rather than about a holding.

The 2-ratio test

The single most useful application in this article is to build 2 ratios for every holding, not 1.

• Stock ÷ broad index. Should you own a company at all rather than a fund?
• Stock ÷ its own sector index. Given that you wanted exposure to this sector, did you choose well inside it?

Four outcomes, and each implies something different.

The second row is the one that changes behaviour, because it looks like success in every other measurement.

Relative strength is not RSI

Two different things with almost the same name, and this confusion is everywhere.

Relative strength compares one instrument to another. Your stock against the index. It is a ratio.

The Relative Strength Index, or RSI, compares an instrument to its own recent history. It measures the size of recent gains against the size of recent losses in the same instrument. It never looks at any other instrument.

Say the full name of whichever one you mean, every time.

Relative rotation graphs

A relative rotation graph, or RRG, is a way of plotting many securities against one benchmark on a single picture. It was developed by Julius de Kempenaer and is available on several platforms under licence.

It has 2 axes.

• The horizontal axis is RS-Ratio, a normalised measure of how strong the security's ratio against the benchmark currently is.
• The vertical axis is RS-Momentum, a normalised measure of the rate of change of that ratio.

Both are centred on 100, which represents the benchmark. That produces 4 quadrants.

Each security is drawn as a point with a short trail showing the last several periods. The claimed tendency is that securities rotate clockwise through the quadrants, from improving to leading to weakening to lagging and back.

What an RRG actually is. It is a scatter plot of a ratio and the ratio's rate of change. That is the same information as looking at a ratio line and its slope. The value is that you can see 30 of them at once, which is genuinely convenient when comparing 11 sectors or 30 index constituents.

Four limits you must know before using one.

1. The values are relative to the set you plotted. The normalisation depends on which securities are on the chart. Add or remove one and everybody else's position can shift. Two people plotting different sets get different pictures of the same security.
2. The rotation is a tendency, not a rule. Securities jump quadrants, reverse direction inside a quadrant, and sit in one corner for a year. Counter-clockwise movement occurs and it is not rare.
3. The tail length is a setting. A longer tail looks like a smooth rotation. A shorter tail looks like noise. Both are the same data.
4. It adds no information to the underlying ratios. It is a display. Anything an RRG tells you can be obtained from the ratio lines it was built from.

None of that makes it useless. It makes it a visualisation with settings, and the settings are choices you should be able to state.

Correlation, and why it changes

A ratio compares 2 things. Correlation measures how much they move together, and it is not stable.

Francois Longin and Bruno Solnik showed in the Journal of Finance in 2001 that correlations between international equity markets increase in the tails of the return distribution, and that the increase is concentrated in market declines rather than in market rises. In plain terms: things that look unrelated on ordinary days move together on bad days.

That has a direct consequence for anybody using ratios to construct a portfolio. The diversification you measured is measured mostly on ordinary days. It will be smaller than measured exactly when you need it.

What it tells you, and what it does not

A ratio tells you who is winning between 2 things, over the window you chose. That is a fact, it is free, and it is not available from any absolute chart.

It tells you where flows have been going, and flows persist for months. That is the momentum effect, documented by Jegadeesh and Titman in the Journal of Finance in 1993 and replicated widely since.

It does not tell you why. A rising ratio looks identical whether the cause is accelerating profits, index inclusion buying, a takeover rumour or a small number of participants pushing a thin stock.

It does not tell you about valuation. The strongest ratio in a list is often the most expensive company in it.

It does not tell you direction. A stock falling 10% while the index falls 25% has a rising ratio and is still losing you money. Every ratio needs an absolute chart beside it.

And it is sensitive to construction. Two mistakes are common enough to name. Price index against total return index is a mismatch, because one includes dividends and the other does not, so the ratio drifts downward for reasons that have nothing to do with performance. Unadjusted prices produce false jumps at every split, bonus issue and large dividend.

The decision rule

Build 2 ratios for every holding, not 1.

If the stock is rising against the broad index and rising against its own sector index, the position is doing the job you bought it for.

If it is rising against the index but falling against its own sector, the sector is carrying you. A sector fund or a different constituent would have paid more for less risk. This does not mean sell today. It means the reason you hold this specific company needs to be stated in writing.

If it is falling against both over 6 months, write 1 sentence saying why you still own it. If the sentence mentions your purchase price, you are holding out of hope.

Unless the whole market has just turned upward after a long decline. In that one condition rankings invert for a period, and the previous laggards lead.

Try this now

Ten minutes, on your own holdings. This is the 2-ratio test and most people find at least 1 holding in the second row of the table.

1. Open your holdings list. For each holding, note its sector.
2. Find each holding's percentage change over the last 6 months. Your broker app or any free chart shows this directly.
3. Find your broad index's percentage change over the same 6 months. Use the Nifty 50 or the Sensex in India, the S&P 500 in the United States.
4. Find each holding's sector index percentage change over the same 6 months. In India use the NSE sectoral index for that sector. In the United States use the sector exchange traded fund or the GICS sector index.
5. For each holding, compute 2 numbers. Number 1 = stock change − broad index change. Number 2 = stock change − sector index change.
6. Write both numbers next to each holding, and sort the list by number 2.
7. Mark each holding into 1 of the 4 boxes: both positive, positive and negative, negative and positive, both negative.

What you should see. Most portfolios contain at least 1 holding with a positive first number and a negative second number. That is a position that beat the market and lost to its own sector. It has been reporting success to you the whole time.

The bottom of your sorted list is the second finding. Holdings that are negative on both numbers over 6 months are the ones being kept out of hope. For each of them, write 1 sentence saying why you still own it, and then read the sentences back. Sentences about the business — a new plant, a contract, a margin recovery you are waiting for — are a thesis, and a thesis is allowed to take time. Sentences about the price are not a reason. "It will come back" and "I am down too much to sell now" are the same sentence, and neither is about the company.

Then add up the value of everything in the both-negative box. That total is how much of your money is losing to something you could have bought in 1 click.

Three real cases

1. The S&P 500 equal weight index against the standard S&P 500, 2023 and 2024 — a ratio that measured narrowness directly The S&P 500 is weighted by market value, so the largest companies dominate its return. S&P Dow Jones Indices also publishes an equal weight version, in which every constituent has the same weight.

Dividing one by the other produces a direct measure of breadth. Through 2023 and into 2024 this ratio fell substantially, meaning the average constituent underperformed the index badly, because a small number of very large companies produced most of the return.

The point of this case is what the ratio told you that the headline could not. "The market is up 24%" and "most companies in the market are barely up" were both true at the same time. An investor holding a broad selection of companies could have been well behind the index while doing nothing wrong, and the ratio was the only chart that explained it.

2. Indian midcaps against the Nifty 50, from January 2018 — the ratio turned before the story did Indian mid and small capitalisation shares rose strongly through 2017. The turn came in the first quarter of 2018, and mid and small caps underperformed the Nifty 50 substantially over the following 2 years.

Two things make this a good case. First, the ratio of the midcap index to the Nifty 50 turned down early in 2018, at a point when the Nifty 50 itself was still rising, so an investor watching only the headline index saw a market making progress. Second, part of the cause was structural rather than economic: SEBI's scheme categorisation rules for mutual funds, issued in October 2017, required funds to align their holdings with defined capitalisation buckets, which forced adjustment in fund portfolios during this period.

That second detail is the honest complication. The ratio measured the flow accurately. The cause of the flow was a regulation, not an economic cycle, and no ratio can tell you that.

3. Longin and Solnik, Journal of Finance, 2001 — the number you computed does not apply on the day you need it The authors studied correlations between major international equity markets and tested whether correlation is constant across the distribution of returns. They found that correlation increases in the tails, and that the increase appears in large negative returns rather than in large positive ones.

The practical translation is direct. If you built a portfolio using ratios and correlations measured over the last 3 years, most of those observations came from ordinary days. On the days when your portfolio falls hardest, the relationships you relied on will be tighter than you measured, and the protection you thought you had will be smaller.

This is not an argument against ratio analysis. It is an argument for sizing positions as though the diversification is weaker than the number says, because on the days that matter it is.

The question that resolves it

A novice asks: is my stock going up?

An expert asks: is it going up faster than the sector it belongs to, and faster than the index I could have bought instead?

Two ratios, 2 different questions. The first one asks whether you should own a company rather than a fund. The second asks whether, having chosen a sector, you chose well inside it.

Almost every argument about stock picking dissolves into those 2 questions. A person who beats the index but loses to their own sector has demonstrated a sector skill and not a company skill, and the correct response is to keep the sector exposure and stop choosing constituents.

What would make this wrong

The claim here is that ratios measure relative performance reliably and forecast weakly.

The measurement half would be wrong only if the arithmetic were wrong, which it is not, provided both series are constructed consistently. The real risk is construction error rather than concept error: mismatched total return and price series, unadjusted prices, or 2 series in different currencies.

The forecasting half rests on momentum, and momentum is a live question. Ranking by past 6 to 12 month relative performance has predicted future relative performance in many markets and decades. It is also a published anomaly, and published anomalies tend to weaken. There have been long periods where it did not work, and its worst losses come immediately after a market bottom, when previous losers rebound hardest. If the next 20 years show no relative-strength effect, the ranking use of ratios loses its justification and only the measurement use survives.

The RRG claim is the weakest thing in this article and should be treated as such. The clockwise rotation tendency is presented in marketing material as a regular cycle. I am not aware of a published independent test of how often the rotation actually completes in order. Until one exists, treat the quadrants as a description of a security's current state and ignore the promise of a predictable path between them.

And the honest limit of the whole approach. A ratio cannot tell you the cause. The Indian midcap case above shows a ratio moving correctly for a regulatory reason. If you attach an economic story to a ratio move, the story is yours and the ratio does not support it.

Carry this

• A ratio is A divided by B. Direction is the message. The level means nothing.
• Build 2 ratios per holding: against the broad index, and against its own sector index. The gap between them is the finding.
• Flat is a result. It means you took single-company risk and received index returns.
• An RRG is a scatter plot of a ratio and its rate of change. It shows many at once. It adds no information.
• Correlations rise in declines. The diversification you measured is smaller on the days it matters.

Knowledge check

Related

• Intermarket analysis: how markets move together
• Sector rotation and the business cycle
• Relative strength, and choosing what to own
• What a stock index actually measures
• ← Intermarket analysis and sector rotation