Which of Two Instruments Is Stronger? Reading Price Ratios in the Arbitrage Checker

Cover image: a red price-ratio line runs across the frame with six horizontal dashed lines laid over it. The grey lines at the top and bottom mark the maximum and minimum, the orange line in the middle is the average, the purple line is the median, and the two light-blue lines either side of the average are plus and minus one standard deviation. A short segment at the right end of the line is magnified into a staircase, with a division sign and an arrow swapping A and B beside it

The Arbitrage Checker divides the price of one instrument by the price of another and plots the result as a single ratio line. Pick Symbol A and Symbol B from any of five asset categories, and the chart shows how A ÷ B has moved on every trading day over the past ten years. Six horizontal dashed lines sit on top of it, marking the maximum, minimum, average, median and plus or minus one standard deviation, so you can see where the current ratio sits within its range.

Open the tool and two basic questions come up before anything else: what does this line actually represent, and which period are the six statistical lines calculated over? Both depend on the order you chose for the two symbols and on the period you have on screen, and the tool does not flag either.

Confirm what the ratio represents first, then confirm which period the average belongs to. Only then do the four patterns in the guide read correctly. The sections below cover how symbol order and quote convention change the meaning of the ratio, why the higher-priced instrument belongs in Symbol A, what happens to the six statistical lines when you switch periods, and finally a reading order that puts it together.

Key Takeaways

The order of A and B decides what the ratio means: EURUSD ÷ GBPUSD is the real EURGBP rate; EURUSD ÷ USDJPY corresponds to no rate at all, and both legs bet on the dollar twice
Swapping A and B gives the reciprocal: the same information with the direction reversed, so "rising" reads the other way
The ratio is kept to four decimal places. Putting the lower-priced instrument in A turns the line into a staircase; put the higher-priced one in A instead
The six statistical lines and the overlaid % Change series are calculated only over the range on screen. The 1m average is a one-month average; the long-term average the guide refers to lives under All
Touching ±1σ does not mean the ratio will return to the average; the lines describe where the selected period's data sits, nothing more
Reading order: confirm what A ÷ B means → build the long-term picture under All → narrow the period to see the recent deviation → overlay prices to see which leg moved

Table of Contents

1. What the Arbitrage Checker Is and When to Use It
2. What A ÷ B Represents: Quote Convention Changes the Answer
3. Put the Higher-Priced Instrument in A: The Four-Decimal Problem
4. Which Period the Average and Standard Deviation Cover: Switching Periods Moves the Baseline
5. How to Read It: Long-Term Picture First, Recent Deviation Second
6. FAQ
7. Summary

1. What the Arbitrage Checker Is and When to Use It

The Arbitrage Checker divides the price of Symbol A by the price of Symbol B and plots the result, one point per trading day, as a single line. A rising ratio means A is strengthening relative to B; a falling ratio means B is strengthening relative to A.

The question it answers is "how has the relative strength of these two instruments changed?" A visible deviation on the chart means the relationship between them is shifting. It does not mean there is a risk-free arbitrage waiting to be executed. The name invites that reading; the guide's own term, pair analysis, is closer to what the tool does.

The tool page carries a detailed guide below the chart: four typical patterns, the logic of pairs trading, a five-step workflow and an FAQ. It is worth reading once before you start interpreting the line.

Open the Arbitrage Checker

The Arbitrage Checker main screen: category and symbol dropdowns for Symbol A and Symbol B at the top, the Overlay Prices checkbox below them, and in the middle a red ratio chart with six horizontal dashed lines over it. The period buttons 1m, 3m, 6m, YTD, 1y and All sit at the top left, the editable start and end dates at the top right are outlined with a dashed box, and a draggable navigator and nine legend items sit beneath the chart. The three blocks are numbered 1, 2 and 3

The screen has three parts:

① Symbol A and Symbol B: each has a category dropdown (forex, indices, commodities, US stocks, crypto) and a symbol dropdown; A and B can be combined freely across categories
② Overlay Prices: ticking this adds the % Change of A and of B to the same chart, so you can see which side is driving the ratio
③ The ratio chart: six period buttons at the top left (1m, 3m, 6m, YTD, 1y, All); the start and end dates at the top right can be clicked and typed over, which is how you view any two dates you like; a navigator beneath the chart whose ends can be dragged. The legend lists the ratio line plus six statistical lines, and clicking a legend item hides that line

There is one point per trading day, going back roughly ten years. Hovering over the line shows the ratio for that day.

It suits situations like these:

Your situation	What the tool gives you
You want to know which of two related instruments is currently stronger	Ten years of A ÷ B and where it sits now
You are planning a pairs trade and want to know how far the ratio has deviated	The average and ±1σ lines, calculated over the period you select
You hold two positions and want to check they are not the same bet	Overlay Prices, to see which way each leg has moved
You want to compare instruments from different categories, say gold against a US index	Any pairing across the five categories

Gold against silver has a fixed version elsewhere on the site: the Gold Silver Ratio page shows the live ratio and its history directly, so that one pairing does not need to be built in the Arbitrage Checker.

2. What A ÷ B Represents: Quote Convention Changes the Answer

Every forex symbol is quoted in a direction. EURUSD is "how many dollars for one euro"; USDJPY is "how many yen for one dollar". What you get when you divide one by the other depends on which side of each pair the dollar sits.

Combination	Example	What the ratio is
Dollar is the quote currency in both	EURUSD ÷ GBPUSD	The real EURGBP rate
Dollar is the base currency in both	USDJPY ÷ USDCHF	The real CHFJPY rate
One of each	EURUSD ÷ USDJPY	No rate at all

In the first two cases the ratio is a cross rate that is actually quoted in the market. This is easy to check. Set A to EURUSD and B to GBPUSD, match the period to the "Last 30 Trading Days" chart on the site's Historical Exchange Rates page for EURGBP, and every turn in the ratio line lands on the close of the same day's candle. Compare closes day by day and the difference only shows up in the fourth decimal place.

Two charts stacked. The top one is the Arbitrage Checker's EURUSD ÷ GBPUSD ratio line with the start and end dates set to the same 30 trading days as the chart below. The bottom one is the EURGBP Last 30 Trading Days candlestick chart from the Historical Exchange Rates page, with a five-day moving average. Every high and low on the top line corresponds to the close of the same day's candle below, and both vertical axes sit in the 0.85 range

The third combination is the product of two dollar-denominated prices: EURUSD ÷ USDJPY equals EURUSD multiplied by "how many dollars for one yen". When the dollar weakens against both the euro and the yen the ratio rises; when it strengthens against both, the ratio falls.

That is exactly what produced the biggest move in this line over the past ten years. In the autumn of 2022, with USDJPY closing in on 150 and EURUSD below 1, the ratio hit its ten-year low. Tick Overlay Prices and you can see that over that stretch the EURUSD % Change heads down while the USDJPY % Change heads up. Both legs are saying the same thing: the dollar is rising.

The EURUSD ÷ USDJPY ratio chart under All with Overlay Prices ticked. The red ratio line drops to its lowest point of the whole period in the autumn of 2022; at the same position the blue EURUSD % Change is below zero and the black USDJPY % Change is above zero, in the highest region of the whole period. Two red circles mark the low in the ratio and the high in the USDJPY % Change

This matters directly for pairs trading. The guide's method is to sell the strong side and buy the weak side when the ratio deviates from its average. Applied to EURUSD and USDJPY, a low ratio means buying EURUSD and selling USDJPY: one leg buys euros and sells dollars, the other sells dollars and buys yen, so both legs contain a short dollar. The dollar exposure stacks rather than cancelling, and treating the position as a market-neutral pairs trade understates the directional risk you are actually carrying.

Mixed-direction pairings can still be plotted and analyzed, as long as you know the ratio corresponds to no single rate. If you want the ratio to be a cross rate and the pair to bet only on the relationship between the two instruments, forex pairings need the dollar on the same side in both. The combinations recommended in the guide's FAQ, EUR/USD with GBP/USD and USD/JPY with USD/CHF, both qualify. Pairings within a category, such as gold against silver or two equity indices, have no quote-direction issue; there the question is whether the two are economically related.

3. Put the Higher-Priced Instrument in A: The Four-Decimal Problem

The page carries a note: if Symbol A has a small price and Symbol B a large one, the calculated value may be too small for the chart to display properly, and swapping A and B fixes it. The cause is precision. The ratio is kept to four decimal places. The axis labels and the hover values both show four decimals, and the six statistical lines are calculated from these rounded values too.

EURUSD ÷ USDJPY sits around 0.007, which leaves only two significant figures after rounding. Switch the period to 1m and the line becomes a staircase: twenty-odd trading days jumping between five tick values from 0.0072 to 0.0076, with every movement in between discarded.

Reverse it, with USDJPY in A and EURUSD in B, and the ratio becomes roughly 132. Four decimals are more than enough, and the same month draws as a normal line.

Two charts stacked, both on the 1m period. The top one has EURUSD as A and USDJPY as B: the red ratio line is clearly stepped, moving horizontally along five tick values between 0.0072 and 0.0076 and then jumping vertically. The bottom one swaps them to USDJPY ÷ EURUSD: the ratio sits between 131 and 138 and the same month draws as a continuous line

Swapping A and B gives you the reciprocal of the original ratio: B ÷ A = 1 ÷ (A ÷ B). The two charts carry the same relative-price information with the direction fully reversed; wherever A ÷ B was rising, B ÷ A is falling. A rising USDJPY ÷ EURUSD means the dollar is strengthening against both the yen and the euro. Check which symbol is in A before deciding which side "rising" or "breaking the upper bound" refers to.

Wider price gaps make the problem more obvious. Divide EURUSD by Bitcoin and the ratio is around 0.00001, which rounds to 0.0000 and draws as a flat line along zero. That is the "display problem" the page note describes. The rule is the same: the higher-priced instrument goes in A.

4. Which Period the Average and Standard Deviation Cover: Switching Periods Moves the Baseline

The six lines in the legend, Maximum, Minimum, Average, Median, Standard Deviation (+1σ) and Standard Deviation (-1σ), are calculated over whatever range is currently on screen. Under All they are ten-year statistics; press 1m and all six are recalculated over the last month and move accordingly. Dragging the ends of the navigator or typing new start and end dates does the same thing.

Compare it on EURUSD ÷ GBPUSD, using just the left side of the chart where the axis is. Under All, the orange average line sits near 0.87 and ±1σ brackets the band from 0.85 to 0.89. Switch to 1m and the six lines squeeze into the month's high-low range, with ±1σ now between 0.855 and 0.859, a few ticks wide.

Side-by-side comparison, both EURUSD ÷ GBPUSD, each cropped to the left side of the chart with the axis and period buttons. On the left the All button is active, the axis runs from 0.8 to 0.925 and the six dashed lines spread across the whole range: the grey maximum near 0.94 at the top, the light-blue +1σ near 0.888, the orange average and purple median overlapping around 0.866, the light-blue -1σ near 0.847 and the grey minimum near 0.823 at the bottom. On the right the 1m button is active, the axis only runs from 0.853 to 0.859, and all six dashed lines sit between 0.854 and 0.86, with +1σ and -1σ at about 0.8588 and 0.8552 hugging the 0.857 average

This changes how to read the guide's recurring phrase "how far from the long-term average". A ratio touching +1σ on the 1m screen means only that it is one standard deviation above the average of the last twenty-odd trading days; it may still be far from the ten-year average. For the long-term range and long-term average the guide talks about, All is the closest fit.

The two % Change lines under Overlay Prices work the same way. Their baseline is the first trading day on screen, and it changes with the period: under All you see ten years of cumulative change, under 1m the last month's.

One more thing to keep in mind: touching plus or minus one standard deviation does not mean the ratio will return to the average. When A ÷ B is in a long-term trend or a structural break, the average and the standard deviation move with it. The statistical lines describe where the selected period's data is distributed; they are not fixed support and resistance.

In practice the periods divide up like this:

What you want to know	Period to use
Where the ratio sits in ten years of history, the long-term range and average the guide refers to	All
Whether the last year has started to drift from the longer-term relationship	1y
Whether this quarter's deviation is widening or narrowing	3m or 6m
Detail over the last few weeks	1m. Only twenty-odd trading days, so the average and standard deviation react to single events and are not a baseline for long-term mean reversion

5. How to Read It: Long-Term Picture First, Recent Deviation Second

① Confirm what A ÷ B represents. For forex pairings, check whether the shared currency is in the numerator or the denominator, so the two legs do not stack the same currency exposure. For cross-category pairings, confirm the two are economically related first. If the value is too small, swap A and B, and remember the direction flips.

② Build the long-term picture under All. Ten years of line show whether this ratio has broadly trended, ranged or broken structurally. The six statistical lines at this step are ten-year statistics, and "how far from the long-term average" is read here.

③ Narrow the period to see the recent deviation. Switch to 1y or 6m to check whether the ratio is still in the same regime or has changed character, then whether the latest deviation is widening or narrowing. Remember the six lines are now this period's statistics.

④ Overlay prices to see which leg moved. A rising ratio can be A rising or B falling, and the position you need to deal with is different in each case. Tick Overlay Prices and the two % Change lines separate the answer.

⑤ Return to the individual instruments. The ratio only describes the relationship; the volatility, trend and events of A and of B need checking separately. A ratio that looks range-bound over ten years is a visual screen, not statistical proof that the two are cointegrated; that is the further test the guide's FAQ mentions. Whether two instruments usually move together can be checked in the Correlation Matrix, and there is a separate article on reading it:

Open the Correlation Matrix How to Read the Correlation Matrix

6. FAQ

Q1: Can the Arbitrage Checker find arbitrage opportunities?

It plots the ratio of two instruments' prices and shows how their relative strength changes. There is no executable price gap on the screen. The guide positions it as a pair-analysis aid, and that is the sense in which "arbitrage" appears in the name.

Q2: Does the absolute value of the ratio mean anything?

It depends on the pairing. When A ÷ B converts to a relative price with a clear meaning, the absolute value can be interpreted: EURUSD ÷ GBPUSD is EURGBP, and gold divided by silver is the gold-silver ratio. Dividing two prices with no unit relationship, such as EURUSD ÷ USDJPY, gives a number with no intuitive market meaning, and the focus shifts to how it changes over time.

Q3: After switching to 1m, what does the average line represent?

The average of the last month's data points. All six statistical lines are calculated over the range currently on screen and are recalculated whenever you switch periods, drag the navigator or change the start and end dates. For the long-term average the guide refers to, use All.

Q4: Why does the line look stepped?

The ratio is kept to four decimal places. When A's price is far smaller than B's, only one or two significant figures survive and the line becomes a staircase over short periods. Putting the higher-priced instrument in A fixes it, with the direction reversed.

Q5: Can I compare instruments across categories, say gold against the Nasdaq?

You can select them and the chart will draw. The guide notes that only economically related pairings are meaningful, and across categories the absolute value of the ratio usually corresponds to no market price, so what you read is the direction of the move and the size of the deviation.

7. Summary

The Arbitrage Checker plots the A ÷ B ratio line plus six statistical lines calculated over the range on screen. The tool page's guide explains the four patterns and the pairs-trading workflow well; two things still need confirming before that line is read.

The first is what the ratio represents. When two forex symbols have the dollar on the same side, the ratio is a cross rate and can be checked against the site's historical rates. When they do not, the ratio corresponds to no rate, the dollar exposure of the two legs stacks, and "sell the strong, buy the weak" becomes a double bet in one direction. The higher-priced instrument goes in A, or four-decimal rounding cuts the line into steps; after swapping, you have the reciprocal and the direction reads the other way.

The second is which period the statistics cover. The six lines and the overlaid % Change follow the range on screen; the 1m average is a one-month average, and the guide's long-term average is read under All. Touching ±1σ does not mean the ratio will return to the average.

Confirm what the ratio represents first, then confirm which period the average belongs to: the four patterns can only be read correctly on that footing.

Further Reading

✏️ About the Author

Titan FX Trading Strategy Lab. We produce educational content for investors across a broad range of instruments, including forex, commodities (crude oil, precious metals, agricultural products), stock indices, US equities and digital assets.

Primary Sources

Tool specification: the symbol dropdowns, Overlay Prices, period buttons and navigator of the Titan FX Research Arbitrage Checker, the on-page note about values that are too small, and the four patterns and FAQ in its guide
Measured data: ten years of daily ratios for EURUSD ÷ USDJPY, EURUSD ÷ GBPUSD and USDJPY ÷ USDCHF from the Arbitrage Checker, compared day by day with the EURGBP and CHFJPY daily closes on the site's Historical Exchange Rates pages
Chart behavior: how the six statistical lines and the overlaid % Change are recalculated when switching between 1m and All, dragging the navigator or changing the start and end dates, and the number of decimal places kept in the ratio