RATIOPLOTTER.EU

General Notes

Currency Consistency: Ensure tickers are in the same currency to avoid exchange rate noise affecting the ratio.
See the currency on the Ticker Selector Page.

ETF Consistency: When plotting the ratio between two ETF's, always check that both are either distributing or accumulating. If this is not the case dividends can effect the results significantly!

R² and ADF p: Ensure the R² and ADF p point to a good quality model which can be used for trading (see table below).

Recommendation: Always check the seasonality plot of the ticker you intend to swing trade; ensure the historical seasonality isn't moving against your position.

Run Regressions on Arbitrary Datasets

Upload Your Own Data: You are not limited to our default data feeds. The platform allows you to run logarithmic regression analysis on arbitrary datasets by securely uploading your own custom data. When you upload a CSV of your proprietary time series, our system automatically maps it to the USR-* ticker space. This enables you to seamlessly run the constrained ratio spread or exponential growth models on your own data, regressing it against major global indices or other custom vectors you have provided.

Why Log Plots Often Beat Ratio Plots for Trading/Investing?

Financial asset prices, in the long term, typically behave in an exponential manner. This exponential behaviour can eliminated by ratio plotting for instance the T-VOO ticker divided by an 8% compound annual growth per year curve: RAT(T-VOO, MATH-CAGR_PCT-8). This exponential behaviour means our typical asset doubles in price every x years (if they are doing what an asset is supposed to do and not going bankrupt).

The problem with the above division by an exponential curve above is that assumes the asset keeps same average CAGR, compound rate pear year throughout its price history. Which is often not true.

By applying the LOG() function to such prices, we bring them to a scale where doubling from 0.5 to 1, covers the same distance on the y axis as doubling from 2 to 4. Notice that on a regular plot of T-URTH for instance, a price climb from 0.5 to 1 has distance 0.5 on the y axis, and notice that a price climb from 2 to 4 has distance 2 on the y axis (price axis). But on the LOG(T-URTH) chart, both price climbs have the same distance! If you want to work out the numbers, we have: climb 1: LOG(0.5,2)=-1 and LOG(1,2)=0, distance 1. And for climb 2: LOG(2,2)=1 LOG(4,2)=2, distance 1. In the LOG(CURVE) chart, an exponential curve looks like a diagonal line. The stronger the exponential, the steeper the diagonal line. With the advantage that such line can be used for a linear regression model, it can be fit to an average price line with intercept and coefficient for how steep it climbs the price up.

Moreover, if you are using the ratio plotter instead of the log plotter for trading, you will have the following problems: (1) On the ratio plot, there are distortions causing you to miss a doubling trade from 0.5 to 1 because the trade from 2 to 4 looked more profitable, they are equally profitable. (2) The ratio is further corrupt when the denominator doubles from 0.5 to 1 for instance, and the numerator moves from 2 to 4. They actually both moved the same distance and the LOG(A) - LOG(B) plot on this page will revel that, while the RAT(A, B) plot will not reveal that. By the way, (RAT(A,B)) is equivalent to the ratio plot.

To illustrate the above I show a case where such distortions are very clear:

This means the ratio plotter charts are useful for some cases such as: (1) Buffett indicators, (2) When two stocks that are very similar like two World Stock Indexes or two competing stocks. (3) When you want to play with the curve, divide it by an exponential, apply other funtions such as RAT(TICKER, LAG(TICKER,30)) which divides a dicker by itself lagged 20 days. Even in the above examples, the upside of the curve will be typically stretched-up more than the downside below the average because of the doubling from 0.5 to 1 covering smaller distance than doubling from 2 to 4, and also the average will be shifted upwards by a considerable amount, impacting your reversal to the mean judgement. Also over the long term the curve on the ratio plot often looks like an exponential which makes it difficult to see past trends on the same scale as current trends. Dividing the ratio curve by an exponential may lessen this, but it is not the automated, ideal approach offered here.

ETF Consistency: When plotting the ratio between two ETF's, always check that both are either distributing or accumulating. If this is not the case dividends can effect the results significantly!

R² and ADF p: Ensure the R² and ADF p point to a good quality model which can be used for trading (see table below).

Recommendation: Always check the seasonality plot of the ticker you intend to swing trade; ensure the historical seasonality isn't moving against your position.

Stationarity & Mean Reversion (ADF Test)

Traders often assume that over the long term, stocks and commodities will reliably mean-revert to a historical relationship. This dynamic reflects Benjamin Graham’s famous maxim: in the short term, the market is a voting machine driven by momentum, but in the long term, it is a weighing machine. The challenge for pairs traders is quantifying this underlying fundamental gravity when short-term price action rarely moves in perfect lockstep, which often causes R² to break apart.

The solution to the problem above is the Augmented Dickey-Fuller (ADF) test. While traditional correlation measures such as R² measure how assets move together, the ADF test measures the statistical gravity pulling their spread back to equilibrium by testing the regression residuals for stationarity (the longer term weighing machine from Benjamin Graham).

Understanding the ADF p-value: Lower ADF p-values are strictly better for mean-reversion strategies. A p-value of 0.01 means there is only a 1% probability that the spread's divergence is a permanent drift. It confirms that the residuals of the model will eventually gravitate back to zero.

Comparing the R² against the ADF p-value reveals the true structural relationship of the assets:

In our stock and commodity model, a mediocre R² of 0.37 simply means the assets do not perfectly mirror each other day-to-day. However, a statistically good ADF p-value (e.g. 0.14) proves that the market will eventually act as a weighing machine, pulling the asset prices back into their historical relationship.

Stationarity & Mean Reversion (ADF Test)

ADF Statistic (The Tension): Measures the mean-reverting "rubber band" effect. A highly negative number (e.g., -3.85) means strong tension pulling the spread back to the baseline. Numbers closer to zero (e.g., -1.10) indicate a loose, drifting spread.

p-value (The Fluke Probability): The chance this tension is just a random coincidence. A p-value of 0.0120 means there is only a 1.2% chance the signal is a fluke, meaning you can trust the signal with 98.8% confidence. A p-value of 0.6500 means there is a 65% chance it is a fluke, indicating a random walk you should avoid trading.

R² and Beta Analysis Summary for Ratio Trading

To ensure a Ratio trade is based on structural correlation rather than random price movement, the R² and Beta must BOTH be significant.

A low R² indicates that Asset A and Asset B are "decoupled," meaning any apparent pattern in the Ratio is likely statistical noise with no mathematical pressure to return to the mean. Conversely, a high R² confirms the assets are "tethered," making mean-reversion strategies reliable.

Besides the R² we also need to make sure the Beta is healthy. The Beta between two assets indicates how much the numerator moves relative to the denominator. To use the Beta you can use this simple formula: Expected Numerator performance ≈ Denominator performance × Beta value.

A static Beta may mask recent shifts in relative volatility. To ensure your position sizing remains accurate, compare the overall Beta with the rolling Beta windows in the bottom dashboard pane. Monitoring these short-term fluctuations helps distinguish between normal market noise and a fundamental shift in how aggressively one asset moves compared to the other.