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Why use 2 axes in a chart anyway?

Since the dawn of excel analysts have been using 2 axes in a chart, some to mislead, some to deceive, some to illuminate clear and logical correlations, some to just squeeze two important series into one space, some to show a signal vs a market, and some just because they can.

In this article I'm going to take you through what the issue is first of all, why I use two axes, when it's appropriate (and not), how to do it without looking like an idiot, and some alternatives.

The context is macroeconomic and market analysis for the purposes of generating investment relevant insights (i.e. what I do here at Topdown Charts).

What do we mean by 2 axes?

(firstly, I am talking about time series analysis here)

This is when you put a chart together with two vertical axes (i.e. a Left Hand Y-Axis and a Right Hand Y-Axis), and at least 2 data series. Key point: 2+ series, 2 Y axes, 1 chart (and usually only 1 x axis). Or said differently, 2 axes, 2+ series, and usually 2 different (types of) scales.

Why use 2 axes?

There's a few reasons, the main point is to effectively communicate market/economic insights. Here are some specific examples:

A. Market Signals: by this I mean you will have a market/asset class on the chart in one line, but you manipulate the axes so that it appears as effectively like 2 panels (market up the top, signal down the bottom), see example: commodities valuation signal. The point of this is to practically use the signal and present a clear visual map for how the signal works, how it can be used, and what it's saying now. Practicality.

B. Intermarket Analysis: when you are looking at two different but related markets and are attempting to see how they trade vs each other. Usually the reason is there's 2 markets that usually trade closely together but a divergence shows up and that divergence adds to some investment thesis or prompts a closer look. See example: oil price vs energy stocks.

C. Economic Analysis: often this involves either attempting to confirm the trend in one series by using a similar series (or a market price series which would be economically relevant); or tracking one slower frequency e.g. monthly/quarterly series against a higher frequency data series e.g. daily/weekly. The purpose of comparing different frequencies is to try and get a lead on the slower moving series. See example: China PMI vs copper price.

D. Leading Indicators: typically with this type of analysis you put a lag/lead in and overlay against the series you're trying to forecast. That is, one series has a logical and statistically relevant correlation with another, but with a slight lead, and so you show it on the same chart to imply a future possible scenario. See example: loan growth vs lending standards

E. Less Charts, More Info: basically when you want to cram more info into a single chart (rather than showing 2 or 3 separate charts). See example: global trade vs global IP growth

When is it appropriate to use 2 axes?

Whenever it makes sense*. The above examples are common ways where it makes sense to use 2 axes for practical purposes and to gain an analytical edge.

But more specifically it makes sense to use 2 axes:

-when the 2+ series are in different units (e.g. z-score vs price level, percent change vs diffusion index, one price vs another price, etc), yet are some how relevant or related, and you want to see how one moves in relation to another

-checking whether a signal works (plot your signal against the market, see if it's obvious)

-displaying an indicator against a market (although you might argue this is like using 2 charts)

-displaying a leading indicator overlayed against the series it predicts

-checking how 2 or more related but different assets are trading in relation to each other

...basically, it's appropriate where there is a practical reason and ideally an economically logical relationship (and ideally when you are being honest with yourself and others).

When is it not?

It's not appropriate basically when there is no economic logic between two series, or when you are blindly data mining. For instance, looking at the price of copper vs the China PMI makes economic sense because China is the world's largest consumer of copper and therefore changes in the economic pulse in China will logically impact on the price of copper.

It's not appropriate when you are using far too short a time-frame, or indeed if the supposed correlation breaks down completely if you use a much longer time-frame. [but sometimes it can make sense to compare 2 markets on comparable terms over a short time frame]

It's not appropriate when you don't know why you are using 2 axes, and/or can't explain clearly and simply why you are doing so. [on that note, if you do use 2 axes and it's not immediately obvious why, then you should explain why you are doing so in your work (people will ask anyway)]

It's not appropriate when you are trying to show something that isn't there.

It's not appropriate if you are more concerned with confirming your agenda/biases than engaging in honest analysis. Fooling others or yourself is equally inadvisable.

How to do it without looking like an idiot?

Well, basically follow what I said above and below in terms of the key principles, but in terms of actual implementation, in excel click one of the series and select series options and click plot series on secondary axes and then go from there.

Above all, since the context of this article is market and economic analysis, what we are most interested in at all times is the signal and the so-what. So keep that in mind.

Some alternatives...

The alternatives basically involve transforming the original series into something comparable. [Note: in some ways using 2 axes works as a short-cut to many of these options, but it's also worth noting, that with methods like rate of change you may still need to use 2 axes due to different ranges - when you are more interested in the signal than the absolute figures].

Z-Score: a z-score is when you normalize a series based on its average and standard deviation; for two or more stationary series this can be a very useful way of comparing.

Rate of Change: for two or more non-stationary series this is a good option e.g. YoY change.

Indexing: you can rebase two or more non-stationary series to a common starting point e.g. 100.

Normalizing: normalizing a series against another variable e.g. debt as a proportion of GDP or market cap, etc (as appropriate).

To sum up...

The use of 2 axes and/or 2 different scales in a chart can be a very useful analytical technique for shedding light on correlations, inter-relations, and market signals. Like all tools and techniques it is something that can be abused/misused. The most important thing is to not fool yourself (never mind anyone else), and know why you're doing what you're doing.

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