Rabbit Hole #10: Correlation Mediation

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Long EURCHF @ 0.9444

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December 8, 2023

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Rabbit Hole #10

Correlation Mediation

Welcome to Rabbit Hole #10. The Rabbit Hole series offers deep dives into random trading and macro topics that fascinate me. Today I discuss an evolution in my thinking on correlation and why it’s useful to identify mediators of correlation. This thought process would have been useful when I was unprofitably going long AUD on rising terms of trade in recent years.

10-minute read, 1600 words (plus an appendix)

Why we need good explanations

I have written extensively about trading cross-market over the years and my thinking on how this all works has evolved over time. My first observation, in the 2003-2006 periods was simply: Hey! When this happens, this other thing tends to happen after. For example, when gold goes up, AUDUSD goes up.

That was fine for a while, then I tried to put some rigor behind it and found most of the mathematical approaches I used didn’t add value over and above simple observation + overlays. If anything, regression created false precision, useless complexity, and created the impression of a static or forward-looking mathematical relationship when the relationships between assets are anything but consistent or purely scientific.

Still, simply observing the relationships doesn’t give you enough insight to allow you to predict the future of the correlations. If all you know is that when oil goes up, the USD goes down (as was the case for much of my career), you are not going to be in a strong position when that regime changes and the relationship breaks down, disappears, or reverses. I wrote about the changing relationship between the USD and oil in am/FX: One Less Vulnerability.

So, I have tried to uncover the logic and transmission mechanisms behind correlations by thinking a bit more deeply. Some of this was inspired by a personal philosophy that has gained momentum as my career progressed: If you can’t explain what’s going on, you’re going to struggle to predict what happens next. Explanations are useful. Also, the less you can explain a phenomenon in markets, the more likely it’s random. That’s why I spend time trying to explain why seasonality is real (or not), and why correlations make sense (or don’t). Good explanations lead to better forecasts.

Causes and mediators

In April 2021, I wrote a piece titled “What causes cross-market correlation” and I have posted it as an Appendix at the end of today’s piece. It ties in with the rest of what I am about to write and it’s my primary thinking on why correlations can be real and somewhat persistent, not imagined and ephemeral.

Recently, I have been reading The Book of Why by Judea Pearl and Dana Mackenzie (HT Bose). As a non-statistics person who is interested in correlation and causation, I really enjoyed the book. It’s niche and a bit wonky but mostly comprehensible.

Chapter 9 is “Mediation: The Search for a Mechanism.” It begins as follows:

In ordinary language, the question “Why?” has at least two versions. The first is straightforward: you see an effect, and you want to know the cause. Your grandfather is lying in the hospital, and you ask, “Why? How could he have had a heart attack when he seemed so healthy?” But there is a second version of the “Why?” question, which we ask when we want to better understand the connection between a known cause and a known effect. For instance, we observe that Drug B prevents heart attacks. Or, like James Lind, we observe that citrus fruits prevent scurvy. The human mind is restless and always wants to know more. Before long we start asking the second version of the question: “Why? What is the mechanism by which citrus fruits prevent scurvy?” This chapter focuses on this second version of “why.”

The search for mechanisms is critical to science, as well as everyday life, because different mechanisms call for different actions when circumstances change. Suppose we run out of oranges. Knowing the mechanism by which oranges work, we can still prevent scurvy. We simply need another source of vitamin C. If we didn’t know the mechanism, we might be tempted to try bananas.

The word that scientists use for the second type of “Why?” question is “mediation.” You might read in a journal a statement like this: “The effect of Drug B on heart attacks is mediated by its effect on blood pressure.” This statement encodes a simple causal model: Drug B → Blood Pressure → Heart Attack.

In this case, the drug reduces high blood pressure, which in turn reduces the risk of heart attack. Likewise, we can summarize the effect of citrus fruits on scurvy by the causal model Citrus Fruits → Vitamin C → Scurvy. We want to ask certain typical questions about a mediator: Does it account for the entire effect? Does Drug B work exclusively through blood pressure or perhaps through other mechanisms as well? Mediation is also an important concept in the law. If we ask whether a company discriminated against women when it paid them lower salaries, we are asking a mediation question. The answer depends on whether the observed salary disparity is produced directly in response to the applicant’s sex or indirectly, through a mediator such as qualification, over which the employer has no control.

I thought this was an interesting excerpt as it applies to the now-solved AUD currency vs. Terms of Trade puzzle. For years, market participants (including me) relentlessly banged their heads on keyboards, going long AUD in response to a massive surge in the country’s terms of trade. But as I wrote in March 2023, the mediator in this case is RBA policy.

If a booming terms of trade transmits to the jobs market, capex, inflation, and eventually interest rate policy (as it did during the commodity supercycle 2010-2013), it matters for the AUD. If it doesn’t transmit (like in 2018 and 2021), it matters—but it matters much less.

Here’s the start of a piece I wrote in March 2023:

One could think about the causes and mediators of the USD vs. oil correlation and do similar work. The cause (US energy import dependence) is no longer in force because the US is now a net exporter of energy. And in the later years, as US net energy imports waned, one mediator (sovereign wealth funds and central banks recycling and diversifying out of dollars as quickly as possible) no longer worked because foreign exchange reserves were smaller and dollar diversification was less instantaneous.

The idea is to think about the process by which a correlation works. What are the direct and indirect causes, and what are the mediators? We can do this by creating a diagram. In the book, they use simple cause-effect diagrams and I think those can be useful. They force the analyst to think about logic before constructing models or calculating r-squareds. Does AUDUSD listen to copper, for example? That makes sense to me given Australia’s reliance on copper exports. I would say “yes”.

Does copper listen to AUDUSD? I would say “no”. That direction of causality is hard for me to get my head around and therefore when I draw a causality diagram, I put the arrow from copper to AUD, not the other way around. This exercise is subjective, but going through a logical thought process and coming to a conclusion is more likely to work out of sample (in future) vs. brute force data mining to find a relationship that defies logic.

Maybe a well-trained statistician can datamine successfully, but I strongly prefer cause / effect statements that I can explain with some sort of underlying logic (see Appendix for my six main sources of such logic).

For fun, I created a causality diagram for copper and AUD. There isn’t really any new information for me in here, but the idea is that creating these diagrams for other relationships will help to understand them. And so I plan to do so in the future with less obvious apparent relationships like bitcoin and NASDAQ. In the diagram, I used “higher copper” and “higher AUDUSD” to make it easier to understand, but everything would work in reverse, too.

Much of the relationship between variables in markets can be handled by a simple explanation: A third variable drives them both. That’s point #2 in the appendix. Here I’ve listed global growth, Chinese growth, the direction of the US dollar, and global risk appetite as four important confounders (third variables) of the copper / AUD relationship because all four of those things drive both copper and AUD. I’m doing my best to use the correct statistical terminology here but if you have a PhD in applied mathematics from MIT you may be giggling to yourself here and there at my noobitude. I’m still learning!

I added one new dimension to the Judea Pearl diagram. Time is measured on a logarithmic scale where time passes quickly at first and then more slowly as you move left to right. Here’s my diagram. It is not meant to be a complete list of everything that happens when copper and AUD tango, it’s just supposed to tickle the idea generation and explanation machines inside your parietal lobes.

I believe that constructing accurate diagrams of this type can help me predict when correlations will change in the future. They certainly help me think through the mechanisms of correlation and possible causation. Over time I can compare my cause-effect diagrams to empirical reality and decide whether or not they are still valid. This should help avoid mistakes like the AUD ToT Puzzle and warn of coming regime changes.


The consensus from readers is that I should provide the calendar on Friday to help you get ready for next week and then repeat it as an appendix on Monday so you don’t have to dig up the Friday am/FX every Monday when you sit down. So that’s what I’ll do. Here’s the calendar for next week. Plenty of meat! Check out that manic 9-hour stretch on Thursday.


Final Thoughts

14 Amazon Leadership Principles and Why They Matter via MM.

Have an intergalactic weekend.

good luck ⇅ be nimble

End of Appendix

Map of the path of Voyager 1

It is currently about 15 billion miles away from Earth.

It will exit the other side of the Oort Cloud in about 30,000 years.

Graph showing the number of solar particles hitting Voyager 1 as it approaches and clears the edge of interstellar space

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