CHG Issue #190: The Problem with Probability
Random but interconnected thoughts and observations
In his Pensees, Blaise Pascal differentiates between the mathematical mind and the intuitive mind. He describes the principles of the mathematical mind as clear but removed from common use, whereas the principles of the intuitive mind are both clear and commonplace. However, because these principles are so numerous, some are inevitably overlooked. When any principle is missed, it leads to error. In its pursuit of accuracy, the mathematical mind focuses only on the clearest but most remote principles. Therefore, all mathematicians would become more intuitive if they had a broader perspective, and intuitive minds would become more accurate if they could focus on the principles of mathematics with which they are unfamiliar.
While Pascal categorized people based on this distinction, the late Daniel Kahneman explored how these two minds interact within each individual. He identified our fast, intuitive System 1 mind and our slower, more deliberate System 2 mind, which corresponds to Pascal's mathematical mind. While Pascal and Kahneman provided models of thought processes, the actual anatomy of the brain also plays an important role. The triune brain theory, proposed by the late Dr. Paul MacLean, an evolutionary neuroanatomist and senior research scientist at the National Institute of Mental Health, posits that the brain consists of three distinct sub-brains: the reptilian, the limbic, and the neocortical. The reptilian brain is the oldest and fastest functioning part of the brain, while the neocortical brain is the youngest, slowest, and largest part. Following the reptilian brain, which controls vital functions such as breathing, swallowing, and heartbeat, the limbic brain evolved as mammals diverged from reptiles and began forming attachments to other mammals. According to this theory, emotions like love and intuition originate in the limbic brain, while reasoning occurs in the neocortical brain.
In ancient times, when science was nonexistent or underdeveloped due to our less developed neocortical brains, nature was viewed as divine. Rain was considered a gift from the gods, and phenomena like famine and drought afflicted those who had offended them. Over time, this naturalism evolved into determinism: the nobility was seen as divine, and the poor as sinners, with one's social status largely determined by lineage. As our neocortical brains advanced, we developed better reasoning capabilities, made scientific discoveries, and constructed improved models and theories of the world. Perhaps one of the most significant, yet largely underappreciated, advancements is the theory of probability.
Émile Cailliet states in Journey into Light: "The calculus of probabilities would aim at reducing to numbers, as far as feasible, both the perplexing aspects of the universe about us and of the uncertainties of life." In other words, the sources of meaning that once guided us have been distilled into probabilities, offering accurate answers but little certainty. Probability and science have unveiled the mysteries that once dictated our experiences.
Realizing that chance was not the will of the gods, harnessing atomic power, and now creating thinking machines have transitioned us from uninformed confidence to informed uncertainty. As we peeled back the layers of nature, the realm of the divine and its radical indeterminacy, as characterized by Heisenberg, came into focus, undermining the foundations of belief and meaning. If statistical laws can explain everything that once provided meaning, then the only gods that matter are us. The idea of absolute truth has become absurd, and relativism now prevails as our ability to ensure fair and equal outcomes, previously left to providence, has strengthened with our expanding neocortical brains. We have, in a way, become too smart for our own good, as society has grown increasingly unhappy despite our capacity to shape the world to our liking. Alex Karp and Nicholas Zamiska succinctly articulate this issue in their book The Technological Republic: Hard Power, Soft Belief, and the Future of the West: "The problem is that tolerance of everything often constitutes belief in nothing," and without belief, we struggle to find meaning.
Markets Round Up
The markets have returned to calm in time for summer and we have seen correlations fall across the board.
The strongest correlations today are those between gold, the dollar, stocks, and the yield curve, which means these are the markets in the driver’s seat. They have also been the ones to see the most change over the last twenty days as correlations have come down in general.
The market has settled into the dollar being a risk asset and now apparently bonds are as well.
The recession theme does not appear to be a primary concern when looking at these correlations because of the bond market but it does emerge when we look at crude oil. Crude has underperformed this year (down just over 11% YTD) as the risk to growth and increasing trade barriers have presented dual headwinds for crude. Typically bonds rally in expectation of a recession, and the yield curve steepens, but the uncertain impact of trade policy on inflation has anchored bonds. However, if we look across the USO line in the correlation matrix above we can see that the largest negative correlations are still against the bond ETFs. This creates an interesting pair-trade between bonds and oil as we have the unusual occurrence of both oil and bonds both trading at the low end of their respective ranges, which has resulted from the market pricing in an increased risk of stagflation. Therefore, that risk premium superficially appears to be attractively priced as oil is already pricing a recession which will cause bonds to rally eventually, and if there is no recession oil should rebound strongly while bonds could stay in range.
Chart Crimes
I was recently asked about switching from an actively managed fund to an index fund to save fees which made me think of this Substack account that has been popping into my feed that highlights the cumulative outperformance of different strategies through the use of the ubiquitous "cumulative return of $1 invested" charts. While explaining the virtues of reducing fees and the benefits of compounding over long periods of time it struck me that I could commit a sort of reverse chart crime to make this argument.
Here we have a chart that shows $100 invested in two identical strategies that both return 10% annually and the only difference is that one charges a 1% annual fee. We can see the miracle of compounding at work here as that 1% a year grows exponentially over time and results in ~50% difference after 45 years.
With the help of some fancy marketing, we see charts like this used to raise billions of dollars all the time. In the quest for the next hot investment investors overlook the sure-fire, but less sexy strategies that deliver consistent and reliable returns.
However, they only see this version of that same chart when looking at "boring" investments. It's as if our minds were wired to dream exponentially and reason logarithmically. It is important to acknowledge how fluid our perceptions are to these sleights of hand. Both charts represent the same data but tell very different stories. When chasing novel strategies investors would be well-advised to look at things logarithmically, but when being penny wise over fees they should also remember to think exponentially to avoid being pound foolish. It is all too easy to get anchored in one absolute truth or another, but what is required is a balancing of all these truths at the same time.
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