Logica Captial Advisers letter for the month of July 2019, titled, “Macro Micro.”
“Sometimes probabilities are very close to certainties, but they’re never really certainties.” -Murray Gell-Mann, Nobel Physicist
These are my thoughts on relevant investment topics. In our ongoing research of our own dilemmas, we recognize that the same issues are likely at the heart of struggles that we all face. With equal measure of frustration and excitement, we hope to contribute to the marketplace of ideas and discussion. And with the goal of interaction and feedback, please reach out with responses or topics of interest.
I’m not much of a consumer of mass media, with a tendency to reading anything other than headline news. What I do pay attention to is news within the world of science and discovery. I am forever fascinated with the advancements of humankind and the innovations that are catapulting our species toward a deeper understanding of our universe, and alongside that, great technological advancements. To this end, my various feeds are filtered toward those areas of science that most captivate me; astronomy, physics, and mathematics. A little over a month ago, on Friday, May 24th I came across a headline that struck a nuanced chord of memory; the passing of the Noble-winning physicist, Murray Gell-Mann. The end of human life is normal, and of course, happens every day of the week in multitudes, but the event associated with this particular physicist moved me due to his association to a specific memory of mine at an exploratory moment in my life. I was therefore inspired to write about it.
Lessons on Entropy
A little over twenty-five years ago, fresh out of school, I was obsessed with learning all I could about the nature of the universe. I had a deep curiosity for how things worked, and in particular, the mechanisms at the heart of the most fundamental physical laws. During this exploration, I recall that for some time, I wrestled with a profound idea that really bothered me, as it seemed to create a grave contradiction inside the deepest laws of our universe. Above all, I have a hard time sitting still with inconsistencies, and especially those fall at the very core of human understanding. My issue was this: entropy, as a natural process, effectively ensures that things always get crazier. Given the physical characteristics of energy, heat, and work, order will always, and quite naturally, beget disorder. If one wants to further order a dynamical system, new work needs to be done. There is no free lunch to how things get accomplished — even nature has to work for a living! Accordingly, if the requisite work is not done, then the second law of thermodynamics demands that entropy increase, such that any semblance of order will tumble, head first, into relentlessly accreting disarray. This wasn’t just an idea, it was a law — established and hard-coded into the architecture of our universe.
At the same time, complexity arises everywhere; all the planets and stars are structures full of chemical compounds, and here on earth, we see intricate plants and flowers, crystals and waterfalls, and the vast diversity of life across the animal kingdom. The universe is not filled with amorphous blobs that float, aimless, through an expansive ocean of disorderliness. It is filled with complex and refined things, all of which contain precise operating procedures, and some of which write blog posts about physics and finance. We, as producing and acting conscious beings, are intricately ordered. I understood very well the notion of a creator, of a being greater than ourselves, as a shared explanation that manifested itself in a range of variants across the globe. But I still wondered whether there was an answer provided within nature itself, or more specifically, whether there was an answer that existed within nature that was not a blazen contradiction to the physical laws as taught in university.
Order in Chaos?
I pondered how physical law can allow its own components to drift toward increasing order, moreover, to extreme intricacy and sophistication, if one of its fundamental laws said it must do exactly the opposite? Seemingly, a thing cannot “naturally” become more ordered while the second law of thermodynamics mandates it toward disorder. The logic just did not compute. With this contradiction tapping away at my brain, I had little choice but to dig deeper; and so I did. Eventually, after some reasonable amount of digging, I came upon a beautiful answer by none other than the Nobel Prize winning physicist Murray Gell-Mann. He resolved the contradiction by explaining that there most certainly is entropy, on average, throughout the universe. But the key was “on average,” which does not mean all the time, nor everywhere. The average net worth in our country does not illuminate the billionaires and the homeless. The point was that the average entropy, by far, exceeds the local complexity, as if complexity itself was the left tail of a distribution of disorderliness which, due to entropy, has a positive mean. “The universe began in a state far from thermal equilibrium. As it winds down, disorder increases, on average, throughout the system, but there can be local violations of that tendency,” Gell-Mann explained.
And that was it; the solution to the conundrum was the distinction between what goes on at the macro level versus at the micro, i.e. it was an issue of scale. The “local violations” were possible so long as the entirety did what it was supposed to. Separately, the blurring of this distinction was compounded by the summary statistic, wherein describing the distribution with general parameters (a negative mean) hid the tail behavior; the large scale average drifts downward while extreme leaps occur at the small scale. In totality, there was both a solution to the contradiction, and a framework for identifying, and unwinding, the very essence of the contradiction. It was all a function of scale; and how summary statistics can blur the differences for a behavior that is not scale invariant, that is, for some process that acts one way at larger scale and an altogether different, or even opposite way, at a smaller scale.
Entropy and Investing
To bring this to the here and now, I am humbled to be able to connect the passing of this famous physicist to his having settled my itching mind in the distant past, and concurrently, to bring it full circle to very different issues that I confront today. I see this same contradiction (and resolution of the contradiction) not within the governing laws of our universe, but deeply embedded inside the capital markets. I am immediately struck by the distinction of time frames for investment decisions, of what we believe happens at the macro vs what we live through at the micro. One can be long a stock for a multi-year turn around and growth play, while an equally well informed relative value manager is short that very same position only for this month because it has leaped a little bit too far and too fast and a pullback is expected. The macro can offer a long term positive mean while a profitable trade can be made taking an intermediary downside bet on that very same security. Or similarly, one can make money on a long day trade during a bear market. The contradiction, as to how two highly informed and thoughtful investors can have precisely opposing views and take polar opposite positions, is not at all a contradiction. It is resolved much like entropy with embedded complexity; the larger environment does not have to align with the local environment.
The Triple Screen Trading System
Taking this idea a few steps further out, it becomes apparent that the diversity of opinions across markets is often one of perspectives, or rather of scale, driven by respective time horizons. Time, as it turns out, is part and parcel of strategic decision-making. When I first started trading about 25 years ago, I initially learned about the “triple screen” trading system, which recommended surveying price behavior across, at the very least, three different time scales, perhaps selecting ideal periods within an hourly, daily, and weekly chart, in order to make better trading decisions. By capturing, and then assessing, the similarity vs. diversity across investor’s time horizons, one can potentially extract how much agreement or disagreement there is amongst participants. If all time frames agree, this seemed to send one type of message vs high discordance across the different frames.
This all makes sense to me on the performance side of things, investors each choose their time horizon, but I wondered, does this also hold true if I flip this concept on its investment head; or said otherwise, does risk have a different character with respect to its time-frame? Risk, of course, is not chosen, but simply the collateral damage that comes with the chosen time-frame for the return horizon. In my prior post, I talked about volatility being the music of the market, of listening to the undulations of the market to get a feel for the character of its volatility. But much like a good song amalgamates a range of frequencies, from the midrange of the beautiful vocals, to the bass of the drumbeat and the treble of the violin strings, so does volatility operate at multiple frequencies.
Volatility and Time
Academic literature has established that volatility has a very natural relationship to time, namely that it propagates at precisely the square root of time. For example, if the S&P 500 demonstrates a monthly volatility of 4.5%, then over 12 months, the mathematically pure outcome should be an annual volatility of 4.5% times the sqrt(12), which equates to 3.5×4.5%=15.75%. Lo and behold, the annual volatility of the S&P 500 is about 16%. The problem is, within the 16% annual volatility, we can most certainly experience a daily move greater than 8%. That is, we can literally see half of our annual volatility, or better yet, twice our monthly volatility, in a single day! Much like the entropy of the larger universe, there are outrageous local violations. The macro hides the micro, where much like our broader universe, there is tremendous complexity at the micro-scale. Moreover, the summary statistics distort the picture, with the standard calculation blurring the extreme local violations. Volatility, as it turns out, is like entropy, moving outward, on average, at some pure law (the sqrt of time), only to hide the complexity that lives inside it.
We can of course refer to other parameters of the distribution, like the higher moments of skew and kurtosis, to more accurately describe the micro character of the volatility, or more aptly, to highlight those few events that could make all the difference to the big picture. But even in those parameters there is tremendous room for blurring the most extreme units of micro. When the S&P 500 cracked 22% on October 22, 1987, it violated not only the measures of deviation, but also those of historically computed skew and kurtosis. Taking single day events like this into account, the cold and hard reality is that there really is no summary statistic that can ever capture the complexity of a single moment in the trajectory of “financial market” time. It is not that any fundamental laws of the universe or measurements of the financial markets ever contradict our equated outcomes at the macro, its that local violations can comfortably live deep inside the units of our measurement.
Hedging – Front Month or Far Out?
In terms of volatility, and our attempts to hedge market shocks, this poses an interesting issue. If we think that we are protecting our portfolio by buying out of the money put options, but do so on a longer time frame, we are muting the micro. The S&P’s annual volatility priced into a one year out S&P put option will allow for a wide intra-year swing; the market has time to recover. Accordingly, longer term will be relatively immune to short term spikes in contrast to the impact of implied volatility on near term options. Longer term, effectively, varies slowly relative to the shorter term in capturing spikes of short term sentiment. Simply said, a 10% move is big over a day or a week, but no big deal over two years. To this end, implied volatility skews (the oft called volatility “smile”) are much more pronounced for short term options (given moneyness on the x-axis). This also makes sense from a purely statistical perspective, given Central Limit Theorem and Law of Large Numbers, if we assume market behavior gets more Gaussian in the loooooong run, the smile must flatten out.
Vega vs. Certainty?
With all this in mind, there exists an interesting contradiction to the option pricing parameter of Vega, the option’s sensitivity to a change in the underlying’s volatility. The math shows that Vega increases with time, but given the reality as shared above, current events have greater impact on the short term. I know this from my distant rendezvous with the thoughts of Murray Gell-Mann, and in light of his recent passing, would like to honor him for once again bringing fluidity to my thoughts, and resolving a contradiction. My lesson from him is in the deeper understanding of scale invariance, or the distinction between the macro and the micro. Yes, Vega technically expands with time (to maturity), but given local extremes that dissipate over the longer term, it also gets less credible with time. There is therefore an analogous higher expectancy to option payoff; less vega with higher credibility is worth more than higher vega with lower credibility. To this end, the better protection, aka the more reliable insurance, is closer month optionality. Thanks, Dr. Gell-Mann for enlightening me; to you I dedicate my improved ability to insure market risk.
Chief Investment Officer
Logica Captial Advisers, LLC
This article first appeared on ValueWalk Premium