What Power Laws Can Teach Us About Probabilities Around Geopolitical Risk
"Foreign policy is all about a universe of bad decisions, imperfect decisions; every situation is different. The dynamics, the atmospherics, the people, the pressures, the geopolitical realities shift." -Chuck Hagel
The story of Wayne James Nelson is a great one to teach your kids. When your kids ask why they must learn math, you can always tell them about poor old Wayne. His lack of understanding of math landed him five years in the state penitentiary after he improperly tried to enrich himself with checks to fraudulent entities he would funnel to his personal accounts. He was an Arizona state employee. Had he understood math better, he may be enjoying a relatively comfortable retirement, albeit ill-begotten.
Mr. Nelson had initially written himself his checks for modest and routine amounts. Still, as he began to get a taste for extra cash, as can happen to anyone, he became more aggressive in his fraudulent transactions.
Specific natural datasets like IQ scores or winning times in an Olympic 100-meter race are too closely clustered and might conform to only one distribution, like a bell curve, DO NOT conform to Benford's Distribution (pictured above), which is an exponential decline in the frequency of digits in qualifying datasets. Many variables and distributions affect check transaction sizes, so they are subject to Benford's Distribution.
Therefore, when Wayne Nelson's greed took hold, he started writing checks for much more significant amounts while carefully keeping under the $100,000 level, which required extra scrutiny that could expose his ruse. He got so greedy that 90% of his checks were for over $70,000. The implied percentage of Benford's distribution, which applies, is about 15%, and the chances of this happening naturally randomly were one in one quadrillion. So, he drew some unwanted attention to himself. His kids probably think he's on a long mountain climbing trip. Enron was found to have shifty Benford distributions in their accounting, as did the state of Greece during the European debt crisis.
Interestingly, we can infer the effects and likely duration of conflicts affecting markets using a similar method used to catch the greedy Wayne James Nelson: power laws. Since wars are highly random events spanning several orders of magnitude and are affected by many distributions, the casualties and other data from them can be a good candidate for Power Laws similar to Benford's distribution. From this distribution, we can imply specific probabilities about how likely a conflict will last. Of course, any probability is just a guiding tool, not a definitive answer. Still, investing is helpful, mainly when geopolitical risk seems to cause so many buy-the-dip opportunities.
For instance, like Benford's law and other power laws, a researcher named Lewis Richardson found that the same applies to war casualties. In other words, wars in which 1 million people were killed were ten times less likely than wars in which 10,000 people were killed and a hundred times less likely than violent conflicts in which 100 people were killed in action.
This means that the more people die in a war, the sooner it is likely to end. When you get specific information about the regional histories of the particular conflicts, you can also extrapolate a qualitative element to complement this insight. However, one thing is clear from my assessment: consensus overestimates the current impact of geopolitical risk on markets, and the United States is also much more powerful and stable than our reality TV domestic political culture would suggest.
America has been outspending its key adversaries for decades, and the public likely dramatically underestimates the level of its advantage over them. Not understanding this could cause one to overestimate geopolitical risk.
America's overwhelming military superiority is a stabilizing force around the globe that many do not understand properly. Given the high level of casualties in both Ukraine and Israel/Palestine, particularly relative to recent conflicts and governing limitations, it may be inferred that both conflicts have a higher chance of having already culminated than fear-driven consensus predicts. This has a great bearing on markets.
Let's take the Israel-Gaza War as an example. The low-intensity conflict in the Middle East had a low, stable momentum of violence, but the high-intensity spasms of violence that cause many deaths within a short period of time are not likely to last very long. This is compounded by the geographic and strategic realities defining the conflict.
With casualties well into the tens of thousands for a conflict that usually operates at a much slower rumble, there are already signs that international pressure and even internal Israeli political pressure are close to bringing hostilities back to a more statistically normal level that presents far less of a threat to commerce. Ultimately, the natural limitations of conflicts bring them to an end, even though qualitative facts can always contradict this mathematical reality.
The emotionality of human resistance can be a wildcard. No defense analysts expected Ukraine to put up such a strong conventional resistance to Russia's invasion, yet they have ground the world's second-most powerful military (on paper) into a stalemate that resembles the First World War. That wasn't on many people's bingo cards.
So, we can use this reality to infer certain probabilities about the current geopolitical conflagrations that could potentially vex markets across the globe. There's been a lot of worry, yet we are just on the cusp of all-time highs. Let’s talk about how prey can confuse its predators in the same way risks can confuse us as investors. And thinking of risks as prey is a key theme in this column.
Peacocking: Nature's Harsh Competition Can Teach Us About Our More Restrained Competition on Wall Street
Competition has always been at the heart of markets. While many falsely view Wall Street as a purely competitive field like nature, it's imperative to remember that the competitive field we operate in as investors is very significantly and very closely regulated, and ever since the Buttonwood Agreement, there has been a supposed sort of preternatural respect for agreements with your competitors, a certain floor of decency, and a reliability that doesn't seem to be mimicked in much of nature's more unrestrained competitive variety. Indeed, Wall Street, itself still a product of nature, often falls short of the more noble impulses of capitalism that undergirded its formation.
Of course, war is the ultimate form of unrestrained human competition. When we assess the risk that this most unfortunate of all human activities can have on our far more cushy and regulated world of markets, the results, as discussed in this column, are often quite counterintuitive. But there are ways we can assess risk and help ensure that fear of the possible but improbable doesn't derail superior returns that are probable if you master your fear beyond the capability of your peers. Understanding conflict zones and the potential for escalation better than your competition can result in real alpha and returns that are otherwise very hard to achieve in such short periods of time.
A great example of how real alpha can be achieved is a $VIX short I recommended in the days following the October 7th Terror attacks in Israel. The performance of the contracts I recommended to short the $VIX is below:
The December 20 $17 put options paid $4.69 (entry $1.42) per contract on the date of settlement, and the December 20 $16 put options paid $3.69 (entry $0.91). This means they experienced a respective price gain of 230% and 327% in less than three months.
As you can see, we can identify valuable lessons for our relatively restrained competitive field from the unrestrained competitive field of nature and as in war. How these unrestrained planes interact with our constrained competition plane is perplexing. However, understanding competition in less restrained planes can help us understand how companies compete for investor capital. Many strategies used in nature are used in commerce. One of my reasons for shorting volatility in the face of increasing physical volatility in the Middle East is below:
The macroeconomic impact of the Arab-Israeli conflict, particularly in the wake of the Yom Kippur War, was multiplied by two factors: The Cold War magnifying and intensifying the consequences of the conflict and the developed world's dependence on foreign-produced oil. Both of these items have changed. The world is still far more globalized now than it was then, despite recent and apparent setbacks to globalization. The first significant change is that the US economy has become far less reliant on oil and is far more efficient in its use than when the Arab-Oil Embargo roiled global markets and the US economy in particular. -4 Reasons I'm Shorting The VIX Despite Geopolitical Risks by Chris Robb
Despite a lot of people with a lot more acclaim and experience than me suggesting that the Arab-Israeli War would spike the price of oil and bring back inflation, I used plainly observable facts to inform a highly profitable trade. My assessment about how the initial phase of the conflict stemming from the deplorable Hamas attacks would play out in markets with respect to volatility was proven correct, though.
C-Suite Aggressive Mimicry
Much of what companies try to do to attract investor attention or inspire fear in competitors is not all that different from what some of our animal kingdom evolutionary predecessors did to stay alive. Indeed, sometimes, it is very similar. The peacock fools its potential predators with its tail feathers through "eyespot mimicry," a specified form of a trick called aggressive mimicry that we must constantly be wary of as investors. CEOs and CFOs use it, too.
By creating the illusion of having dozens of eyes for potential predators, the would-be victor does not engage because his brain needs help devising a way to get around or sneak up on a target with so many bright eyes. Bright eyes are unsettling to many creatures for understandable reasons, including our own species. And companies can use similar strategies. They can talk about AI on conference calls to make themselves seem commercially fierce, but it can often be an illusion like the peacock shaking its tail feather. It's a perfectly legal one, but it's up to analysts to assess these claims to add value and separate the AI fakers from the makers.
"There were 179 mentions by S&P 500 companies of the term "AI" during fourth-quarter earnings conference calls - second only to 181 instances in the second quarter of 2023 when looking back to earnings from at least 2014, according to FactSet's document-search tool."- Joy Wiltermuth, Marketwatch
Geopolitical risk is not only hard to quantify in its own right; it brings out the fear in us human beings in a particular way that debilitates our reasoning capacity and best thinking in many cases, making it difficult for us to engage the sophisticated parts of the brain. The prefrontal cortex is a helpful and useful piece of anatomy when approaching complex questions regarding how to value and when to buy and sell assets in a way that will make you rich. It shuts down when your brain is consumed by fear. War is scary as all hell.
However, the humble peacock is not just a metaphor for the aggressive mimicry companies can create to attract investor capital. It is also a metaphor for tail risk itself. In the same way that a predator brain can be inundated with the overwhelming appearance of dozens of eyes, we can be overwhelmed by the sheer amount of things that could go wrong. But it is crucial to remember that you can ALWAYS come up with a reason to sell. But there's an old saying that markets climb a wall of worry and fall on a slope of hope. So, when you see a peacock tail full of worries, instead of freaking out, you might want to consider taking some comfort from it.
Seeing Orange: Finding the Real Risks and Making Money on Overblown Ones
When I tell people to short volatility, I get accused of all the sins in the book. Yet, every time I have done so in the last year and a half, it has paid off handsomely and been directionally correct. Some could accuse me of whistling past the graveyard. I was Senior Editor and Vice President for Fundstrat Global Advisors, so some might accuse me of being a perma-bull, simply lucky.
But I would push back and say that I cut my teeth in my career trying to spot and prevent the negative implications of tail risk. Through the experience of trying to actually prevent tail risk from causing mass financial chaos through implementing the Dodd-Frank Act, I learned a very precious lesson about risk.
Most investors are afraid of risks that could derail their assets from appreciating in the way an unsophisticated animal is afraid of a peacock's plentiful fake eyes. But the real risk is like a Tiger, and we are often ill-equipped to see it. You weren't alone if you've ever wondered why a massive predator requiring stealth to get enough caloric intake to survive is bright orange. Recently, they found out why, as you can see above.
If you're reading Zero Hedge, Hedgeye, and other doomsaying bearish sources for markets, you're basically spending your time looking at peacock feathers, leaving yourself vulnerable to the Tiger, which may be sneaking up behind you. Do not disregard risk; pay attention to the ones that actually have a high probability of occurring.
Prior to human mastery of our environment, we weren't technically at the top of the food chain; the ancestors of Tigers were. They are killing machines that are built to stalk and kill prey. They require large amounts of food and hunting territory to obtain it, but they are hugely efficient in the heat of the kill. It's been observed that they have many failed attempts for every kill, though, just like risks that stalk the market. When it comes down to the actual business of killing, the tiger uses three primary strategies:
Concealment/Ambush
Stalking Prey
Sudden Rush on Targets of Opportunity
The Tiger also has different methodologies for killing animals based on weight. It can kill larger animals by destroying their trachea and attacking from the front. For prey less than half its weight, it will crush its spinal column from behind to lead to nearly instantaneous death. Worry about the risks that will lead to forced liquidation and selling, not the ones that are emotionally upsetting to you. That’s the tiger that causes downside action, not irresponsible political posturing in the Middle East.
Key insights on Benford's Law, as well as the opening example, came from Kit Yates's book How to Expect the Unexpected.
