top of page
  • Writer's pictureNathan Black

Volatility and Flowing with Change

Objective: Starting from first principles of uncertainty, why one should invest with a long volatility profile amid increasing systemic turbulence.


- Volatility is the difference between expectation and reality. It emerges from polarization. - More global interconnection → more non-linear relationships → more systemic risk and uncertainty → more volatility. - Volatility is a source of harm or benefit, it’s up to you. Long volatility is antifragile — a positive relationship to uncertainty and turbulence. - Bad decisions feed on a distracted mind, emotional reactivity, and groupthink. Good decisions emerge from presence, convexity bias, and error correction. - Welcome and flow with uncertainty and change.

Volatility is change. Change in markets comes from inherent dislocations in the feedback loop among market participants: expectation → action → reality → error correction.

Volatility emerges and evolves as a function of the disconnect between expectation and reality. It’s a natural byproduct of the need to decide and take action in the present, shaped by speculation and expectation about the future. This disconnect grows with the market’s susceptibility to emotional contagion and other herd behavior, which gets amplified with increasing interconnectedness. We’ll explore these mechanisms and their consequences in this essay.

Markets price volatility according to the aggregate perception of future uncertainty, which often gets encoded as implied volatility. Volatility can be traded directly and indirectly, with various linear and non-linear instruments such as options, VIX, and volatility/variance swaps. This enables specific exposure to change itself. It also allows us to inquire deeper into the dynamics of how uncertainty is measured and priced. Is the market too certain or uncertain? How do we think through these definitions and relationships from first principles?

Econometric models often ignore first principles thinking and empiricism. The (still) widely popular Modern Portfolio Theory is based on the erroneous assumption that market changes are independent and normally distributed. We must rethink volatility from first principles. In reality, markets are fat-tailed, fractal, and turbulent. Additional chaos emerges from our hyper-connected world, but it presents a unique opportunity for volatility traders seeking to flow with change, rather than fight it.

Turbulence: characterized by chaotic change

Despite observing turbulent behavior in many complex systems with chaotic inflows and outflows, from weather patterns to ant colonies to the behavior of markets, turbulence is a poorly understood phenomenon. The field is in its infancy, and the fundamental equations that describe turbulence are still unproven. There’s a $1M prize to the first person who can solve the Navier-Stokes equations describing how fluids flow. And that pales in comparison to how consequential understanding this phenomenon would be on our basic comprehension of the behavior of dynamic systems (just about everything).

The good news is even the most chaotic systems can have elements of local order, such as eddies in turbulent flow. It might seem counterintuitive, but local order can appear among macro disorder. Local order in volatility is a fascinating area of research. Much of investing ultimately boils down to the search for local order among the chaos of markets without fooling yourself into seeing false patterns.

Eddies: order in chaos

Yesterday’s isolated risk is today’s systemic risk

Market turbulence and volatility increase as a function of how quickly emotion spreads through the network of participants. Markets are now global and online. Participants have 24/7 access to news and social media. Our “contagion coefficient” is higher than it’s ever been, meaning emotion spreads very quickly.

Our brains evolved in a linear, local world. This is why we get into trouble when dealing with modern emergent non-linear relationships. It’s a type of change that our brains aren’t equipped to intuitively understand.

This predisposition fear as the dominant emotion present in markets causes an explosion of second order effects. Yesterday’s isolated risk can now spread and reverberate throughout the entire network in a flash. Linear relationships are now non-linear (risks can spread exponentially in interconnected networks). This fattens the tails of probability distributions of financial returns, which are nowhere near “normally” distributed.

As the world is full by these fat tailed processes, linear extrapolation goes out the window, and our ability to predict the future drastically diminishes. Recognizing this fundamental limitation means humbly acknowledging and accepting our shrinking window into how the future will unfold. We must let go of our attachment to certainty and start reasoning from uncertainty.

Surprisingly, it’s contrarian to properly address the non-linearities and fat tails present in market relationships. In traditional markets, the short volatility (fragile) position via VIX futures is near record highs.

Source: Bloomberg

And there’s the continued default use of non-robust statistical techniques such as mean-variance, standard deviation, correlation, Sharpe ratio, CAPM, GARCH, Black-Scholes, etc. The idea that a process has a central “tendency,” quantifiable as “mean,” starts to lose applicability as the system gets too dynamic and non-linear for relationships and observations to converge. Central tendency requires convergence in observations over time. As market turbulence increases, many statistical models on which behavior and confidence are based start to break (if they ever even worked in the first place).

This breakdown in model reliability feeds uncertainty and fear, which feeds volatility, and this feedback loop is what makes volatility a growing and shrinking animal all by itself. It is this recursive self-affinity that makes volatility fractal. This lays the foundation for why one should be interested in one’s relationship to volatility and uncertainty.

Volatility — friend or enemy? Your choice.

Volatility in markets can either harm you or help you — but it’s up to you to decide your relationship to it. It’s both an empowering, but quite under-explored dimension of markets.

Traditionally, volatility is thought to be synonymous with risk. This perception stems from fearing the unknown, rather than not fighting it, or perhaps embracing it. Whether volatility is an asset or liability to you depends on your portfolio’s relationship to it. It is therefore of utmost importance to be mindful of how your asset allocations, and the financial instruments themselves, react to market uncertainty/turbulence. Volatility and tail risk only harm you if you’re unprepared.

Volatility — natural, cyclic dislocations between expectation and reality. (Image: A Luna Blue/

Being prepared for volatility means investing with a long volatility focus. Having a long volatility focus means betting on change, regardless of the direction of price movement.

This simplifies everything by removing a major source of the unknown — direction, and treating turbulence itself as an asset (antifragile). It’s a removal of noise to see reality clearer.

Clarity doesn’t only come from the direct sharpening of what you’re focusing on. Sometimes it emerges from removal of noise.

Volatility is part of the source code of markets. It’s what you get when you strip away story-telling and directional predictions. Needing to be right about one fewer variable means it’s simpler to model, forecast change alone, compared to needing to be right about both change and direction of change. There’s still plenty of noise and difficulty involved, but neutralizing sources of uncertainty is a perpetual goal of students of markets.

Volatility is the market’s pulse. Studying volatility reveals more nuanced and actionable information than what the majority of traders and fund managers turn to: price-derived lagging indicators or narrative-derived predictions that can sound intelligent and emotionally appealing, but ultimately demand faith in manager’s predictive ability, which is a game with a negative expected return.

It’s the difference between thinking you can predict an increasingly uncertain future versus observing the waves directly and surfing when turbulence presents itself. This is why we focus on volatility and learn to surf.

Volatility emerges from polarization. Exhibit A: Bitcoin

Let’s take a look at the financial wild west: the Bitcoin market. I love it because of its wildness.

I believe in the inevitability of money’s evolution towards an internet-native, global, peer-to-peer protocol. Like any information network conceived of and implemented pre-internet, money will get eaten by software. The threat that Bitcoin and other cryptocurrencies present to traditional centralized power structures is quite polarizing. Some strongly believe it’s fake and worth nothing, while others insist it’s the future network of global value exchange.

It’s fashionable to comment on how volatile Bitcoin is as if it’s an intrinsic property of Bitcoin itself. It’s not. It’s simply the manifestation of our own polarization. Volatility can’t exist without polarization. It’s from this polarity of opinion and subsequent expression of it in markets that volatility emerges.

Vol spikes and price direction indifference: Nov‘18 vol spike reflects a 50% meltdown, Apr’19 vol spike reflects a 20% meltup

April 1st saw the 5th largest single day spike in volatility on record

Volatility was at yearly lows before the April melt up

Methodological robustness note: due to the fat-tailedness of Bitcoin’s returns distribution, there is no defined mean from which observations can deviate. This is because large price swings are so frequent and impactful that there is no stable (convergent over time) statistical mean. It’s thus inappropriate to use statistical dispersion calculations that rely on defined means and normally distributed data, such as standard deviation, variance, correlation, etc. We use the robust Median Absolute Deviation method to quantify and interpret market volatility.

“Relationship to volatility” is higher order classification than “asset class”

It’s much simpler to categorize assets by return function rather than the often arbitrary, crude, or irrelevant boundaries of traditional asset class definitions.

Studying historical returns alone of active managers shows they generally fall in one of two profiles: they either exhibit slow, steady growth punctuated by periods of extreme harm (concave, short vol, i.e. banks), or the opposite, neutral or slow decay punctuated by periods of extreme growth (convex, long vol, i.e. top Venture Capital firms).

Chris Cole from Artemis Capital is outspoken on this issue and his writings have helped me crystalize this point in my own head.

“Fund managers should be classified by the nature of their returns rather than their underlying assets. I find it puzzling how institutions are focused on countless asset buckets, such as fixed income, equity value, or macro, but ignore the fact that active manager returns largely fall into two simple categories: (1) short volatility bias or (2) long volatility bias.” - Chris Cole in Volatility: The Market Price of Uncertainty

Nassim Taleb argues for this same distinction in Antifragile, saying that what matters is your payoff function, and refers to these two responses to volatility as fragility and antifragility. It’s the response that counts, not the thing itself.

“Antifragile explains why understanding x is different from f(x) — the payoff or exposure from x. Most of the harm/gains come from f(x) being convex or concave, not from understanding x.” - Nassim Taleb

Since returns can be broken down into these two profiles, we can radically simplify asset bucketing and categorize according to relationship to volatility. It’s refreshingly simple. At the end of the day, everyone is a volatility trader.

Risk-Aware Framework

Volatility is the final boss. Just as what harms you jumping off a cliff is the impact with the ground, what harms traders and portfolios is the impact of volatility. If more market volatility/uncertainty/randomness causes more harm to your portfolio, you are short volatility, whether you know it or not. If it benefits your portfolio, you are long volatility and antifragile. The first step to being more risk-aware is identifying your relationship to volatility. As a heuristic, if you’re in turbulent waters, you don’t want to be short turbulence.

Risk is a very misunderstood concept, but a deceptively simple heuristic works the best — risk is anything that can cause you harm. In markets, harm is the market moving adversely to your position.

I don’t often use the phrase “risk-management” because it implies that risk is a thing that’s quantifiable and manageable. This is fine so long as sources of risk are well defined, well measured, well identified, and live in a linear domain. This is true for some risk (known unknowns), but unfortunately, the financial landscape is plagued with frequent mis-defining, mis-measuring, and mis-identification of risk.

Black swan risk hides in the unknown unknown realm. You can’t predict it but can only hedge against it. This is an important subtlety. When it comes to the behavior of markets, there’s just much more we don’t know than we do know. This calls for humility, ego minimization, and effective tail risk hedging.

Risk awareness is mindfulness of what harms you, regardless of your ability to predict it, and dynamically hedging against it according to your market exposure and relationship to volatility.

The brilliant Benoit Mandelbrot has given us decades of incredible work on fat tails in finance, fractal geometry, and the behavior of turbulent systems broadly that directly apply to risk. He defines 7 states of randomness ranging from mild to wild. Humans have a hard time reasoning about wild systems, but some simple, effective heuristics emerge when thinking about one’s relationship to volatility. The main idea is to have convex exposure to volatility and hedge unknown unknowns (tail risk).

Risk “Management” is Error Correction

Oxford physicist David Deutsch is “interested in anything fundamental.” He’s a pioneer in the field of quantum computation, having developed one of the world’s first quantum error correction algorithms.

A theme of his fascinating work is that everything seemingly boils down to an interaction between information, knowledge, computation, and error correction. Computation is the transformation of information according to certain knowledge, and error correction is the feedback mechanism that’s essential for sustained growth and improvement via iteration or replication. These are fundamental elements of both evolution and his Constructor Theory of Information.

How might this conjecture inform a quantitative trader? Market data is information, how we act on that results from our knowledge, and risk management is error correction. Error correction is key to good decision making and should be built into any holistic learning methodology. It provides a feedback loop that updates our decision-making process with new knowledge attained via analyzing and integrating results from iteration. Rapid, iterative error correction is also the fundamental mechanism that enables machine learning (backpropagation).

Because reality is the ultimate benchmark, error correction is only possible with skin in the game. Error is part of the game, and it’s the best teacher. This is why it's crucial to study losing trades with as much curiosity as winning ones.

The Importance of Mindset, Process, and Convex Habits

Core impediments to being a good trader are a distracted mind, high emotional reactivity, and poor error correction. These are major performance hinderances in any competitive arena that rewards decision-making quality under uncertainty. Naturally, success comes down to mindset and process.

High ambient levels of cognitive distraction and emotional reactivity are positively correlated, as it’s easier for a more distracted mind to get swept up into consensus narratives and group emotion. Low/mild emotional volatility and high agency over one’s attention is necessary to survive and thrive in a highly volatile external world.

Confirmation bias, groupthink, and emotional reactivity are common biases and patterns of herd behavior that the small group of profitable traders seeks to exploit in less experienced traders uninitiated by volatility. If you aren’t ready for financial uncertainty when it shows up, it typically means you lose money.

Instead of being punished for sloppiness, the flip side is being rewarded for clarity and methodology. With skin in the game and the right mindset, markets can positively reinforce clear thinking, bias reduction, and quick error correction. This is why I enjoy systematic and quantitative trading with an emphasis on level-headedness, emotional non-attachment, methodological discipline, and process improvement via iteration.

There’s a class of personal habits and meta-skills that give us compound benefits by inducing positive feedback loops in multiple, connected areas of life. In general, they are health-related habits that promote mental clarity and decision-making quality, such as meditation, exercise, and good sleep. I think of them as convex habits, as they give you a return profile of non-linear gain from a linear investment in time.

It’s important to audit one’s habit portfolio from time to time and adjust as necessary in the direction of added convexity.


The growing global interconnectedness of our species amplifies both the good and the bad, the beautiful and the ugly, the beneficial and the harmful. To be around to enjoy the upside, we must adjust to the associated growing systemic risk.

The chain reaction that amplifies systemic risk is:

Increased interconnection → increased contagion → increased non-linearities → increased volatility/turbulence/unpredictability/fear

The case for long volatility is a case for simplicity. You don’t need to rely on being right about complicated, nice-sounding predictions, nor about the exact cause of specific future change, just on that the future is going to look different from the present. The key is to have a disciplined process, patience in your execution, and convex exposure to change.

The one thing that won’t change is group emotion, and emotions are getting amplified.

Our ability to predict the future is decreasing. Instead of seeing how long we can last in the delusional state of believing we can understand an increasingly non-linear world using the same models and tricks of yesterday, we should recognize the game has changed and treat non-linear systems with respect and humility. This means letting go of many status quo-derived assumptions about the behavior of markets, such as the efficient market hypothesis and the normal distribution, and it means humbly embracing uncertainty and turbulence.

A big thanks to Raghav Gulati for his feedback and error correction in the presentation of these ideas :)


bottom of page