The Convexity Edge: Why Embracing Uncertainty is the Key to Long-Term Success
Introduction
At ATS Trading Solutions, we’ve long recognized the power of convexity in trading. While many investors chase smooth, predictable returns, trend followers have historically thrived by embracing uncertainty, volatility, and non-linearity—hallmarks of financial markets.
The inspiration for this article comes from David Dredge of Convex Strategies, whose deep insights on convexity resonate strongly with us. The principles of convexity have been widely explored by tail-risk specialists like Nassim Taleb, Hari Krishnan, and Wayne Himelsein, but their relevance extends far beyond tail-risk hedging. In fact, trend-following has always been a convex strategy at its core, systematically capturing outlier moves while minimizing downside exposure.
This article explores the role of convexity in markets and investing through three key lenses:
- What is Convexity and Why It Matters – Understanding the fundamental concept of convexity and why it is essential for long-term success.
- The Pitfalls of ‘Sharpe World’ Thinking – Why conventional finance often misinterprets risk, leading to fragile strategies.
- How Trend Followers Integrate Convexity – Why trend-following is a natural convex strategy and how it systematically captures outliers.
Markets reward preparation, not prediction. While traditional investors attempt to suppress volatility, convex traders turn risk into opportunity. The question is: Is your portfolio designed to survive and thrive in an unpredictable world?
1.0 What is Convexity and Why It Matters
1.1 What is Convexity?
Financial markets are anything but predictable. Despite the widespread desire for smooth, steady returns, reality is far more complex—markets exhibit nonlinearity, unpredictability, and fat-tailed distributions. Any strategy that attempts to suppress uncertainty rather than embrace it is doomed to failure.
At the heart of thriving in this environment lies convexity—a principle that transforms volatility into opportunity through asymmetry, adaptability, and compounding power.
1.2 Convex vs. Concave Portfolios: The Risk Tradeoff
All trading and investment strategies ultimately reveal either a convex or concave signature, depending on how they respond to market uncertainty.
- Convex Portfolios (Positive Skew):
- Frequent small losses, punctuated by rare but disproportionately large gains.
- Example: Trend-following, long-volatility strategies, and asymmetric portfolio structures.
- Resilient in volatile environments, with the ability to capitalize on fat-tailed events.
- Concave Portfolios (Negative Skew):
- Frequent small gains, but with occasional, devastating losses.
- Example: Mean-reversion strategies, short-volatility positions, and leveraged martingale models.
- Appear stable in normal conditions but suffer catastrophic drawdowns when market regimes shift.
Many investors unknowingly operate within a concave framework, where the illusion of stability is maintained by suppressing volatility. However, this approach often results in hidden risks that trigger large, unexpected drawdowns. Convexity, on the other hand, ensures that traders and investors benefit from uncertainty rather than being harmed by it.
1.3 The Racecar Analogy: Why Convexity is Like Driving
Attempting to generate smooth, linear returns in a chaotic market environment is like a racecar driver maintaining a fixed speed on all sections of a winding track. Without the ability to brake on sharp turns and accelerate on straightaways, the driver will either crash or fail to compete effectively.
Convexity enables traders to adapt—braking when risks rise and accelerating when opportunities emerge. This approach optimizes compounding and ensures survival through unpredictable market cycles.
1.4 How Convexity Optimizes Compounding
Many investors fall into the trap of targeting an optimal average return, failing to recognize that averages obscure extreme variability. For example:
- The S&P 500 may have an average annual return of 8%, but that statistic hides the reality that:
- Some years see returns of +20% or more.
- Crisis years can see drawdowns exceeding -30%.
This misunderstanding leads to dangerous missteps:
- Leverage, often based on backward-looking volatility models, can increase at the worst possible time, amplifying losses rather than mitigating them.
- Profits are frequently taken too early in strong market regimes, capping upside potential and reducing the benefits of compounding.
Convex strategies do not attempt to force stability onto an inherently unstable world. Instead, they adapt dynamically, allowing for:
- Braking (Risk Mitigation): Reducing exposure during adverse market conditions to avoid catastrophic losses.
- Acceleration (Opportunity Capture): Capitalizing on major market trends and dislocations when favorable conditions emerge.
- Non-Predictive Adaptability: Adjusting exposure based on market structure rather than relying on fragile forecasts.
1.5 The Convexity Mindset: Adapting to an Uncertain World
Those who embrace convexity recognize that attempting to suppress volatility is a losing battle. Instead, they design portfolios that leverage asymmetry, adaptation, and compounding, ensuring that when outlier opportunities arise, they are positioned not just to participate—but to thrive.
A convex strategy is not about predicting what will happen—it is about ensuring that whatever happens, the portfolio is positioned to benefit from it.
Convexity is the ultimate edge in financial markets, transforming uncertainty from a source of risk into a powerful driver of long-term success.
2. The Pitfalls of ‘Sharpe World’ Thinking
2.1 The Illusion of Stability
Modern finance is built around the pursuit of risk-adjusted returns, relying on metrics such as the Sharpe ratio, standard deviation, and Value at Risk (VaR) to define risk. This framework, which David Dredge calls ‘Sharpe World,’ assumes that past volatility patterns can predict future market risk. However, history has repeatedly proven otherwise.
The 2008 financial crisis wiped out nearly $19 trillion in global wealth, yet just months before the crash, risk models showed no warning signs. The problem? These models depend on past data to forecast the future, failing to recognize that the most significant market moves are always unexpected.
Markets are inherently nonlinear, chaotic, and shaped by fat-tailed distributions. Yet, traditional risk models attempt to create an illusion of stability, encouraging strategies that work until they catastrophically fail. This flawed approach leads to systemic fragility, leaving investors vulnerable to the very risks they seek to avoid.
2.2 Why Risk is Not Volatility
A fundamental misconception in finance is the belief that risk equals volatility. This assumption underpins Modern Portfolio Theory (MPT), the Efficient Market Hypothesis (EMH), and conventional risk management strategies. However, volatility and risk are not the same:
- Volatility is just movement—both up and down.
- Risk is the potential for permanent capital destruction.
If risk could be forecasted using historical distributions, risk management would be simple. Yet every major financial crisis—Black Monday (1987), the Dot-Com Bubble (2000), the Global Financial Crisis (2008), and the COVID Crash (2020)—occurred because models failed to anticipate the unexpected.
Nassim Taleb summarized this reality best:
“Understanding is a poor substitute for convexity.”
Risk management isn’t about predicting the next crisis—it’s about ensuring that when the crisis arrives, the portfolio is structured to withstand and exploit it.
2.3 The Flawed Assumptions of ‘Sharpe World’
Traditional risk models rest on several assumptions that repeatedly fail in real markets:
- Risk can be quantified using historical data.
- This assumes that past risk patterns will repeat in the future, but markets evolve dynamically.
- Investors relying on historical metrics are often caught off guard by regime shifts.
- Markets behave in a linear fashion, following normal distributions.
- In reality, markets exhibit fat-tailed distributions, where extreme moves happen far more frequently than models predict.
- Risk strategies built on linearity fail to anticipate large, sudden shifts.
- Correlations remain stable over time.
- Correlations often break down in market crises, rendering diversification ineffective when it’s needed most.
- Portfolio strategies built on past correlation assumptions can suffer simultaneous losses across multiple assets.
- Expected returns can be estimated with confidence.
- Markets do not follow predictable return patterns—macroeconomic conditions, sentiment, and structural shifts drive unpredictability.
- Relying on past returns to forecast future performance leads to poor risk allocation and overleveraging in calm periods.
- All volatility is bad and should be minimized.
- Volatility is often viewed as a negative, but upside volatility presents opportunity.
- Strategies that suppress all volatility limit exposure to outlier gains, capping long-term growth.
These flawed assumptions create a fragile investment framework, leading to dangerous overconfidence in models that work well in normal conditions but fail catastrophically when market dynamics shift.
2.4 Investment Strategies Without Brakes: A Recipe for Disaster
Many traditional investment strategies are designed without brakes, leaving investors fully exposed when market conditions deteriorate. These strategies assume that historical relationships will persist indefinitely—a dangerous bet in an unpredictable world.
Some common fragile strategies include:
- The 60/40 Portfolio:
- Assumes stocks and bonds are negatively correlated.
- Fails when both decline together, such as during inflationary shocks or systemic crises.
- Buy and Hold (Long-Only) Portfolio:
- Provides no downside risk management.
- Exposes investors to deep drawdowns that may take decades to recover from.
- Mean-Reverting Strategies:
- Assume that prices always revert to equilibrium.
- Fail when market regimes shift, leading to sustained losses.
- Trend-Following Without Stop Losses:
- Assumes trends will always correct back into profitability.
- Can suffer prolonged adverse moves that erode capital before a new trend emerges.
Without built-in risk brakes, these strategies leave investors exposed when market conditions change rapidly.
2.5 Why Brakes Are Necessary: The Role of Asymmetry
A strategy that lacks brakes assumes that losses will eventually recover. However, prolonged drawdowns can:
- Erase years of gains in a matter of weeks.
- Impair future compounding.
- Force investors into emotional, reactive decision-making.
Convexity-based strategies solve this problem by embedding asymmetry into portfolio construction:
- Stops and small bet sizes prevent catastrophic losses.
- Convex portfolios ensure that small losses are absorbed while outsized gains drive compounding.
The math is simple:
- A portfolio that loses 50% requires a 100% gain just to break even.
- A portfolio that caps losses at 2% per trade preserves capital, ensuring that a single large outlier gain can offset multiple small losses.
Brakes are not about short-term optimization—they are a long-term survival mechanism that prevents ruin while allowing participation in the biggest market moves.
2.6 Risk is a Possibility Distribution, Not a Probability Distribution
David Dredge highlights a key distinction: risk is not a probability distribution—it is a possibility distribution.
Traditional risk models assume that extreme events have a fixed probability based on historical data. However, convex strategies ask a different question:
“What happens if an extreme event occurs, regardless of its assigned probability?”
Traditional models assume that:
- If a crash has a 1% probability, it is unlikely to happen.
- If markets have been stable for a long time, risk is low.
Convex risk management instead assumes that:
- Market shocks will happen—it’s a matter of when, not if.
- The longer stability lasts, the greater the eventual instability.
The key takeaway: Risk is not about what we think will happen—it’s about being prepared for what blindsides us.
2.7 Escaping ‘Sharpe World’: Embracing Convexity
The failure of traditional risk models leaves only one solution: convexity. A convex portfolio does not attempt to predict or suppress risk; instead, it ensures that when risk emerges, the portfolio is structured to benefit rather than suffer.
A convex portfolio:
- Mitigates adverse volatility by adjusting exposure dynamically.
- Exploits beneficial volatility by allowing winners to run.
- Positions itself on the right side of the return distribution to optimize compounding.
- Builds in asymmetry to turn uncertainty into opportunity.
Key Takeaways from Sharpe World’s Pitfalls
- Traditional finance underestimates tail risks and over-relies on past data.
- Volatility is not risk—risk is the potential for capital destruction.
- Investment strategies need brakes to avoid catastrophic drawdowns.
- Convexity provides the solution—small losses, unlimited upside.
In the next section, we’ll explore how trend followers systematically integrate convexity into their process, making them one of the most resilient and adaptive investment strategies available.
3. How Trend Followers Integrate Convexity
3.1 Trend Following as a Convex Strategy
Trend following is naturally a convex strategy, systematically designed to capture large, asymmetric gains while keeping losses small. Unlike traditional investors who attempt to suppress volatility, trend followers embrace uncertainty, knowing that markets are driven by fat-tailed distributions and nonlinearity.
Instead of attempting to predict future price movements, trend-following strategies operate based on three fundamental principles:
- Cutting losses short – Managing risk by keeping individual losses small.
- Letting profits run – Holding onto winning trades for as long as trends persist.
- Exploiting asymmetry – Structuring portfolios to ensure that occasional large gains outweigh cumulative small losses.
This approach ensures that trend-following portfolios maintain positive skew, where the impact of winning trades far exceeds that of losing trades over time.
3.2 Why Trend Following and Convexity Are a Natural Fit
Convexity is about structuring a portfolio so that risk exposure is asymmetric—small losses are tolerable, while rare, large moves generate substantial gains. This is precisely how trend-following strategies operate.
Unlike conventional investment approaches that attempt to smooth returns and minimize volatility, trend following is designed to capitalize on price movements in any direction. Because markets tend to move in persistent trends, trend-following strategies thrive by exploiting these sustained market moves that other strategies fail to capture.
Trend following succeeds because it:
- Responds to price rather than attempting to forecast it.
- Positions portfolios to capture major market shifts.
- Uses systematic risk management to avoid catastrophic losses.
Unlike traditional investing, which often depends on economic forecasts, valuation models, and predictive analytics, trend following remains agnostic to fundamental analysis. It operates on the principle that price contains all necessary market information.
3.3 Trend Following vs. Options: Two Paths to Convexity
While trend following is a highly effective convex strategy, it differs from options-based convexity, such as long-volatility or tail-risk hedging approaches.
Key distinctions between trend following and options-based convexity include:
- Cost of Implementation: Trend following requires no upfront cost, whereas options require an ongoing premium.
- Time Sensitivity: Options provide immediate convexity but are limited by expiration dates, while trend following requires time for trends to develop.
- Diversification Potential: Trend-following portfolios often span multiple asset classes, whereas options strategies may be more targeted.
- Risk Exposure: Options offer defined asymmetric payoffs, while trend-following requires dynamic position adjustments.
While options strategies provide direct exposure to convex payoffs, they come at a cost—the option premium. Trend following, on the other hand, offers convexity without paying an explicit premium, making it a cost-efficient way to gain exposure to large market moves.
However, trend following demands patience and discipline, as short-term noise can result in small losses before a profitable trend emerges.
3.4 How Trend Followers Construct Convex Portfolios
Trend-following portfolios are designed to maximize convexity through three core principles:
1. Embracing Volatility and Fat-Tailed Distributions
- Traditional investors seek to minimize volatility, whereas trend followers recognize that large price movements drive long-term performance.
- Financial markets do not exhibit normal distributions—returns are often driven by rare but significant price moves.
- Trend followers ensure they are positioned to capture these large, unexpected moves when they occur.
Example: The Cocoa price rally in 2024, where patient trend-followers were rewarded with an explosive price move after enduring a series of small losses in prior months.
2. Asymmetry: Small Losses, Large Gains
Convexity is about structuring trades so that the risk-reward dynamic is favorable. Trend-following strategies achieve this by:
- Predefining exit points to ensure losses remain controlled.
- Using trailing stops to lock in profits when trends extend.
- Allowing price trends to dictate trade duration, rather than exiting prematurely based on arbitrary targets.
Unlike traditional models that assume risk and return are stable, trend-following recognizes that market dynamics evolve over time, requiring adaptive risk management.
3. Diversification: Expanding Convex Exposure
Trend-following strategies do not rely on a single market or sector for returns. Instead, they operate across multiple asset classes and geographies, ensuring broad exposure to potential outlier events.
- Multi-Asset Approach: Trading in stocks, commodities, currencies, and bonds.
- Global Exposure: Participation in diverse markets across different economies.
- Non-Reliance on Correlations: Unlike traditional portfolio allocation, trend following does not assume that past correlations will hold in the future.
Because trends emerge unpredictably, broad diversification ensures that when an extreme market move occurs, the portfolio is already positioned to capture it.
3.5 The Convex Edge: Why Trend Following Thrives
Trend-following strategies maximize convexity by focusing on three critical aspects:
- Risk is predefined. Individual trades have controlled downside, preventing catastrophic drawdowns.
- Returns are uncapped. Unlike mean-reverting strategies, trend-following allows successful trades to remain open as long as the trend continues.
- Survivability ensures participation. Because trend followers manage risk conservatively, they remain in the market long enough to benefit from outliers.
3.51 Key Takeaways: The Convexity Advantage of Trend Following
- Markets are nonlinear and unpredictable—trend following does not resist this reality but capitalizes on it.
- Convexity ensures risk is asymmetric—trend following limits downside while exposing portfolios to unlimited upside.
- Diversification amplifies convexity—trend-following strategies operate across multiple markets, increasing the chance of capturing significant price moves.
- Risk management is essential—the goal is not to win every trade, but to ensure survival long enough to capture outliers.
The Power of Convexity in Trend Following
The markets will continue to reward those who embrace convexity and punish those clinging to outdated risk models. The question isn’t whether convexity works—it’s whether your portfolio is structured to capture it. Are you merely surviving, or are you positioning yourself to thrive?
Traditional investing aims to smooth returns and reduce volatility. But as history has repeatedly demonstrated, volatility is not the enemy—fragility is.
Trend-following strategies succeed by systematically harnessing convexity through:
- Cutting losses short to ensure no single trade can significantly impact the portfolio.
- Letting profits run to maximize the potential of large trends.
- Maintaining broad market exposure to increase the likelihood of capturing significant moves.
By applying these principles, trend followers have built some of the most resilient and successful trading strategies in history.
The real question is: Are you structured for survival, or are you positioned to thrive?
“In a world that rewards those who adapt and punishes those who resist change, convexity is not just an advantage—it’s a necessity.”