How Outlier Hunters Exploit Convexity to Achieve Infinite Yield

How Trend Followers Exploit Convexity: The Art of Capturing Outliers In the world of finance, where smooth returns are often seen as the gold standard, trend followers and outlier hunters dare to embrace the chaos of markets. They thrive in uncertainty, leveraging volatility, diversification, and the principles of convexity to turn rare, transformative events into exponential growth. Introduction: Trend Following and Convexity In previous discussions, we explored the fundamental nature of convexity in financial markets (What is Convexity and Why It Matters) and how traditional risk models, such as those in Sharpe World, fail to capture the chaotic, nonlinear dynamics that define real-world markets. Building upon these principles, this article examines how trend followers—those who systematically hunt for market outliers—harness convexity to create resilient, high-potential portfolios. Trend following strategies are designed not to predict, but to react—to identify and capitalize on emerging trends. The key to their success lies in their ability to cut losses short, let profits run, and exploit asymmetry—a hallmark of convexity. While conventional portfolio managers seek smooth, linear returns, trend followers embrace volatility and the fat tails of return distributions, positioning themselves for rare, transformative market moves. Trend Following and Convexity: A Natural Fit Trend following and convexity are inherently aligned. Convexity is about asymmetry, ensuring that small losses are absorbed while massive gains are captured. This is precisely how trend followers operate: Small, controlled losses – A disciplined approach ensures losses are minimized and predefined. Unlimited upside potential – Once a trend is identified, trend followers let winners run, maximizing potential convex payoffs. Diversification – Trend followers operate across multiple, uncorrelated markets, ensuring they are always exposed to potential outlier events. Trend Following vs. Options: Convexity with Limits While trend following is a highly effective convex strategy, unlike options, it does not offer complete protection against all tail events. Short, sharp corrections – Trend-following models, particularly medium and long-term strategies, take time to adjust to new market conditions. When markets experience sudden reversals, trend-following models can get whipsawed, leading to a string of small losses before identifying a new trend direction. Longer-term corrections – When trends persist for an extended period, trend-following fully invests in convexity, riding out trends and maximizing returns from fat-tailed market events. Options provide immediate asymmetry, where downside risk is clearly defined, and upside is theoretically unlimited. Trend following, by contrast, requires active management and model adjustments, leading to some exposure to short-term market noise. Greater diversification potential – Unlike options, which have a relatively restricted set of choices in terms of strikes and expirations, trend-following portfolios typically comprise hundreds of uncorrelated return streams, spreading convexity exposure across a vast range of markets. No insurance cost – Options require a premium to provide tail-risk protection, effectively acting as an insurance cost. Trend following, on the other hand, does not have an equivalent premium cost, making it a cost-efficient way to harness convexity without needing to pay for insurance upfront. How Trend Followers Construct Convex Portfolios Trend followers integrate three key convexity principles into their portfolio construction: 1. Embracing Volatility and Fat Tails Traditional investing penalizes volatility, assuming it equates to risk. As we discussed in The Pitfalls of Sharpe World Thinking, this is a fundamental misunderstanding. Risk is not about historical volatility, but about future unpredictability. Trend following strategies thrive in volatility, recognizing that large price moves drive long-term compounding. The ability to stay in the game through disciplined risk management ensures participation in the fat-tailed events that drive exponential returns. Example: The Cocoa price explosion in 2024—a classic trend-following convexity play where patient traders who endured small losses were rewarded with an outlier move that transformed their portfolio performance. 2. Asymmetry: Small Losses, Big Gains Convexity is about tilting the risk-reward dynamic to one where the potential reward significantly outweighs the risk. Trend followers structure their strategies to capture this asymmetry: Predefined exit points – Losses are cut swiftly to avoid major drawdowns. Trailing stop mechanisms – Profitable trades are held as long as momentum persists. Path dependency is embraced – Unlike Sharpe World models that assume static market behavior, trend following recognizes that future price movements are influenced by prior trends. This approach ensures that a single outlier can offset dozens of small losses, driving long-term compounded wealth. 3. Diversification: Spreading the Convexity Net Wide Unlike options strategies that rely on a specific market outcome, trend following invests heavily in diversification, spreading exposure across multiple assets to capture convexity wherever it appears. Trading across multiple asset classes – Stocks, commodities, currencies, and bonds. Geographic diversification – Ensuring exposure across multiple economies and risk environments. Reducing correlation dependencies – Avoiding over-reliance on any single sector or region. This broad exposure enhances convexity-driven portfolio resilience, allowing for asymmetric return profiles across different market regimes. Trend Following as the Ultimate Convex Strategy In essence, trend following is a convexity-maximization strategy: ✅ Risk is predefined – No single trade can significantly damage the portfolio. ✅ Returns are uncapped – Trend followers allow market forces to dictate how far a trend can run. ✅ Survivability ensures participation – By keeping bet sizes small, trend followers remain in the game long enough to capture market outliers. Key Takeaways: The Convexity Advantage of Trend Following Markets are nonlinear and unpredictable – Trend following doesn’t fight this reality but capitalizes on it. Convexity ensures risk is asymmetric – Small losses are tolerated for the chance to capture extreme payoffs. Diversification amplifies convexity – Exposure to multiple markets increases the chance of catching outliers. Risk management is paramount – Staying in the game is more important than winning every trade. Conclusion: The Power of Convexity in Trend Following Traditional investing tries to smooth returns and eliminate volatility. Trend following embraces uncertainty, harnessing convexity to transform risk into opportunity. By applying convex principles—cutting losses short, letting profits run, maintaining small bets, and diversifying broadly—trend followers have built some of the most resilient and successful trading strategies in history. The path isn’t about predicting what will happen—it’s about positioning

The Pitfalls of “Sharpe World” Thinking: Why It Fails to Capture Convexity

The Pitfalls of “Sharpe World” Thinking “Sharpe World” thinking is inadequate for today’s complex and unpredictable markets. It fails to account for the chaotic, non-linear realities of financial markets. Introduction: The Pitfalls of “Sharpe World” In modern finance, the pursuit of risk-adjusted returns has led to a widespread reliance on measures like the Sharpe ratio, standard deviation, and Value at Risk (VaR). This framework—what David Dredge aptly calls ‘Sharpe World’—has shaped how investors think about risk, yet it is fundamentally flawed. The 2008 financial crisis wiped out nearly $19 trillion in global wealth, yet just months before, risk models showed no indication of an impending collapse. Why? Because they relied on the past to predict the future—ignoring the fundamental reality that the most significant market moves are always unexpected. The regularity of unforeseen market crises that blindside investors is not an anomaly but a direct consequence of this flawed framework. Risk models work until they catastrophically fail, reinforcing a dangerous illusion of control over markets that are inherently unpredictable. The fundamental issue is that risk models tend to measure what has already happened, rather than preparing for what has never occurred before. When the next major crisis arrives, it will not be a variation of past events—it will be something completely different. Refer to the table below that lists some of the most significant financial crashes that blindsided the investment community despite their reliance on traditional risk models. Risk is Not Volatility One of the greatest misconceptions in finance is the belief that risk equates to volatility. This assumption underpins much of Modern Portfolio Theory (MPT), the Efficient Market Hypothesis (EMH), and standard risk management practices. But history has shown us that the most damaging risk events are not the ones we expect, but the ones we don’t see coming. If risk could be forecasted using historical distributions, then risk management would be easy. But every major financial crisis—from Black Monday to the Global Financial Crisis—occurred because the models failed to anticipate the unexpected. As Dredge, describing Nassim Taleb’s insights, puts it: “Understanding is a poor substitute for convexity.” Risk isn’t about predicting the next crisis; it’s about building a portfolio that can survive and exploit uncertainty. The Flawed Assumptions of ‘Sharpe World’ Traditional financial models rest on several assumptions that, while convenient for theoretical frameworks, have repeatedly failed in real-world market conditions. These flawed assumptions create a false sense of security, leading to systemic fragility and underpreparedness for extreme events. Risk can be quantified using historical data. Why it’s flawed: Risk is not static—it evolves dynamically. Using past data assumes that future risks will mirror historical occurrences, but market crises often stem from unprecedented shocks. Models built on past distributions fail to account for the unpredictability of future events. Implication: Investors relying on historical risk metrics are often blindsided when markets deviate from historical norms, leading to severe miscalculations in risk exposure. Markets behave in a linear fashion, following normal distributions. Why it’s flawed: Real-world markets are nonlinear and exhibit fat-tailed distributions, where extreme moves happen more frequently than predicted by normal distributions. Standard financial models underestimate the probability and impact of rare, high-magnitude events. Implication: Risk management strategies based on linearity fail to anticipate market dislocations, exposing portfolios to devastating tail risks. Correlations persist into the future. Why it’s flawed: Correlations are highly unstable and tend to shift dramatically during periods of market stress. Assets that appear uncorrelated in normal times often become highly correlated in crises, negating diversification benefits. Implication: Portfolio designs that assume stable correlations fail when they are needed most, leading to simultaneous losses across supposedly diversified holdings. Expected returns can be estimated with confidence. Why it’s flawed: Markets do not follow predictable patterns, and expected returns fluctuate based on shifting macroeconomic conditions, sentiment, and structural changes. Using historical averages to project future performance ignores the reality of ever-changing market regimes. Implication: Investors who rely on projected returns may over-leverage during favorable periods and under-allocate when opportunity arises, leading to suboptimal compounding over time. All volatility is bad and should be minimized. Why it’s flawed: Not all volatility is detrimental. While downside volatility can be damaging, upside volatility represents opportunity. Attempts to smooth returns by suppressing volatility often reduce exposure to large, outsized gains, capping long-term compounding. Implication: Strategies focused on reducing volatility at all costs often sacrifice convexity, failing to capitalize on beneficial market trends while remaining overly exposed to unseen risks. These incorrect assumptions lead to a fragile approach to risk management—one that attempts to control and predict risk rather than adapt to and exploit it. Markets are inherently nonlinear, unstable, and shaped by extreme events, yet Sharpe World thinking forces investors into models that are precise in theory but dangerously inaccurate in practice. The failure to recognize these flaws leaves investors exposed to sudden shocks and unprepared for the rare but defining market moments that drive long-term performance. The failure to account for fat-tailed events and changing market regimes means that many investment strategies operate without effective brakes. Investors unknowingly rely on historical relationships to contain risk, assuming that what worked in the past will work in the future. But without proper braking mechanisms, these strategies leave investors fully exposed when markets take an unexpected turn. Investment Strategies Without Brakes: A Recipe for Disaster A core problem with many investment strategies is that they lack brakes—mechanisms that prevent catastrophic drawdowns and allow for adaptability in volatile environments. Without brakes, investors are fully exposed to market downturns and rely on historical relationships that may not hold up in the future. Some examples of strategies without brakes include: The 60/40 Portfolio: Relies on historical negative correlation between stocks and bonds to mitigate risk. However, in times of rising inflation or systemic crises, both asset classes can decline simultaneously, removing any perceived protection. Buy and Hold (Long-Only) Portfolio: Has no mechanism for managing downside risk. Investors are fully exposed to extended drawdowns, hoping for a long-term recovery that may take decades. Mean-Reverting Strategies: Assume