What is Convexity and Why It Matters for Trend Following
What is Convexity and Why It Matters Convexity explains how small changes in certain environments can lead to disproportionately large outcomes. Introduction Financial markets are anything but predictable. Despite the desire for smooth, steady returns, markets inherently exhibit nonlinearity, unpredictability, and fat-tailed distributions. This reality demands a strategy that embraces uncertainty rather than one that attempts to suppress it. The key to thriving in this environment lies in convexity—a principle that transforms volatility into opportunity through asymmetry, dynamic risk management, and compounding power. What is Convexity? Convexity is the concept that small inputs can lead to disproportionately large outcomes—both positively and negatively. Unlike linear relationships, where returns grow proportionally to risk, convexity introduces a curved dynamic, where favorable volatility accelerates gains while unfavorable volatility applies brakes. Markets themselves exhibit convexity, meaning that traders who attempt to force smooth, linear returns onto an inherently wiggly world are destined for failure. All equity curves ultimately reveal either a convex or concave signature, depending on how they respond to market uncertainty. Convex portfolios (positive skew) embrace asymmetry, keeping losses small while allowing for large, outsized gains. Concave portfolios (negative skew) suppress volatility and attempt to smooth returns but ultimately suffer from large, catastrophic drawdowns. Most traders unknowingly operate within a concave framework, where the illusion of stability comes at the cost of hidden risk. Convexity, on the other hand, transforms the frown of concavity into the smile of opportunity, ensuring that portfolios are positioned to benefit from market dislocations rather than be blindsided by them. Convexity and Skew: The Essential Distinction The hallmark of a convex portfolio is positive skew, while a concave portfolio is characterized by negative skew. Positive Skew (Convexity): Frequent small losses, punctuated by rare but disproportionately large gains. This is seen in trend-following, long-volatility strategies, and asymmetric portfolio structures. Negative Skew (Concavity): Frequent small gains, but with occasional, devastating losses. This is typical of mean-reversion strategies, short-volatility positions, and leveraged martingale models. Because markets are inherently nonlinear and fat-tailed, every strategy will eventually reveal a convex or concave profile. Convex strategies thrive by exploiting uncertainty, while concave strategies eventually collapse under its weight. The Goal of Convexity: Optimizing Compounding Many investors fall into the trap of targeting an optimal average speed in a market environment that is anything but smooth. A prime example is the S&P 500, which has an average return of 8% per year—but this average obscures extreme variability: In some years, returns exceed 20%. In crisis years, losses exceed 30%. Attempting to target the average leads to dangerous missteps: Leverage increases exposure during downturns, compounding losses. Profits are taken prematurely in favorable regimes, capping upside. This is akin to a racecar driver maintaining the same speed on all parts of a winding track. Without the ability to brake on sharp turns and accelerate on straights, the driver will either crash or fail to compete effectively. Why Convexity Wins the Compounding Race Convexity prioritizes risk-adjusted adaptability rather than forcing an artificial smoothness onto a chaotic market. The convex trader slows down when uncertainty rises and accelerates when conditions become favorable, creating an optimal trajectory for long-term compounding. Braking (Risk Mitigation): Avoids devastating losses by cutting risks during adverse regimes. Acceleration (Opportunity Capture): Capitalizes on major market trends and dislocations. Non-Predictive Adaptability: Adjusts dynamically rather than relying on fragile forecasts. Those who embrace convexity understand that attempting to force stability in an unstable world is a losing battle. Instead, they design portfolios that thrive on adaptation, asymmetry, and compounding, ensuring that when opportunity arises, they are positioned not just to participate, but to dominate the market landscape.
Understanding Warehoused Risk and Why Stops are Critical Risk Management Tools for Classic Trend Followers
Understanding Warehoused Risk and Why Stops are Critical Risk Management Tools for Classic Trend Followers This blog explores the concept of warehoused risk and how effective portfolio management can enhance returns while mitigating risk. When trading, we often focus on individual strategies and their performance metrics, such as drawdown (DD) and compound annual growth rate (CAGR). However, the real power of trading lies in managing a portfolio of these strategies. This blog explores the concept of warehoused risk and how effective portfolio management can enhance returns while mitigating risk. Importantly, it demonstrates a curious conservation law in investing: “Risk cannot be eliminated from a portfolio; it can only be transferred within it.” The only way to release risk from a portfolio is by eliminating the risk contribution of an individual return stream by exiting that position. We will demonstrate why stops, though often criticized as inefficient for mitigating risk, are essential at the portfolio level. They provide risk release valves to mitigate current risk and allow the portfolio to absorb new risk in the future. Not having stops in place can detrimentally affect portfolio performance, especially when market conditions arise that have never been seen before in backtests. These new, unforeseen environments can expose the warehoused risk that exists in a portfolio, which may not have been previously observed. Single Strategy vs. Multiple Strategies Consider a single trading strategy on a single market. This strategy might produce a return profile with a 20% drawdown and a 7% CAGR. If we multiply this strategy five times, trading five identical systems on the same market with the same allocation, the drawdown increases to 100%. This happens because the drawdown in each system occurs simultaneously, resulting in a linear relationship between leverage and drawdowns. Multiplying the position size by 5x causes the drawdown to increase fivefold. However, the relationship with CAGR is not linear. While multiplying the strategy 5x might achieve a drawdown of 100%, the corresponding CAGR might only increase to around 30%. This is because CAGR is a path-dependent and nonlinear metric, where increased volatility suppresses compound growth. Now, what happens if we diversify our approach? Suppose we develop 10 different, uniquely configured trend-following (TF) strategies for the same market. Each of these strategies has a 7% CAGR and a 20% drawdown occurring at different points in time. The portfolio of these 10 strategies might then produce a CAGR of 40% but with a drawdown of only 40%. This is because the risks are spread out due to the lack of perfect correlation between the strategies. The drawdowns of each unique strategy do not coincide, and each return stream offers correlation offsets at different points in time across the entire time series. Furthermore, the CAGR is increased as the volatility drag associated with the drawdown of the entire ensemble at 40% is far less than the alternative of 100%. By diversifying, we distribute risk across various strategies, each contributing to the overall performance at different times. This risk spreading, due to the lack of perfect correlation, allows for a more stable and robust portfolio, enhancing returns while managing drawdowns more effectively. The Principle of Warehoused Risk Warehoused risk is a crucial concept in portfolio management. It represents the total risk present in all return streams, calculated as if each return stream went to zero at a specific point in time. By summing the potential risk contributions of each return stream, we arrive at the total risk summation, known as the warehoused risk of that portfolio at a given moment. This theoretical limit adheres to the conservation law that risk can never be eliminated, only transferred within the portfolio. Another term used to describe warehoused risk is “Portfolio Heat.” Many investors overlook this potential risk lurking in their portfolios—the risk of total collapse if all the risk held by a portfolio is suddenly released at once. Think of warehoused risk as akin to a “risk sponge.” The more we diversify and add new return streams to a portfolio, each with the same risk contribution, the more we pack warehoused risk into the portfolio. Despite the presence of warehoused risk, the risk investors typically pay attention to are measures such as the Sharpe ratio, Sortino Ratio, MAR (maximum drawdown), Ulcer Index, and other risk metrics. These measures are always far lower than the warehoused risk that actually resides in a portfolio. They reflect how individual risks within a portfolio offset each other and how risk events are dispersed across the time series of different return streams. However, these metrics often understate the actual risk potential within a portfolio. These risk measures typically assess the volatility of portfolio returns over time, a consequence of how discrete return streams interact. Some risks cancel each other out, resulting in a net portfolio variance measure, such as standard deviation or maximum drawdown, occurring at specific points in time. However, these proxy measures understate the possible risks if a new market regime emerges—one that has never been experienced in backtests and significantly alters these risk metrics, reflecting the higher warehoused risk inherent in the portfolio. Understanding warehoused risk helps investors recognize the potential hidden dangers within their portfolios. By acknowledging this risk and managing it through diversification and strategic use of stops, we can create more resilient portfolios that are better prepared for unexpected market conditions. The Role of Stops in Portfolio Management Trend followers often use stops as a critical tool for managing portfolio risk. Stops should be seen as risk release valves for the entire portfolio, preventing warehoused risk from becoming overwhelming due to any contributing return stream in unfavourable market conditions. While some traders argue that stops detract from performance compared to other exit measures, in portfolio management, stops are crucial for maintaining the positive skew of the entire collection of return streams and managing total portfolio heat. Consider this: in a portfolio comprising potentially thousands of return streams, there is always the possibility that many return streams could suddenly become positively correlated, potentially
