A Mathematical Basis for Believing in Asymmetric Trading Systems
For more than two decades, I've required a mathematical basis to maintain confidence in my decisions, especially during challenging periods inherent in every investment or trading strategy.
Establishing a mathematical basis for a system that determines what to buy, when, how much, and the timing for selling—be it cutting losses, removing laggards, or taking profits—is crucial to avoid outcome bias. Outcome bias refers to judging decisions based on their results rather than the decision's quality at the time it was made.
Most traders and investors focus on finding the “perfect” system—the one that never fails, always wins, and delivers huge returns with little risk.
When they experience a losing position, multiple losses in a row, and a period of mediocre performance, they develop outcome bias and lose faith in their investment strategy.
The reality is no such system exists.
What separates successful investors and traders from the rest isn’t just picking the right strategy but knowing if that strategy is robust before they ever put capital at risk.
A robust asymmetric trading system isn’t one that just works—it’s one that works reliably across different market conditions while maintaining an edge.
The key?
Positive expectation, repeatability, and adaptability.
Positive Expectation: The Core of Robust Trading
A system’s expectancy tells you whether, over a large number of trades, it is likely to make money.
The formula is simple:
Where:
- Pw = Probability of a winning trade
- W = Average win size
- Pl = Probability of a losing trade
- L = Average loss size
If this number is positive, the system is statistically profitable over time.
But here’s the catch: a system with a high win rate but poor risk control can still fail.
A robust system doesn’t just focus on maximizing wins—it structures trades asymmetrically, ensuring downside is capped while upside remains open or exponential.
This principle forms a foundation of asymmetric trading: maintaining a positive expectancy without relying on luck.
Repeatability: One Trade Means Nothing
One winning trade proves nothing. A system’s true value only emerges over hundreds, if not thousands, of trades. This is where the Law of Large Numbers comes in—over time, the edge in a system should become clear.
A robust system should:
- Work across different market environments
- Produce consistent results over a large sample size
- Maintain a positive mathematical expectation even in losing streaks
This is also why traders who over-optimize their system to past data fail—they create a system that fits the past but doesn’t adapt to the future. Robust systems are designed for repeatability, not perfection.
Market Regime Awareness: Context Matters
Markets are non-stationary—meaning what worked yesterday won’t necessarily work tomorrow.
Everything is impermanent; nothing lasts forever.
A system that thrives in one type of market but fails in others isn’t robust—it’s just lucky.
This is where market regime shifts come into play.
A robust system doesn’t blindly apply the same rules in all conditions—it adjusts position sizing, risk exposure, and even strategy selection based on statistical signals of changing volatility, trend, momentum, and portfolio heat.
This adaptability doesn’t mean constantly tweaking the system—it means having rules in place that account for regime shifts and adjusting exposure accordingly.
Risk is Controlled, Not Eliminated
A robust system is not one that avoids risk—it’s one that defines it upfront.
Every position should have predefined risk, whether through:
- Predetermined exits (stop-loss levels)
- Options structures
- Portfolio-level risk limits
Many traders assume that diversification alone makes a system robust.
It doesn’t.
True robustness comes from knowing the total portfolio heat—how much risk is active at any given time.
For example, if we risk 1% per position across 10 positions, we have 10% portfolio heat.
But that doesn’t mean we've allocated only 10% of your capital—it means we've structured trades to ensure total risk exposure stays within predefined limits.
This is why asymmetric trading isn’t just about high payoffs—it’s about structuring risk to maximize compounding efficiency.
Without risk control, compounding breaks down.
Robustness is the Real Edge
While most traders chase performance, the best traders seek robustness.
A system that looks good on paper but lacks adaptability, repeatability, or predefined risk control is just an accident waiting to happen.
If a system is truly robust, it should:
- Have positive expectation
- Be repeatable over time
- Adapt to market regimes
- Control risk at both the position and portfolio level
The mission isn’t just finding a system that works—it’s ensuring it keeps working when the market changes and knowing the difference.
That’s the real edge.
Mike Shell is the founder and Chief Investment Officer of Shell Capital Management, LLC, and the portfolio manager of ASYMMETRY® Managed Portfolios, a separately managed account program with trade execution and custody at Goldman Sachs Custody Solutions. Mike Shell and Shell Capital Management, LLC, a registered investment advisor focused on asymmetric risk-reward and absolute return strategies, and profivides investment advice and portfolio management only to clients with a signed and executed investment management agreement. The observations shared on this website are for general information only and should not be construed as investment advice to buy or sell any security. This information does not suggest in any way that any graph, chart, or formula offered can solely guide an investor as to which securities to buy or sell, or when to buy or sell them. Securities reflected are not intended to represent any client holdings or recommendations made by the firm. In the event any past specific recommendations are referred to inadvertently, a list of all recommendations made by the company within at least the prior one-year period may be furnished upon request. It should not be assumed that recommendations made in the future will be profitable or will equal the performance of the securities on the list. Any opinions expressed may change as subsequent conditions change. Please do not make any investment decisions based on such information, as it is not advice and is subject to change without notice. Investing involves risk, including the potential loss of principal an investor must be willing to bear. Past performance is no guarantee of future results. All information and data are deemed reliable but are not guaranteed and should be independently verified. The presence of this website on the Internet shall in no direct or indirect way raise an implication that Shell Capital Management, LLC is offering to sell or soliciting to sell advisory services to residents of any state in which the firm is not registered as an investment advisor. The views and opinions expressed in ASYMMETRY® Observations and Asymmetric Investment Returns are those of the authors and do not necessarily reflect the position of Shell Capital Management, LLC. The use of this website is subject to its terms and conditions.