How much does the market need to drop for it to be considered a "black swan" event? And if using options for black swan trading, how many put options should one buy? Many believe they are engaging in anti-fragile market trades, but without a clear definition and structure of "extreme" events, they may just be paying a hefty "cognitive tax."

The Golden Ratio of Anti-Fragility: Monthly 5% Allocations to Put Options

In recent years, a "Taleb-style" strategy has gained widespread attention: investing a small portion of capital (e.g., 5% of the principal) each month to purchase deep out-of-the-money (OTM) S&P put options, hoping to achieve substantial returns in a black swan event. However, the practical outcomes are often the opposite: investors may deplete their capital before a market crash, suffer from premature margin calls due to over-leveraging, or be forced to exit during market lows just before a rebound.

The failure of this strategy lies not in the options themselves, but in the lack of a clear definition of what constitutes a "black swan" and the failure to justify whether the "5%" allocation is reasonable in terms of risk control and return potential. Key questions include: Is 1% or 5% of capital better? Which allocation ratio yields the highest efficiency in extreme market conditions? Does an "optimal marginal return point" exist?

Simulation Setup: Black Swan Explosion Profit Model

To isolate market noise, we established the following assumptions for the trading scenario:

Monthly Investment in Put Options: Allocate 1%, 2%, 3%, 5%, and 10% of the principal.

Normal Period Losses: The cost of the options becomes zero each month.

Black Swan Event Trigger: A market decline greater than a preset threshold (e.g., between -5% to -10%) causes a sharp surge in the option value.

Return Multiples Assumption: In the black swan months, the return multiples are assumed to be 20x, 30x, and 50x of the invested principal.

With these assumptions, we can preliminarily calculate the strategy's explosion pattern under different investment allocations.

You might think that the more you invest, the more you'll earn, possibly even opting for purchasing 10% of the principal each month. But the problem lies in the fact that leverage is a double-edged sword. In the real market, black swans don't occur every year; the intervals between explosive returns could stretch to 2 or 3 years, or even longer. During this time, the key challenge for most traders is enduring the prolonged loss periods, which often becomes the breaking point leading them to abandon the strategy.

Frequency of Black Swan Events: Extreme Market Conditions Are Not the Norm

Backtesting the S&P 500 over the past 25 years reveals that the windows where both "black swan" events and volatility surges truly align are few and far between:

2008 Financial Crisis: Meets the criteria.

2010 Flash Crash: Briefly meets the criteria.

2015 RMB Exchange Rate-Driven Correction: Does not meet volatility requirements.

2020 COVID-19 Market Collapse: Meets the criteria.

2022 Russia-Ukraine Conflict: The drop and VIX combination do not align.

2025 Trump Tariffs Fallout: Meets the criteria.

In fact, there are no more than four years in which the combination of "deep market collapse + volatility surge" truly occurred.

The "black swans" in the market may simply be "near-misses." For instance, a slow decline (e.g., -8% spread over two weeks) would cause options to quickly expire worthless; a sharp drop (-5% in one day) without the VIX crossing 50 may fail to trigger enough volatility; while a "false crash" could rebound swiftly due to central bank intervention.

A true black swan trading strategy requires you to first define the trigger conditions. In my view, the conditions for a black swan should be: "SPX daily drop ≥ 5% and VIX exceeding 50." Only under such a combination can you truly align with Taleb's explosion model. Otherwise, you're just betting on small fluctuations and volatility premiums.

Anti-Fragile Strategy: Structural Protection, Not a Gamble

The essence of a fragility-resistant strategy lies not in "buying insurance every day," but in structural protection. Specifically, it involves:

Understanding Market Structure: Identifying high-risk inflection points.

Recognizing Tail Risks: Dynamically assessing the volatility structure, duration curve, and macroeconomic factors.

Dynamic Weighted Allocation: Increasing exposure when signals are imminent, while maintaining low or even no positions during other periods.

Minimizing Costs to Maximize Extreme Returns: Managing drawdowns and maximizing payoffs.

A true fragility-resistant trader is not blindly speculating but combines structural cognition, probability calculation, and disciplined capital management.

To survive in the market over the long term, the question you need to ask is not, "How much can I make if another crash happens?" but rather, "If no crashes occur in the next 3 years, will my strategy still survive?"