Risk & Uncertainty
Risk & Uncertainty
Most people want clean averages in a world ruled by ugly tails.
Many models assume the world is tidy.
The world is not tidy.
Fat Tails
Markets, pandemics, wealth, war deaths, and company outcomes often do not follow a clean bell curve.
They have fat tails.
In a fat-tailed world, one extreme event can dominate the average.
That makes simple averages dangerous.
The mean from your sample may tell you little about the long-run mean. The law of large numbers may converge too slowly to help you. [1]
Response Matters More Than Event
The event is X.
The consequence is F(X).
F(X) is often what matters.
Fragile systems hate volatility. A glass cup can survive many tiny taps and still shatter from one hard fall. [3]
Antifragile systems benefit from some volatility. Muscles need stress to grow. Options can gain from big moves. [4]
The average input is not enough when the response is non-linear.
Averaging speeds between 10 and 300 km/h does not make the trip safe. The crash at 300 dominates the outcome. [2]
Survival Comes First
In investing, business, and life, you must survive to compound.
A single ruin event ends the game.
Average return is not the right target if the path can kill you.
The order of wins and losses matters. A big loss early can destroy the base that future gains need. [5]
Risk management is not cowardice.
It is protecting the compounding process.
Metrics Can Lie
Standard tools often fail outside clean, thin-tailed domains. [6]
- Standard deviation: Outliers distort it.
- Correlation: Captures linear relationships and misses many real ones.
- P-values: Easy to game and fragile under bad assumptions.
- R-squared: Can look impressive while explaining the wrong thing.
Metrics are not reality.
They are tools with assumptions.
When the assumptions fail, the metric can make you confident and wrong.
Forecasts Need Discipline
Forecasts behave like prices.
If probabilities move wildly for no reason, something is wrong.
In betting markets and option markets, arbitrage punishes inconsistency. [7]
That is useful: a forecast should not only sound plausible. It should be hard to exploit.
The Unseen Can Still Kill You
Past data underestimates tail risk.
That is the Lucretius problem: the biggest thing you have seen is not the biggest thing that can happen. [8]
Absence of evidence is not evidence of absence when the downside is ruin.
For pandemics, ecological collapse, nuclear risk, and financial contagion, the burden should shift.
Do not demand proof of harm after it is too late.
Demand proof of safety before the irreversible bet.
Thoughts
Do not reject models.
Use them carefully.
Models are approximations. The mistake is forgetting that.
Knowing where a model breaks is part of knowing what it says.
References & Further Reading
[1] Concepts like standard deviation or variance become treacherous in fat tails. Policies based on average outcomes invite catastrophic failure because they ignore the rare event's disproportionate impact.
[2] The shape of F(X) matters. Fragility is not mere weakness; it is accelerated harm from volatility.
[3] For fragile concave systems: Average(F(X)) < F(Average(X)). In the driving example: E[F(X)] < F(E[X]).
[4] For antifragile convex systems: Average(F(X)) > F(Average(X)).
[5] The focus shifts from maximizing average gain to maximizing long-term compounded growth through survival.
[6] Metrics are not reality. Understand their assumptions. Visualize. Be skeptical of statistical "significance" without model validity, effect size, and gaming risk.
[7] Dynamic consistency is a useful test for forecast rationality. Treating forecasts as tradable instruments reveals flaws. Mathematical consistency implies the Martingale property.
[8] Use methods such as Extreme Value Theory to extrapolate beyond the observed sample. Apply the Precautionary Principle when uncertainty is high and downside is catastrophic.
Illustrations Referenced Above
- Fat Tails: Pandemic/War tail analysis, Bernoulli Simulation's tail extension, critiques of financial risk models, Mini-Lessons on Fat Tails & LLN.
- Non-Linearity: Fragility/Antifragility lectures, Kelly Criterion (bet sizing), Black-Scholes (gamma convexity), GMO critique (unforeseen system effects), Base Rate Fallacy.
- Survival & Compounding: Kelly/Shannon/Thorp video, Bernoulli Simulation, Drawdowns & Logs, Path Dependence, Bitcoin critique (value hinges on avoiding absorption).
- Flawed Metrics & Illusions: Mini-Lessons on StdDev/Correlation/P-Values/Metrics, IQ Swindle, Twin Studies critique, Psychology Quackery, Genetics Reports.
- Consistency & Arbitrage: Election Pricing, Black-Scholes derivations (no-arbitrage core), Bitcoin valuation arguments.
- The Unseen & Precaution: Hidden Moments, Bernoulli tail extension, GMO/Mao critique, COVID arguments (initial response, vaccine risk profile analysis), Base Rate Fallacy (ignoring prior probabilities).
Thanks to Yi Yao Tan for reading drafts of this.