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Engine vs. Journey
Excess Mu is the raw power of the engine. Real Growth is the average speed on the road.
If volatility is high, the engine "screams" but the car doesn't move forward.
Goal: Maximize Growth.
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Crash Test (CVaR)
Volatility is the rocking of the boat. VaR is the normal limit of loss.
CVaR (Tails) is the loss in the worst-case scenario (Real Crisis).
Focus: Tail Protection.
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Cost-Benefit (Sharpe)
How much return do you buy with 1 unit of risk?
The Sortino Ratio is even better: it ignores price surges (good volatility) and only measures downside risk.
Efficiency > Gross Profit.
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The Tide (Beta)
How much does your portfolio follow the herd?
Beta < 1: Your portfolio is a submarine, it feels the surface waves less.
Beta > 1: You are in a sailboat in a storm.
Real Diversification = Low Beta.
Hurst Exponent
Market Memory (Persistence)
H > 0.5: Fractal Trend
H = 0.5: Random (Brownian)
Fat Tails
Real vs. Theoretical Risk
■ Levy (Real): Extreme events are 10x more likely than in ■ Normal.
Multifractal Time
Volume Clock vs. Chronological Time
Market time "accelerates" during crises (high volume) and "stops" in calm periods.