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Mathematical Mechanics of Percentage Change, Asymmetry & Basis Points
A rigorous mathematical inquiry into percentage metrics, evaluating the non-linear asymmetry of recovery gains, geometric compounding, and basis point (bps) standardization.
Key Quantitative Findings:
- Capital restoration equation: $R_{recovery} = \frac{L}{1 - L}$, where $L$ represents drawdowns. As $L \to 100\%$, required restorative returns accelerate toward infinity.
- Percentage Point (pp): Absolute algebraic arithmetic difference $A\% - B\%$. Moving from $5\%$ to $6\%$ represents an absolute $+1\text{ pp}$ increase, yet reflects $+20\%$ relative growth.
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