Definition
Volatility drag (variance drain) is the mathematical phenomenon where higher volatility reduces compound returns even if the average return is the same. The geometric mean approximately equals the arithmetic mean minus half the variance. This explains why reducing portfolio volatility can increase terminal wealth even without improving average returns.
functions Formula
Geometric Mean ≈ Arithmetic Mean − (σ²/2)
lightbulb Example
Two portfolios have 10% arithmetic mean return. Portfolio A has 10% vol: geometric mean ≈ 10% - 0.5% = 9.5%. Portfolio B has 20% vol: geometric mean ≈ 10% - 2.0% = 8.0%. B's higher volatility costs 1.5% per year in compound returns.
verified_user Key Points
- Higher volatility reduces compound returns
- Geometric mean ≈ arithmetic mean − variance/2
- Explains why risk reduction increases terminal wealth
- Critical for understanding leveraged strategies