Geometric Mean vs. Arithmetic Distortions
Arithmetic average returns produce severe upward bias when volatility is present. If a portfolio increases 50% in Year 1 and contracts 50% in Year 2, the arithmetic average is 0%, while real capital is impaired by 25%. CAGR resolves this by computing the true geometric mean rate: \(CAGR = (\frac{V_{final}}{V_{initial}})^{\frac{1}{n}} - 1\).