Volatility Drag (variance drain)
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Definition
The gap between the arithmetic average return and the realized compound (geometric) growth rate caused by volatility. Approximately: geometric return ~= arithmetic return - sigma^2 / 2. Higher volatility mechanically erodes compounded wealth even with the same average return.
How to read it
Compounding is multiplicative, so a -50% loss needs a +100% gain to recover: symmetric percentage moves are NOT symmetric in wealth. That asymmetry means volatility itself costs you growth, quantified by the sigma^2/2 term. Two strategies with identical arithmetic means but different volatilities will compound to very different terminal wealth. This is also the mathematical reason over-leveraging (past Kelly) destroys capital: scaling positions by leverage L multiplies the mean by L but the drag by L^2, so beyond the optimum the drag term overwhelms the return.
How practitioners use it
Used as context among multiple indicators — never as a standalone signal to act.
Less common professional uses
Under leverage L, geometric growth g(L) ~= L*mu - L^2*sigma^2/2, a concave parabola maximized at L* = mu/sigma^2 - exactly the Kelly/Merton(log) fraction; beyond L* the L^2 drag term causes growth to FALL and eventually go negative, which is why over-betting is catastrophic rather than merely aggressive. The sigma^2/2 approximation is the second-order (Gaussian) term; with fat tails and jumps the true drag is larger because higher even moments add further negative contributions to log-growth (E[ln(1+r)] pulls down faster than -sigma^2/2 suggests). Vol drag is why REBALANCING a diversified portfolio can add a 'rebalancing premium': lowering portfolio variance raises the geometric mean above the weighted average of component geometric means, even absent any return forecast. Path dependence: two assets with the same start/end price but different volatility deliver different compounded returns to a daily-rebalanced leveraged position - the drag is realized volatility, so it is a cost you pay for the path, not the destination.
Sources & provenance
Fernholz, 'Stochastic Portfolio Theory'; Booth & Fama (1992), 'Diversification Returns and Asset Contributions', Financial Analysts Journal
This page is educational content published by Pachira Aquatica Global LLC. It is not investment advice and not a recommendation.