Reverse Rebalancing and the Volatility Tax: Why Chasing Winners Loses to 1/n Equal-Weight Rebalancing

In a non-ergodic investment world, long-run outcomes are governed by time-compounded log growth rather than one-shot expected returns. This technical note starts from a deliberately strict axiom: short-horizon returns are not forecastable (a no-forecast stance). Under this axiom, the key decision is not “what to predict,” but “how to update portfolio weights after prices move.” We parameterize weight-updating rules by a single feedback exponent β, spanning constant-weight (equal-weight) discipline, buy-and-hold drift, and procyclical “reverse rebalancing” (chasing recent winners and selling recent losers). Using a discrete-time log-wealth identity, we decompose relative log growth into (i) an exposure/drift component, (ii) a concavity (Jensen/AM–GM) component generated by contrarian rebalancing, and (iii) costs and implementation frictions (turnover, convex market impact, taxes, and non-tradability constraints). Reverse rebalancing forfeits the concavity component and can be interpreted as paying a “volatility tax” for convex behavior, even when no forecasting edge exists. The note also provides a reproducible empirical roadmap for decomposing realized EW–CW performance (e.g., RSP–SPY; CSI 500 equal-weight vs cap-weight) into exposure, concavity, and cost components, and summarizes high-quality evidence on the robustness of naive 1/N (1/n) rules. In particular, out-of-sample portfolio optimization can be dominated by estimation error (DeMiguel, Garlappi, and Uppal, 2009), and a large share of the equal-weight premium is attributable to rebalancing itself rather than size tilt (Plyakha, Uppal, and Vilkov, 2012). The overall message is pedagogical but operational: for ordinary investors, disciplined rules can constitute a practical form of “alpha” by systematically avoiding self-inflicted convexity losses.