Inertia or Reversal? Cost-Aware Optimization of Growth–Value Rotation with Exchange-Traded Funds

We examine growth–value rotation across seven ETF triplets using completed signals, next-open execution, matched benchmark dates, and self-financing costs. A Gaussian autoregressive model shows that negative persistence produces more switching than positive persistence of equal magnitude, and a reduced Bellman calculation retains that sign. The model’s implied gains and break-even costs track the realized cross-market results (correlations of 0.84–0.86), explaining why the evidence concentrates in the Russell 1000 and Russell 2000, and its no-trade band raises the Sharpe ratio of every daily rule. At a one-way cost of 2 basis points, monthly inertia earns 12.47% annually versus 10.39% for the Russell 1000 benchmark and 11.74% versus 9.56% for the Russell 2000, with Sharpe ratios of 0.62 versus 0.53 and 0.51 versus 0.43. The advantage survives volatility-dependent cost schedules, but its information ratio implies that decades of data are needed to confirm it. Family-level SPA tests yield p=0.055 and p=0.022; neither survives adjustment across triplets, although a pooled test of the six US overlays gives p=0.027. No monthly strategy has a significant six-factor intercept, and the active overlay is nearly orthogonal to the factors. The evidence supports a conditional historical timing benefit for slow rotation, not optimal timing or factor-unexplained alpha.