Regime Effects Are Turnover Effects: Matched Controls for Conditional Portfolio Optimization

A substantial literature reports that conditioning portfolio allocation on an
inferred market regime improves risk-adjusted performance, particularly net of
transaction costs. We show that in a realistic cardinality-constrained setting the
measured effect, at all three points where such a signal can enter, is attributable
to a variable the mechanism was never designed to control: how much the resulting
portfolio trades.

We evaluate 32 arms on CRSP daily data from 2011 to 2024, with 30 matched seeds and
four cost levels, injecting a three-state hidden Markov signal at each point where
it can act on a mean-variance decision: the optimizer's preferences, its covariance
estimate, and its expected returns. Measured conventionally all three work, gaining
+0.113, +0.388 and +0.294 Sharpe at 150 bps. Across 27 comparable arms, net-of-cost
performance is ordered almost perfectly by realized turnover alone (Spearman
rho = -0.95, p = 2.1e-14), while the same correlation gross of costs is
insignificant.

We introduce a control that resolves the confound: an unconditional strategy,
identical in optimizer, constraints and seeds, whose turnover penalty is solved by
bisection to match the treatment's trading. Against it the regime effect is -0.069,
-0.034 and -0.047 Sharpe, negative at every injection point and cost level, the
sign holding in 20-27 of 30 seeds. Reseeding one arm moves Sharpe by 0.233,
exceeding four of five effects measured. The finding survives solving the weighting
sub-problem exactly. We do not establish that regime conditioning cannot work, but
that a turnover-matched control was necessary to find out.