Sharpe Invariance of Static Hedge Ratios and Regime-Conditional Crude Hedging: Evidence from Indian Refiners

We document a Sharpe-invariance property of static hedging: because hedge-relative savings scale linearly in the hedge ratio, every constant-coverage policy delivers an identical Sharpe ratio of savings, so the choice among static hedges is one of scale, not risk-adjusted quality. Only state-dependent coverage can move that ratio. We exploit this result in a 192-month backtest (2010–2025) of nine hedging policies on Brent crude priced in Indian rupees — the natural exposure of Indian refiners, whose disclosed hedge coverage spans two orders of magnitude with no published rule linking intensity to market conditions. A regime-aligned policy that hedges more heavily in calm regimes raises the savings-Sharpe from 0.092 to 0.114 under a look-ahead-free rolling-quantile classifier, at a shallower peak drawdown than static policies of comparable coverage. A full-sample Markov-switching classifier amplifies the edge to 0.182, but strict walk-forward re-estimation eliminates the amplification, identifying it as a look-ahead artifact: real-time crisis labels necessarily lag the crashes they detect. Bootstrap confidence intervals on the surviving edge straddle zero, and the advantage inverted after 2020, when supply-driven volatility coincided with rising rather than falling prices. We recommend conservatively sized regime-conditional hedging where a classifier can be operated. Q40, G11, G32, C58