Hedge Ratio Calculator - Beta and Risk Reduction

A hedge ratio expresses the size of a hedge relative to the exposure being protected. A ratio of 0.75 suggests a hedge with three quarters of the exposure's value after adjusting for contract units and prices. A negative ratio indicates that the chosen hedge instrument should be held in the opposite direction implied by a positive relationship. The appropriate implementation also depends on contract multiplier, notional value, currency, duration, and basis risk. The minimum-variance hedge ratio uses correlation and volatility: correlation multiplied by portfolio volatility divided by hedge-market volatility. This is equivalent to covariance divided by market variance. When the market index is the hedge instrument, the same expression is the portfolio's market beta. If portfolio volatility is 15%, market volatility is 12%, and correlation is 0.85, both the estimated beta and hedge ratio are 1.0625. Hedging a $1 million exposure therefore implies about $1.0625 million of market notional before contract rounding. The return inputs support two additional diagnostics. Sharpe ratio is portfolio return minus the risk-free rate, divided by portfolio volatility; it expresses excess return per unit of total volatility. Market risk premium is market return minus the risk-free rate. These inputs do not replace a regression built from a return series. A single average return, volatility, and correlation cannot show instability, nonlinear exposure, or confidence intervals. Under the simplified two-return model, the maximum proportional variance reduction from an optimally scaled hedge is correlation squared. A correlation of 0.85 implies a theoretical 72.25% reduction. This is not a guaranteed loss reduction. Correlations and volatilities change, tail behavior may differ from historical averages, and mismatches in asset, maturity, location, quality, or timing create basis risk. Use consistent return intervals and the same historical window for both volatility measures and correlation. Do not mix daily volatility with annual volatility unless properly annualized; the ratio is scale-consistent only when both use the same convention. Backtest rebalancing costs, margin requirements, liquidity, taxes, and stress scenarios. A statistically optimal hedge can still be unsuitable when the hedge instrument gaps, becomes illiquid, or introduces cash-flow demands.