Model and input conventions
The hedge-notional ratio equals correlation multiplied by spot-return standard deviation divided by futures-return standard deviation. Multiply that ratio by spot portfolio value and divide by the notional of one futures contract. Positive reported contracts mean a short hedge, while a negative correlation can produce a long hedge. Both standard deviations must refer to matching observation intervals and annualization conventions; futures deviation must be positive.
Worked numerical example
For a 100,000 portfolio, spot deviation of 30%, futures deviation of 25%, correlation 0.80 and contract notional of 10,000, the ratio is 0.96. The fractional optimum is 9.6 contracts short, while the nearest whole count is ten. Modeled residual deviation is 18%, and variance falls by 64%. That is a variance reduction: volatility itself falls by 40%, so the two percentages should not be confused.
Read the scenario table
The table compares several hedge ratios, the optimum and the rounded-contract equivalent. It shows residual deviation and variance relative to the unhedged exposure, making over-hedging visible. A zero correlation produces a zero optimum in this limited variance calculation. Negative correlation reverses the required hedge direction; do not remove that sign merely because hedges are often described informally as short futures.
Where the model stops
The optimization assumes the supplied second moments describe the relevant future window and ignores fees, margin, liquidity and estimation error. Correlation can change during stress. Whole-contract rounding can increase variance relative to the fractional optimum. When spot deviation is zero, a percentage variance reduction has no denominator and is left undefined. This is a return-based notional model, not a hedge ratio built from unmatched raw price changes.