Strategy #0000000047 · Hedging and risk management
Futures hedging and cross-hedging
Estimate a minimum-variance hedge ratio from correlation and volatility, then inspect scenario moves in both legs.
A holder of cash or future physical exposure can reduce price risk with an opposing futures position. The minimum-variance hedge ratio is h*=ρσS/σF; contract count also scales spot and futures notionals. Rate hedges may match DV01/BPV. When the contract is an imperfect proxy, prices desynchronise or correlation falls, the hedge will not eliminate P&L variation.
Minimum-variance sizing depends on historical estimates; an imperfect hedge instrument leaves basis risk.
Three ways in
Understand the story. Then inspect the risk.
Start with a familiar situation, check the payoff, then test how the numbers change.
The idea · in two minutes
How much scenario exposure does a futures hedge remove, and how much basis risk remains?
Jack will sell a physical input later and fears falling prices. Rose enters spot and futures volatilities and their correlation to estimate a minimum-variance ratio.
She then enters spot and futures price-change scenarios and compares hedged with unhedged notional returns. Squared correlation is only a theoretical variance-reduction reference, not a guarantee.
Mismatched contract month, grade, location or delivery timing creates basis risk. Re-estimate with point-in-time data, test hedge effectiveness and plan rolls.
- Assumed spot exposure returnEnter correlation, spot/futures volatility, hedge fraction and both return scenarios to compare unhedged and hedged returns.
- Assumed futures returnDoes not estimate actual contract count or historical hedge effectiveness; assumes fixed volatility/correlation and excludes basis, calendars and margin.
- Residual return after model hedgeIllustrative expiry outcome.
Illustrative research examples only. They are not live signals or a recommendation.
The mechanics · payoff and exposure
h^*=\rho\frac{\sigma_S}{\sigma_F}=\frac{Cov(\Delta S,\Delta F)}{Var(\Delta F)},\quad N^*=h^*\frac{V_S}{V_F}
h* is futures hedge exposure per unit of spot exposure; N* converts that ratio using spot and per-contract futures notionals. Rate hedges can scale by cash DV01 over futures DV01.
Greeks: the directional intuition
- 相關性估計
- Measures sensitivity to implied volatility.
- 口數與期限
- Measures sensitivity to implied volatility.
- 保證金路徑
- Measures sensitivity to implied volatility.
h^*=\rho\frac{\sigma_S}{\sigma_F}=\frac{Cov(\Delta S,\Delta F)}{Var(\Delta F)},\quad N^*=h^*\frac{V_S}{V_F}
Practical context · published observations
Futures hedging and cross-hedging: read the record with its caveats.
The chart uses the published figures or explicitly labelled study inputs below. A historical index or model replay is not the same as an investor’s realised account return.
不估計實際最適口數或歷史避險效果；假設波動和相關性固定，不含基差、交易日曆及保證金。 Source ↗ · Methodology ↗
Change assumptions and inspect the scenario
Inputs illustrate the strategy mechanics; they are not live quotes, forecasts or investment advice.
Variants · same family, different risk levers
Related methods change the mechanism or risk.
Compare their signal, hedge and model assumptions.
| Related strategy | Relationship | What changes | New cost or risk |
|---|---|---|---|
| Cross-hedge | Proxy contract | Uses a correlated futures contract for an exposure without a direct contract. | Correlation and basis can change. |
| DV01 matching | Rate futures | Matches dollar duration rather than face value. | Cheapest-to-deliver, conversion factor and curve risks. |
| Dynamic GARCH ratio | Conditional volatility | Updates hedge ratio as conditional covariance changes. | Model complexity and regime breaks. |
Does not estimate actual contract count or historical hedge effectiveness; assumes fixed volatility/correlation and excludes basis, calendars and margin.
Read beyond the summary
References
Primary sources and research used to describe the strategy and its limits.
- 01CME Group, Hedging with E-mini S&P 500 Futureresearch
- 02Methodology and assumptionsprimary