Minimum-Variance Cross-Hedges and Equity Index Futures

Summary

The notes explain how to hedge an exposure with a futures contract on a related but different asset. They define the minimum-variance hedge ratio using the correlation and volatility of spot and futures price changes, then use that ratio and contract size to estimate the optimal number of contracts. The notes also describe equity index construction and illustrate how index futures can hedge a diversified stock portfolio.

For portfolio hedging, the document gives a contract-count relationship based on portfolio value and futures value. It discusses using futures to reduce market exposure while retaining a view on stock selection, and adjusting portfolio beta toward a chosen target. A final section outlines stack-and-roll hedging: closing a nearer-dated contract and replacing it with a later one as the hedge horizon extends. The material is a textbook-style conceptual summary, not an empirical test; it does not quantify transaction costs, basis risk, or the practical effects of changing correlations and contract liquidity.

Key ideas

• A cross-hedge uses a futures contract on an asset related to, but different from, the exposure being hedged.
• The minimum-variance hedge ratio depends on the correlation and relative volatility of spot and futures price changes.
• The optimal contract count scales the hedge ratio by exposure size and futures contract size.
• Index futures can reduce a diversified equity portfolio’s market exposure or shift its beta toward a target.
• Stack-and-roll hedging replaces expiring futures with later-dated contracts to extend a hedge.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.