Hedging a Stock Portfolio with Index Futures Using Beta

Summary

The document explains how to estimate an index-futures hedge for a portfolio of stocks under the Capital Asset Pricing Model. For each holding, multiply its market value by its beta to the chosen index, then add those amounts. The resulting exposure estimates how much index value to short to offset the portfolio’s sensitivity to broad market moves, leaving returns more dependent on stock-specific performance.

This is a model-based approximation: it assumes CAPM beta describes each stock’s response to the index, and the hedge targets index risk rather than all portfolio risk. The document gives no empirical test or guidance on estimating beta, updating it, or accounting for changing correlations. Futures also trade in whole contracts, so the desired exposure may need to be rounded, leaving residual market exposure.

Key ideas

• Estimate each stock’s beta to the index chosen for the hedge.
• Multiply each holding’s value by its beta and sum the results to estimate portfolio index exposure.
• Short index futures against the estimated exposure to reduce sensitivity to market moves.
• The hedge leaves stock-specific risk and may be imprecise because futures contracts are indivisible.

Tags

# Hedge ratio with future contract


# Hedge ratio with future contract












I want to buy some stocks and short future contract instead. I wonder whether I can calculate the hedge ratio?

## Answer by Dimitri Vulis (score 0)

https://quant.stackexchange.com/a/53514

Assuming that CAPM works, for each stock $s$ in your portfolio, you need to find this stock's "beta" $\beta_{s,I}$ to the index $I$ (such as the S&P 500 if these are U.S. stocks). Assume that an N% index change causes the price of stock $S$ to change by $\beta_{s,I}×$N%. If the value of each stock position is $V_s$, then an N% index change will cause $\sum_s V_s \beta_{s,I}$ change in the stocks in your portfolio. This is exactly the amount of the index that you need to short in order to obtain a portfolio that will not react to index moves, but whose return would come only from the idiosyncratic changes in your stock prices not caused by the index movement (and you hope that you picked stocks that would outperform the index). In order to short index futures, you will need to round to a whole number of contracts.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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