# Hedge ratio with future contract [closed]

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

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.