Index futures are widely used to hedge a well diversified portfolio. Recall
that the CAPM states that for a well diversified portfolio --where
,
It is clear that by shorting
contracts, the beta of the
portfolio becomes zero. Then the volatility of the portfolio is zero and of
course the value of the portfolio will grow at the risk free rate.
contracts.
.
The differences in the above example occur because we have ignored the distinction between continuously and discretely compounding returns, and we did not take into account the daily settlements --tailing the hedge. Nevertheless, the return of the hedge is roughly equal to the risk free rate of return.