This procedure is effective in the reduction of risks associated with discrete hedging.
Empirically, one finds that the standard deviation of return on a randomly selected equal-weighted portfolio of common stocks rapidly approaches about one-half the standard deviation of a single stock’s return as the number of stocks held increases. Because of the above result, the return on a similarly constructed portfolio of option hedges will, in the limit, be perfectly correlated with the square of the index return. diversification among. option hedges will reduce the standard deviation of return on the portfolio of option hedges to about one-quarter of the standard deviation of return on a single hedge.