Suppose that the S&P 500 index currently is at 1,000. A decrease in the index to 975 would represent a drop of 2.5%. With a portfolio beta of .8, you would expect a loss of 2%, or in dollar terms, .02 * $30 million = $600,000. Therefore, the sensitivity of your portfolio value to market movements is $600,000 per 25-point movement in the S&P 500 index.

To hedge this risk, you could sell stock index futures. When your portfolio falls in value along with declines in the broad market, the futures contract will provide an offsetting profit. The sensitivity of a futures contract to market movements is easy to determine. With its contract multiplier of $250, the profit on the S&P 500 futures contract varies by $6,250 for every 25-point swing in the index. Therefore, to hedge your market exposure for 2 months, you could calculate the hedge ratio___ (short).

Calculate the number of hedge contracts