A fund manager manages a portfolio of mid-cap stocks. She

A fund manager manages a portfolio of mid-cap stocks. She anticipates receiving $30 million in cash four months from today to be invested in the portfolio in a manner that maintains the current relative proportions invested in each stock. The portfolio’s return is highly correlated with the S&P MidCap 400 index; the portfolio has a beta of 0.75 with this index. The S&P MidCap 400 index futures contract has an index multiplier of $500. The manager plans to hedge her purchase with December futures. The current futures price for the December contract is 1,340. If the manager wants to hedge her future purchase of stocks in November, what is the optimum number of December contracts to use?