Q.639 Julia Lange, an investment manager, has constructed a portfolio that somewhat mirrors the S&P 500 index. The investment manager intends to hedge the portfolio by taking a short position in S&P 500 futures. The current worth of the portfolio is $672,000,000, and the S&P 500 index futures price is 2,906, with each contract on $250 times the index. If the portfolio's beta is 0.78, then estimate the number of contracts Lange should short to hedge her portfolio.