Example: an institution promised in April 15 that it would receive 3 million yuan in June 10. The institutions value three stocks, A, B and C, and the current prices are 20, 25 and 50 yuan respectively. If you have funds now, you can buy 50,000 shares, 40,000 shares and 20,000 shares for each stock, with an investment of 6,543.8+0,000 yuan. As the market is now in a bull market, they are worried that when the funds arrive, the stock price will have risen and they will not be able to buy so many shares. So lock in the cost by buying stock index futures contracts. Suppose the corresponding futures index due in June is 1500 points, and the multiplier of each point is 300 yuan. The β coefficients of the three stocks are 1.5, 1.3 and 0.8 respectively. They must first calculate how many futures contracts they should buy.

The beta coefficients of the three stock portfolios are1.5×1/3+1.3×1/3+0.8×1/3 =1.2.

Number of futures contracts bought = [3 million yuan /( 1500×300 yuan) ]× 1.2 = 8.