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The relationship between stock index yield and risk-free interest rate and stock index futures price
The spot index of stock index is the subject matter of stock index futures contract, and the pricing of stock index futures must be based on the spot price of stock index and cannot be completely separated from the spot price of stock index. Now let's discuss the pricing of stock index futures.

The stock index represents the spot price of the assets that make up the stock portfolio of the index. Assuming that all stocks in the portfolio do not pay dividends, the holding cost is the risk-free market interest rate (R). Obviously, if investors choose to sell their portfolios in exchange for cash in the bank or buy government bonds, they can get risk-free market returns. This means that the opportunity cost of investors choosing to continue holding the portfolio is equal to the risk-free rate of return.

For a stock portfolio, the investment assets usually pay a certain dividend to the holders. Divide the dividend by the asset price to get the dividend yield.

Usually, when we actually study the financial market data, we will take its logarithm first and then analyze it further. After logarithmic transformation of the above futures pricing formula, we find that the logarithmic spread of stock index futures prices is proportional to the maturity time.