OPTIONS, FUTURES, AND OTHER DERIVATIVES 第五章期货定价一个课后问题，对答案不理解，请教各位大大

5.22 题目The Value Line Index is designed to reflect changes in the value of a portfolio of over 1,600 equally weighted stocks. Prior to March 9, 1988, the change in the index from one day to the next was calculated as the geometric average of the changes in the prices of the stocks underlying the index. In these circumstances, does equation (5.8) correctly relate
the futures price of the index to its cash price? If not, does the equation overstate or understate the futures price?

F=S^e((r-q)T)  公式5.8
F=future price
r=risk free rate
q=dividend yield
T= maturity of the future contract

答案中说
“The change in the value of the portfolio are monitored by an index calculated from the arithmetic average of the prices of the stocks in the portfolio. Since geometirc average is always less than arithmetic average, the equation overstate the futures price.”

我搞不懂为什么future price of the index 会被高估，既然index 的变动是几何平均，小于portfolio的算数平均，那index的价格变动就小于portfolio，根据这个公式 F 价格也应该小于portfolio的价格，应该被低估嘛，怎么会高估？

谢谢各位大大，急求
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