If we add one to the return, then you've got a number that's never negative and we can then use geometric returns.

然后加上1,你永远也得不到一个负数,然后我们对这个值求几何平均

耶鲁公开课 - 金融市场课程节选

Jeremy says in the text that the geometric return is always lower than the arithmetic return unless all the numbers are the same.

杰里米在书里说几何平均,总是比算术平均小,当然如果所有数字都一样,两个均值相等

耶鲁公开课 - 金融市场课程节选

To calculate the expected utility of your wealth, you might also have to look at the expected return, or the geometric expected return, or the standard deviation.

要计算你财富的期望效用,你也许还要研究预期收益曲线,或几何预期收益率,或是标准差

耶鲁公开课 - 金融市场课程节选