<prompt> Human: I realized something the other day, and it hit me like a truck because Id never thought about it fully. So I wanted to share it here, in case it helps someone else. If I were to tell you that I had averaged a 12 annual rate of return over the past 30 years or any other randomly long period of time, youd probably think that I was some kind of financial genius. If I was a financial adviser telling you that, youd probably be inclined to consider giving me your business, right?But heres the thing. If I lose 50 of my assets in one year and the remainder grows by 75 the next year, its an average of 12.5 return over the 2 years. In real numbers, Im in the hole. If I repeat the same pattern for 10 years, it still looks like Im averaging a 12 return per year, but in reality, Im down almost 50 of my initial assets.So make sure you get not only the average rate of return for your investments but also the year-by-year breakdown so you know what your actual results will be.  <response>: You are referring to the different between arithmetic mean and geometric mean. The arithmetic mean of -50 and 75 is indeed 12.5, but the geometric mean is -6.5. Its calculated as sqrt.51.75. Annual rate of return is usually quoted as geometric mean. Anyone who uses arithmetic mean for return rates is being disingenuous. 