how the arithmetic mean works
the arithmetic mean maintains its place in finance as well for example mean earnings estimates typically are an arithmetic mean say you want to know the average earnings expectation of the 16 analysts covering a particular stock simply add up all the estimates and divide by 16 to get the arithmetic mean the same is true if you want to calculate a stock s average closing price during a particular month say there are 23 trading days in the month simply take all the prices add them up and divide by 23 to get the arithmetic mean the arithmetic mean is simple and most people with even a little bit of finance and math skill can calculate it it s also a useful measure of central tendency as it tends to provide useful results even with large groupings of numbers limitations of the arithmetic meanthe arithmetic mean isn t always ideal especially when a single outlier can skew the mean by a large amount let s say you want to estimate the allowance of a group of 10 kids nine of them get an allowance between 10 and 12 a week the tenth kid gets an allowance of 60 that one outlier is going to result in an arithmetic mean of 16 this is not very representative of the group in this particular case the median allowance of 10 might be a better measure the arithmetic mean also isn t great when calculating the performance of investment portfolios especially when it involves compounding or the reinvestment of dividends and earnings it is also generally not used to calculate present and future cash flows which analysts use in making their estimates doing so is almost sure to lead to misleading numbers the arithmetic mean can be misleading when there are outliers or when looking at historical returns the geometric mean is most appropriate for series that exhibit serial correlation this is especially true for investment portfolios arithmetic vs geometric meanfor these applications analysts tend to use the geometric mean which is calculated differently the geometric mean is most appropriate for series that exhibit serial correlation this is especially true for investment portfolios most returns in finance are correlated including yields on bonds stock returns and market risk premiums the longer the time horizon the more critical compounding and the use of the geometric mean becomes for volatile numbers the geometric average provides a far more accurate measurement of the true return by taking into account year over year compounding the geometric mean takes the product of all numbers in the series and raises it to the inverse of the length of the series it s more laborious by hand but easy to calculate in microsoft excel using the geomean function the geometric mean differs from the arithmetic average or arithmetic mean in how it s calculated because it takes into account the compounding that occurs from period to period because of this investors usually consider the geometric mean a more accurate measure of returns than the arithmetic mean example of the arithmetic vs geometric meanlet s say that a stock s returns over the last five years are 20 6 10 1 and 6 the arithmetic mean would simply add those up and divide by five giving a 4 2 per year average return the geometric mean would instead be calculated as 1 2 x 1 06 x 0 9 x 0 99 x 1 06 1 5 1 3 74 per year average return note that the geometric mean a more accurate calculation in this case will always be smaller than the arithmetic mean 