Hi
@Maxim Rastorguev Yes, your period (annual) returns are +15%, -15%, +15%, -15%, 0% such that the arithmetic return is given by (+15%, -15%, +15%, -15%, 0%)/5 = 0. This is meant to illustrate the same distinction explained in Hull's Business Snapshot 15.1 (
see below). Just as you are suspicious of the zero, Hull says "What average return should the fund manager report? It is tempting for the manager to make a statement such as: ‘‘The average of the returns per year that we have realized in the last 5 years is 14% [i.e., his
arithmetic average]’’ Although true, this is misleading. It is much less misleading to say: ‘‘The average return realized by someone who invested with us for the last 5 years is 12.4% per year. [i.e.,
his geometric mean, analogous to your -0.91%]’’ In some jurisdictions, regulations require fund managers to report returns the second way."
Similarly, the standard deviation of your series is about 13.4% and--this is always interesting to me--we can see that the geometric average of -0.91% is, in fact, less than zero by 1/2 the variance: 0% - 13.4%^2/2 ~= -0.91%. Put another way, volatility erodes returns. Thanks,
053119-cagr-vs-arith
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