I am aware of the differences between an Exponentially Weighted Moving Average (EWMA) and a Simple Moving Average (SMA), with the weights of the latter being fixed and equal for each observation in the calculation compared to exponentially decaying weights for the former. Is there a rule of thumb to relate the lookback-period / formation-period of a SMA to the half-life of an EWMA? In other words, if I am working with a SMA of, say, 10 days, is there an approximate of the half-life of an equivalent EWMA? A former colleague told me once that a SMA is approximately equivalent to about 3x the half-life of an EWMA but I do not recall why. He claims that e.g., if you're using a SMA of 10 days, the equivalent EWMA will have a half-life of 3.3 days. Does anyone have an analytical solution to the equivalence?