If a stock moves from 90 to 100 the increase in price is 11.11%, if we go from 100 to 90 the change is -10%, ie. They are not the same which means that it would not fit a normal distribution where going up and down is the same i.e. the distribution is symmetrical. By doing the LN of 90/100 and LN 100/90, we get -10.54% and +10.54 which is neutralised i.e. symmetrical.

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