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Percentages are scaling operators and are not invertible operations. If a stock X grows by x%, that's given by
>X_new = X_old(1+x).
Whereas if a stock falls by x%, that's given by
>X_new=X_old(1-x)
These are additively invertible but not multiplicatively invertible. And since consecutive rates are multiplicative, you get that a rise and a fall of x% is given by
>X_new = X_old (1-x^2)
I.e. you'll always lose x^2. In your pic rel that's 0.1*0.1=0.01 = 1% lost.
