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0

The most correct way if you want to do it with log returns is the way you stated on your first edit, but indeed for daily data the approximation error is negligible.


0

If the value is $1 today and was $10 yesterday return = today/yesterday - 1 = 1/10 - 1 = -0.9 = -90% log return = ln(1 - 0.9) = -2.302585 check : A = P e^rt = $10 * e^-2.302585 = $1 (i.e. today's value) Since investments can end up in the red it's interesting to consider a return that exceeds -100%, for instance if today's value is -$1 return = ...


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The result is: $ e^{(-230%)} - 1 = -89% $


4

Large? ? The relationship between normal and log returns is $$(normal return) = exp(log return)-1$$ Therefore log-returns can be from $-\infty$ to $+\infty$ while normal ones can only be between $-1$ and $+\infty$.



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