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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 -$1 return = ... 2 The result is:$ 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\$.