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Negative properties of continuously compounded returns
You cannot use continuous compounding for returns less than or equal to 100% because a natural logarithm can only be taken for a positive amount.  This answer includes the accurate way to ascertain r, for which many people use an approximation. For example, using -20% monthly return for 12 months:- -0.2 -0.223144 0.0687195 Checking: 0.0687195 True Now trying -100% monthly return:- -1. Indeterminate Why?  Because a natural logarithm can only be taken for a positive amount.  So the latter calculation can not be done using (logarithmic) continuous compounding. Of course, the calculation can still be done using regular compounding.  For -100% the results go to zero in the first month, but -150% produces a more interesting result: -1.5 -11920.9