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Read the growth factor before taking a logarithm
A simple return r corresponds to factor 1+r. The log return is ln(1+r), so a −20% simple return has factor 0.8 and log return approximately −0.223144. The negative log value does not imply a negative wealth level.
Add logs of positive factors
For +20% followed by −20%, ln(1.2)+ln(0.8) = ln(0.96). Exponentiating the sum gives factor 0.96. Logs add across periods because positive growth factors multiply, not because simple returns are additive.
Every included factor must be strictly positive.
Handle a complete loss separately
At −100%, the factor is zero and there is no finite real log return. The linked terminal simple return can still be −100%. A later contribution would create a new capital base; a subsequent return cannot be formed on the exhausted zero base in this no-flow model.
Keep the quotation explicit
A log return of 0.10 corresponds to simple return exp(0.10)−1, approximately 10.517092%. Printing the log number as a 10% simple return changes the meaning. Label both the measure and the interval.