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Simple returns

The plain percentage change, (P1 - P0)/P0. What your account statement shows, and the right choice when adding returns across positions in the same period.

Simple returns aggregate across assets: a portfolio's return in one period is the weighted sum of the simple returns of its holdings. Log returns do not have this property, which is why portfolio arithmetic uses simple and time-series statistics use log-returns.

They do not aggregate across time. Two consecutive +10% periods are +21%, not +20%. Anyone who averages daily simple returns and multiplies by 252 is computing something that does not correspond to any achievable account balance.

Practical rule: convert to logs for modelling, convert back to simple for reporting, and never mix them in one table without labelling which is which.

Related: log-returns, arithmetic-vs-geometric-return, equity-curve, compounding

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