Simple Returns
The percentage change in price from one period to the next: the new price divided by the previous one, minus one.
Simple Return = Pₜ / Pₜ₋₁ − 1 Total = (1 + r₁)(1 + r₂)…(1 + rₙ) − 1
A simple return measures the change between two prices as a fraction of the first: (Pₜ − Pₜ₋₁) / Pₜ₋₁, or equivalently Pₜ / Pₜ₋₁ − 1. A move from 100 to 103 is a simple return of +3%. In pandas it is a single call: close.pct_change().
Simple returns are what an account actually earns, and they combine neatly across assets: a portfolio's return is the weighted average of its holdings' simple returns. Over time, though, they compound by multiplication rather than adding up. To get a total return across several periods, multiply the growth factors (1 + r) and subtract one. Summing the returns misstates the result.
Log returns, ln(Pₜ / Pₜ₋₁), are the alternative that does add up over time. For small daily moves the two are nearly identical; for large moves they differ, so results should say which one was used.
On the desk
A price moves 100 → 110 → 99. The simple returns are +10% and −10%. They sum to zero, but the total return is 1.10 × 0.90 − 1 = −1%: compounding, not addition, gives the real result.