How to calculate daily and monthly returns
Period return = (Value_end − Value_begin) ÷ Value_begin × 100
Compounded = ∏(1 + rᵢ) − 1
Geometric mean = (1 + Compounded)^(1 ÷ n) − 1
Worked example
- A balance moves from 37,903.02 to 42,528.98 in a month: 42,528.98 ÷ 37,903.02 − 1 = +12.20%.
- The next month it moves to 44,855.48: +5.47%.
- Compounded over both months: 1.1220 × 1.0547 − 1 = +18.34%.
How to interpret daily and monthly returns
A series of period returns shows the rhythm of performance: how often you have positive months, how large the bad ones get, and how consistent results are. The geometric average is the true growth rate; the arithmetic average is what you need for volatility and Sharpe ratio calculations.
Limitations and common mistakes
- Use values that exclude deposits and withdrawals, otherwise cash flows show up as returns.
- Always use the same point in each period (e.g. month-end) so periods are comparable.