Definition
A return is the proportional change in the value of an asset over a defined period. In its simplest form it is the ending value minus the beginning value, divided by the beginning value, often expressed as a percentage. Despite the apparent simplicity, the practical computation of returns hides a series of choices — which prices, over which period, in which currency, with what reinvestment assumption — that materially change the resulting number.
Two parallel conventions dominate. Simple returns are arithmetic and compose by multiplication across periods: a five percent month followed by a three percent month produces a compound return of 1.05 times 1.03 minus one, or 8.15 percent. Log returns are the natural logarithm of the price ratio and compose by addition, which makes them analytically convenient for statistical modeling. The two converge for small period returns and diverge for large ones, so the choice matters more for monthly and quarterly data than for daily.
Why it matters
How it works
The mechanics are straightforward but the conventions matter. A simple total return divides the ending value (including any cash distributions reinvested) by the beginning value and subtracts one. A price return ignores dividends entirely. A log return takes the natural log of the same ratio. Excess return subtracts a risk-free rate, or sometimes a benchmark, period by period to isolate the contribution of active decisions. Annualised return scales a sub-annual return up to a one-year figure by either compounding or multiplying by the period count, depending on the convention.
The richest analytical work begins once a clean return series is in hand. Volatility is the standard deviation of returns. Sharpe ratio is the mean excess return divided by its standard deviation. Drawdown traces the cumulative product of returns and measures the maximum peak-to-trough decline. Every backtest, every portfolio analytic, every risk model takes returns as its input — so the data hygiene that produces an accurate return series is more consequential than any individual downstream metric.