Return is the gain or loss on an asset, position or portfolio over a specified interval, expressed relative to a defined starting value. A one-period simple holding-period return can be written as R = (V1 - V0 + C) / V0, where V0 is the beginning value, V1 is the ending value and C represents cash income or distributions generated by the investment during the period. The denominator and the treatment of cash flows are part of the measurement, not bookkeeping details.
Price return and total return are different measurements
A price return captures only the change in quoted price or market value. A total return also incorporates economically relevant income or distributions, such as dividends or interest. For multi-period total-return series, the treatment and reinvestment of those distributions must be defined consistently. Settlement versus closing price, local versus base currency, adjusted versus unadjusted data, fees and financing can also change the result, while investor contributions and withdrawals must be separated appropriately from investment performance.
For example, suppose an asset begins at 100, ends the period at 105 and pays a cash distribution of 2 during the interval. Its price return is 5%, because the price increased by 5 relative to the initial value of 100. Its simple total holding-period return is 7% before costs and taxes: (105 - 100 + 2) / 100. Both percentages are valid, but they measure different things. Reporting only that “the return was 5%” would therefore be incomplete if the intended measure included the distribution.
For a consistently defined wealth or total-return series, multi-period simple returns compound rather than add: cumulative return is the product of the individual growth factors, (1 + R), minus one. The common log-price return, ln(P1) - ln(P0), is additive across time and convenient in statistical work, but it requires positive price observations. That restriction matters in derivatives research because futures prices can become non-positive. The May 2020 WTI crude oil futures contract, for example, settled below zero, making a conventional log-price return undefined whenever a required price observation is zero or negative.
A market move is not always the investor’s return on capital
Futures make the denominator especially important. Futures margin is a performance bond rather than the purchase price of the contract, and positions are marked to market as gains and losses are credited or debited. If a futures quotation moves from 100 to 102, the quoted price has risen 2%, but the trader has not necessarily earned 2% on the cash committed to the strategy. Contract profit or loss depends on the price change and the contract multiplier; percentage return then depends on the capital base chosen for measurement, including how margin, collateral, financing and cash reserves are treated.
For research, “return” is reproducible only when the horizon, price field, cash-flow treatment, compounding convention and denominator are specified. Two analysts can begin with the same market history and obtain different return series without either making an arithmetic error; the difference may come from construction choices. The practical question is therefore not only “what was the return?” but “return on what, measured how, over which interval?”