Rate of return

In finance, return is a profit on an investment. It comprises any change in value of the investment, and/or cash flows (or securities, or other investments) which the investor receives from that investment over a specified time period, such as interest payments, coupons, cash dividends and stock dividends. It may be measured either in absolute terms (e.g., dollars) or as a percentage of the amount invested. The latter is also called the holding period return.

A loss instead of a profit is described as a negative return, assuming the amount invested is greater than zero.

To compare returns over time periods of different lengths on an equal basis, it is useful to convert each return into a return over a period of time of a standard length. The result of the conversion is called the rate of return.

Typically, the period of time is a year, in which case the rate of return is also called the annualized return, and the conversion process, described below, is called annualization.

The return on investment (ROI) is return per dollar invested. It is a measure of investment performance, as opposed to size (cf. return on equity, return on assets, return on capital employed).

The return, or the holding period return, can be calculated over a single period. The single period may last any length of time.

The overall period may, however, instead be divided into contiguous subperiods. This means that there is more than one time period, each sub-period beginning at the point in time where the previous one ended. In such a case, where there are multiple contiguous subperiods, the return or the holding period return over the overall period can be calculated by combining the returns within each of the subperiods.

The direct method to calculate the return or the holding period return ${\displaystyle R}$ over a single period of any length of time is: