In finance, rate of return (ROR), also known as return on investment (ROI), or sometimes just return, is the ratio of money gained or lost (realized or unrealized) on an investment relative to the amount of money invested. The amount of money gained or lost may be referred to as interest, profit/loss, gain/loss, or net income/loss. The money invested may be referred to as the asset, capital, principal, or the cost basis of the investment. ROI is usually expressed as a percentage rather than a fraction.

ROI does not indicate how long an investment is held. However, ROI is most often stated as an annual or annualized rate of return, and it is most often stated for a calendar or fiscal year. In this article, "ROI" indicates an annual or annualized rate of return, unless otherwise noted.

ROI is used to compare returns on investments where the money gained or lost — or the money invested — are not easily compared using monetary values. For instance, a $1,000 investment that earns $50 in interest generates more cash than a $100 investment that earns $20 in interest, but the $100 investment earns a higher return on investment.

• $50/$1,000 = 5% ROI
• $20/$100 = 20% ROI

When considering a continuous process of gaining or losing money with a constant rate of return, the annual rate of return is any value greater than -100%; a positive percentage corresponds to exponential growth of the capital, a value between -100% and 0% exponential decay.

Calculation

The initial value of an investment, $V\_i$, does not always have a clearly defined monetary value, but for purposes of measuring ROI, the initial value must be clearly stated along with the rationale for this initial value. The final value of an investment, $V\_f$, also does not always have a clearly defined monetary value, but for purposes of measuring ROI, the final value must be clearly stated along with the rationale for this final value.

The rate of return can be calculated over a single period, or expressed as an average over multiple periods.

Arithmetic return

The arithmetic return is defined as the following:

$r\_\{arith\}=\backslash frac\{V\_f\; -\; V\_i\}\{V\_i\}$

If the final investment value excludes capital gains, then $r\_\{arith\}$ is sometimes referred to as the yield. See also: effective interest rate, effective annual rate (EAR) or annual percentage yield (APY).

If the final investment value includes both capital gains and intermediate income such as dividends, then $r\_\{arith\}$ is the holding period return.

Logarithmic or continuously compounded return

The logarithmic return or continuously compounded return, also known as force of interest, is defined as: