Rate Of Return

Rate of return In finance, rate of return (ROR), also known as return on investment (ROI), rate of profit or sometimes just return, is the ratio of money gained or lost (whether 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 intrest , 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.

Calculation The initial value of an investment, Vi, 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, Vf, 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.

Single-period Arithmetic return

The arithmetic return is:

rarith is sometimes referred to as the. Logarithmic or continuously compounded return

The logarithmic return continously rate of return, also known as force of intrest , is defined as:

It is the reciprocal of the e-folding time.

Multiperiod average returns Arithmetic average rate of return

The arithmetic average rate of return over n periods is defined as:

Geometric average rate of return

The geometric average rate of return, also known as the time-weighted rate of return, over n periods is defined as:

The geometric average rate of return calculated over n years is also known as the annualized return.