Rate of return

Lore & Background

The rate of return is derived from the concept of return, which comprises any change in the value of an investment plus cash flows received, such as interest, dividends, or stock dividends. It can be calculated over a single period or multiple contiguous subperiods by combining returns. The direct formula for a single period is R = (Vf - Vi) / Vi, where Vf is final value and Vi is initial value. A negative initial value, as with liabilities or short positions, can yield a positive return representing a loss. If the initial value is zero, no return can be calculated.

Reader's Guide

The rate of return is significant because it allows investors to compare returns over time periods of different lengths on an equal basis by converting them to a standard period, typically a year, through annualization. Without reinvestment, the rate of return r equals R/t, where R is the return over time t. With reinvestment, compounding applies: 1+R = (1+r)^t, so r = (1+R)^(1/t) - 1. The CFA Institute's Global Investment Performance Standards (GIPS) state that returns for periods of less than one year must not be annualized, as such annualized rates are statistically unlikely to be indicative of long-term performance due to risk. This rule does not apply to low-risk interest rates or yields, where annualized quotes are common for short-term borrowing or lending. The rate of return also depends on the currency of measurement; for example, a 2% return in USD may translate to a 12.2% return in yen if the exchange rate changes.

Did You Know?

• A loss is described as a negative return, assuming the amount invested is greater than zero.
• The return on investment (ROI) is return per dollar invested, a measure of investment performance as opposed to size.
• If the initial value is zero, no return can be calculated.
• The rate of return depends on the currency of measurement; exchange rate changes can significantly alter the return.