# Return

**Return** is the amount of profit, expressed in dollars or percentages, earned on an investment.

## Contents

## Expanded Definition

There are two common uses of return:

- Simple
- Compounded

### Simple return

Simple return is just the amount of money made on the investment compared to the original. It is calculated as follows:

= (\frac{EV}{BV} - 1)*100%

where

EV = ending value, the value of the investment today (or at some point in the future),

BV = beginning value, the value of the investment when purchased.

For instance, if a stock was purchased at $14.43 on Jan. 2, 2003 and its value today is $32.79, then the simple return would be

= (\frac{$32.73}{$14.43}-1)*100%=(2.2682-1)*100%=126.82%

### Compounded return

Compounded return is the average return per year. This can be thought of an interest rate, compounded annually, paid upon the investment. This uses the concept of compound interest. It is calculated as follows:

= ((\frac{EV}{BV})^{(1/YR)} - 1)*100%

where

EV = ending value, the value of the investment today (or at some point in the future),

BV = beginning value, the value of the investment when purchased,

YR = number of years since the purchase.

For instance, using the same example above, but saying we sell on Jul. 2, 2008 (5 years, 6 months or 5.5 years), the compounded average annual return (also called compound annual growth rate, CAGR) is:

= ((\frac{$32.73}{$14.43})^{(1/5.5)} - 1)*100%=((2.2682)^{0.1818}-1)*100%=(1.1606-1)*100%=16.06%

## Uses

Rate of return is most often published for mutual funds, but can be calculated for any stock.

Usually you sum the market value on the final date plus all the dividends and distributions you received during the period and divide that by the market value on the first day (subtract 1 and multiply by 100 to get % gain).

You can get similar numbers off of published charts for the stock, but then dividends and other distributions are not usually included.

Note further that stock prices vary throughout the period. The precise number you get depends on exactly which points you choose to use in the calculation. If the stock did a big jump in value or decline stair-step fashion, the number can be deceiving. (So be careful what you use the data for.) Usually the number is done for the year. You can calculate it for the quarter (or some other period) too, but then multiply by four to get an annual value for comparison to annual values.

For a stock that makes rather smooth changes you can average out the variations by doing a curve fitting routine (usually least squares) available in most spread sheet programs. Then the return is the calculated slope of the calculated straight line drawn through the data. On a linear stock chart, you can also draw a straight line by hand and calculate the slope to get a value.

Like most investment tools return is a guide, not a hard and fast rule. It is most useful to collect items into groups, but minor differences are probably not so important.

Return is your paper profit. Most of it is realized only when you sell. Then it becomes taxable too. Use it to judge performance. Other factors are often a better indicator of when to sell. But it can help you identify under achievers and get you looking for something better.

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