Rates of return

In finance, return is a profit on an investment. It comprises any change in value and interest or dividends or other such cash flows which the investor receives from the investment. 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.

Rate of return is a profit on an investment over a period of time, expressed as a proportion of the original investment. The time period is typically a year, in which case the rate of return is referred to as annual return.

To compare returns over time periods of different lengths on an equal basis, it is useful to convert each return into an annual equivalent rate of return, or annualised return. This conversion process is called annualisation, described below.

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

The return, or rate of return, can be calculated over a single period, or where there is more than one time period, the return and rate of return over the overall period can be calculated, based upon the return within each sub-period.

The return over a single period is:

where:

For example, if you hold 100 shares, with a starting price of 10, then the starting value is 100 x 10 = 1,000. If you then collect 0.50 per share in cash dividends, and the ending share price is 9.80, then at the end you have 100 x 0.50 = 50 in cash, plus 100 x 9.80 = 980 in shares, totalling a final value of 1,030. The change in value is 1,030 - 1,000 = 30, so the return is 30 / 1,000 = 3%.

The return, or rate of return, depends on the currency of measurement. For example, suppose a 10,000 USD (US dollar) cash deposit earns 2% interest over a year, so its value at the end of the year is 10,200 USD including interest. The return over the year is 2%, measured in USD. Let us suppose also that the exchange rate to Japanese yen at the start of the year is 120 yen per USD, and 132 yen per USD at the end of the year. The value in yen of one USD has increased by 10% over the period. The deposit is worth 1.2 million yen at the start of the year, and 10,200 x 132 = 1,346,400 yen at the end of the year. The return on the deposit over the year in yen terms is therefore:

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