### What is Average Return

Average return is the simple mathematical average of a series of returns generated over a period of time. An average return is calculated the same way a simple average is calculated for any set of numbers; the numbers are added together into a single sum, and then the sum is divided by the count of the numbers in the set.

The simple average of returns is an easy calculation, but it is not very accurate. For more accurate returns calculations, analysts and investors also frequently use the geometric mean return (sometimes called the time-weighted return), or the money-weighted return.

There are several return measures. Three of the most popular are return on assets (ROA), return on investment (ROI) and return on equity (ROE).

### BREAKING DOWN Average Return

One example of average return is the simple arithmetic average. For example, suppose an investment returns the following annually over a period of five full years: 10 percent, 15 percent, 10 percent, 0 percent and 5 percent. To calculate the average return for the investment over this five-year period, the five annual returns are added together and then divided by 5. This produces an annual average return of 8 percent.

In business, there are three main ways to calculate return. One way is with a simple growth formula, where the return on the investment is a function of growth. Other measures of return, such as ROI, ROA, and ROE, focus on investment performance rather than growth.

### Return From Growth

The simple growth rate is a function of past and present values. It is calculated by subtracting the past value from the present value and then dividing by the past value. The formula is: (Present - Past) / Past.

For example, if you invest $10,000 in a company and the stock price increases from $50 to $100, the return can be calculated by taking the difference between $100 and $50 and then dividing by $50. The answer is 100 percent, which means you now have $20,000.

### More Accurate Average Return Measures

When looking at average of historical returns, the geometric average is a more precise calculation. One benefit of using the geometric mean is that the actual amounts invested do not need to be known; the calculation focuses entirely on the return figures themselves and presents an "apples to apples" comparison when looking at two or more investments' performance over more various time periods. The geometric average return is sometimes called the time-weighted rate of return (TWRR) because it eliminates the distorting effects on growth rates created by various inflows and outflows of money into an account over time. The geometric formula is:

[(1+Return_{1}) x (1+Return_{2}) x (1+Return_{3}) x ... x (1+Return_{n})]^{1/n} - 1

Alternatively, the money-weighted rate of return (MWRR) incorporates the size and timing of cash flows, so it is an effective measure for returns on a portfolio that has received deposits, dividend reinvestments, interest payments or has had withdrawals. The money-weighted return is equivalent to the internal rate of return (IRR) where the net present value (NPV) = 0. The MWRR is calculated using this formula:

### Average Return on Assets and Return on Equity

ROA, also referred to as return on average assets and return on investment (ROI), is a function of profit margin and asset turnover. The rate of return on assets is both a profitability and efficiency measure. ROA is calculated by dividing net income by average total assets. For example, assume the net income of Company A grows from $1 million to $2 million, while assets increase from $10 million to $100 million. Using the basic growth formula, we know that net income rose by 100 percent, while assets grew by 1000 percent. This may sound great, but the return on assets is only 3.6 percent.

ROE is calculated by dividing net income by shareholders' equity. It measures asset efficiency and the degree to which the company is using debt to pay for assets. For example, if Company A has stockholders' equity of $1 million one year and $10 million the next, it means ROE is calculated by dividing $2 million by the average of $1 million and $10 million, or $5.5. The answer is 36 percent.