How to calculate Arithmetic Average Return?

The Arithmetic Average Return is calculated by adding the rate of returns of "n" sub-periods and then dividing the result by "n". In other words, the returns of "n" sub-periods are added and then divided by "n" to find the value of the average return. As it is also the process of finding the average of a series of numbers, the average return is sometimes called as "Arithmetic Average Return".

Here is the formula to calculate Arithmetic Average Return −

$$\mathrm{Average\:Return =\frac{Total\:Value\:of\:the\:Return}{Total\:Number\:of \:Returns}}$$

Investors and market analysts normally use the arithmetic average return to check the past performance of a stock. It is also used to establish the company’s portfolio.

Annualized Return vs. Average Return

There are differences between "annualized returns" and "average returns". Annualized returns are calculated on a yearly basis and they are compounded over time in general. However, average returns are not compounded and expressed as a simple interest in the calculations.

Average annual return is used to measure the return on equity investments. As the annual returns are compounded, they are not considered as an ideal calculation method and so, it is only sparingly used to find the value of changing returns. The yearly return is calculated using a regular mean.

Calculating Average Return Using Arithmetic Mean

It is easy to calculate the average return in the arithmetic average model. Compare the following 5 years’ returns −

  • 2005: 10%
  • 2006: 7%
  • 2007: 12%
  • 2008: 10%
  • 2009: 5%

So, the arithmetic average return will be,

$$\mathrm{\frac{10 + 7 + 12 + 10 + 5}{5}=8.8}$$

Average Return vs. Geometric Average

Geometric average is ideal when analyzing average past returns. It takes into consideration the actual value invested in stocks or any other investment vehicle. The calculation only considers the return values and applies a comparison model when analyzing the performance of a single investment on multiple time periods.

The geometric average return considers the outliers resulting from Cash inflows and outflows over various periods. That is why it is also called the Time-Weighted Tate of Return (TWRR). TWRR also factors the timing and size of cash inflows and outflows into account.

TWRR is a perfect way to measure the net returns on a portfolio that had withdrawals from the account or other transactions, such as interest deposits and receipts. The Money-Weighted Rate of Return (MWRR) resembles the internal rate of return, but the net current value, in this case, is zero.