What is the Arithmetic Average Return?In short, the “Arithmetic Average”, or “Mean”, is the sum of a series of numbers divided by the count of a series of numbers”, according to Investopedia. Arithmetic returns are calculated using a simple average over a period of time. Fund managers and mutual funds will often use arithmetic returns.
How can Arithmetic Returns be Calculated?The spreadsheet below shows three traders each with a beginning account balance of $100,000. Trader A, B, and C all have the same arithmetic average return of 5% for the year.
Example A. Annual Returns Arithmetic and Geometric (Includes Volatility)In Example A, the calculation for the arithmetic return is achieved by adding each month's return and dividing it by the number of months. To calculate the arithmetic return for Trader A, the returns for each month are added together, which equals 60, and divided by the 12 month period, which equals a 5% arithmetic return. Now let's look at Trader B's returns for the year:
Example B. Trader B Arithmetic Return CalculationAs you can see in Example B, the arithmetic return for Trader B is also 5%. Adding the monthly returns of Trader C also equals 60, and when divided by the 12-month period also equals a 5% arithmetic return.
However, arithmetic returns often do not show the true impact on the annual returns. The volatility of returns plays an important role when calculating the actual annual returns, as explained below.