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# Average Return

## What Is Average Return?

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

### Key Takeaways

• The average return is the simple mathematical average of a series of returns generated over a specified period of time.
• The average return can help measure the past performance of a security or portfolio.
• The average return is not the same as an annualized return, as it ignores compounding.
• The geometric average is always lower than the average return.

## Understanding Average Return

There are several return measures and ways to calculate them. For the arithmetic average return, one takes the sum of the returns and divides it by the number of return figures.

$\text{Average Return} = \dfrac{\text{Sum of Returns}}{\text{Number of Returns}}$

The average return tells an investor or analyst what the returns for a stock or security have been in the past, or what the returns of a portfolio of companies are. The average return is not the same as an annualized return, as it ignores compounding.

## Average Return Example

One example of average return is the simple arithmetic mean. For instance, suppose an investment returns the following annually over a period of five full years: 10%, 15%, 10%, 0%, and 5%. 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%.

Now, let’s look at a real-life example. Shares of Walmart returned 9.1% in 2014, lost 28.6% in 2015, gained 12.8% in 2016, gained 42.9% in 2017, and lost 5.7% in 2018. The average return of Walmart over those five years is 6.1%, or 30.5% divided by 5 years.

## Calculating Returns From Growth

The simple growth rate is a function of the beginning and ending values or balances. It is calculated by subtracting the ending value from the beginning value and then dividing by the beginning value. The formula is as follows:

\begin{aligned} &\text{Growth Rate} = \dfrac{\text{BV} -\text{EV}}{\text{BV}}\\ &\textbf{where:}\\ &\text{BV} = \text{Beginning Value}\\ &\text{EV} = \text{Ending Value}\\ \end{aligned}

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

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

## Average Return Alternatives

### Geometric Average

When looking at average historical returns, the geometric average is a more precise calculation. The geometric mean is always lower than the average return. One benefit of using the geometric mean is that the actual amounts invested need not 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’ performances over more various time periods.

The geometric average return is sometimes called the time-weighted rate of return (TWR) because it eliminates the distorting effects on growth rates created by various inflows and outflows of money into an account over time.

### Money-Weighted Rate of Return (MWRR)

Alternatively, the money-weighted rate of return (MWRR) incorporates the size and timing of cash flows, making it an effective measure for returns on a portfolio that has received deposits, dividend reinvestments, and/or interest payments, or has had withdrawals.

The MWRR is equivalent to the internal rate of return (IRR), where the net present value equals zero.

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