What is Average Return?
Average return is the simple mathematical average of a series of returns over a specified period. For example, if you have annual returns from an investment over five years, you can calculate the average return by summing these returns and dividing by the number of years.
It’s important to distinguish between average return and annualized return. While average return ignores compounding effects, annualized return takes into account the compounding effect over multiple years. This distinction is crucial because it affects how accurately you can predict future performance based on past data.
Methods of Calculating Average Return
Arithmetic Average Return
The arithmetic average return is perhaps the most straightforward method. It involves summing up all the individual returns and then dividing by the number of return figures. Here’s an example:
If Walmart had annual returns of 10%, 12%, 8%, 15%, and 11% over five years, you would calculate the arithmetic average return as follows:
[ \text{Arithmetic Average Return} = \frac{10\% + 12\% + 8\% + 15\% + 11\%}{5} = \frac{56\%}{5} = 11.2\% ]
This method is easy to compute but does not account for compounding effects.
Geometric Average Return
The geometric average return, also known as the time-weighted rate of return (TWRR), is more precise when dealing with historical returns because it accounts for compounding. Here’s how you calculate it:
[ \text{Geometric Average Return} = \left( (1 + R1) \times (1 + R2) \times \cdots \times (1 + R_n) \right)^{\frac{1}{n}} – 1 ]
Using the same example as above:
[ \text{Geometric Average Return} = \left( (1 + 0.10) \times (1 + 0.12) \times (1 + 0.08) \times (1 + 0.15) \times (1 + 0.11) \right)^{\frac{1}{5}} – 1 \approx 10.7\% ]
This method provides a more accurate picture when considering the effects of compounding.
Money-Weighted Rate of Return (MWRR)
The money-weighted rate of return (MWRR) is particularly useful for portfolios that involve deposits, withdrawals, or other transactions during the period being analyzed. It is equivalent to the internal rate of return (IRR) where the net present value equals zero.
To calculate MWRR, you need to solve for ( r ) in the following equation:
[ \sum{t=0}^{n} \frac{Ct}{(1+r)^t} = 0 ]
where ( C_t ) represents cash flows at time ( t ).
This method is complex but essential for accurately reflecting changes in capital outlays.
Average Rate of Return (ARR)
The Average Rate of Return (ARR) is commonly used in capital budgeting to evaluate investment projects. It is calculated by dividing the average annual profit by the initial cost and multiplying by 100 to get a percentage.
The formula for ARR is:
[ \text{ARR} = \left( \frac{\text{Average Annual Profit}}{\text{Initial Cost}} \right) \times 100 ]
For instance, if an investment property generates an average annual profit of $50,000 and was purchased for $200,000:
[ \text{ARR} = \left( \frac{50,000}{200,000} \right) \times 100 = 25\% ]
Practical Applications and Limitations
Average return is widely used in real-world scenarios such as evaluating past performance of securities or portfolios. However, it has several limitations:
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It does not account for compounding effects.
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It does not consider different capital outlays or future costs.
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It can be misleading if used alone without considering other metrics like standard deviation or Sharpe ratio.
Despite these limitations, understanding average return helps investors and analysts make more informed decisions about their investments.
Comparative Statistics and Examples
To illustrate the differences between various methods of calculating average return, let’s compare two investments using arithmetic and geometric averages:
Investment A: Annual returns of 10%, 12%, 8%, 15%, and 11%.
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Arithmetic Average Return: 11.2%
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Geometric Average Return: Approximately 10.7%
Investment B: Annual returns of 5%, -3%, 20%, -10%, and 15%.
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Arithmetic Average Return: Approximately 5.4%
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Geometric Average Return: Approximately 4.3%
These examples show how different methods can yield different results due to compounding effects.
Additional Resources
For further assistance in calculating average returns, you can use online calculators or financial software such as Excel or specialized tools like Bloomberg Terminal or Morningstar Direct. These resources can streamline your calculations and provide additional insights into your investments.
By mastering these techniques and leveraging available tools, you’ll be well-equipped to navigate the complex world of finance with confidence.