How to Calculate the Arithmetic Average Return: A Clear and Confident Guide
Calculating the arithmetic average return is an essential step in determining the overall performance of an investment. It is a simple calculation that provides investors with a sense of how much money they can expect to earn on their investment over a given period. The arithmetic average return is also known as the mean return, and it is calculated by adding up the returns from each period and dividing the sum by the number of periods.
Investors use the arithmetic average return to evaluate the performance of their investment portfolio. It is a useful tool for comparing the returns of different investments over the same period. The arithmetic average return is also used to estimate the future returns of an investment. While it cannot predict the exact return that an investor will receive, it provides a reasonable estimate of what to expect based on past performance. Understanding how to calculate the arithmetic average return is an essential skill for any investor who wants to make informed investment decisions.
Understanding the Arithmetic Average Return
Definition of Arithmetic Average Return
Arithmetic average return is a simple and straightforward method of calculating the average return of an investment over a period of time. It is also known as the mean return and is calculated by adding up the individual returns for each period and then dividing by the total number of periods. The formula for calculating the arithmetic average return is:
Arithmetic Average Return = (Total Return / Number of Periods)
For example, if an investment had returns of 5%, 8%, -2%, 12%, and 9% over five years, the arithmetic average return would be (5% + 8% + (-2%) + 12% + 9%)/5 = 6.4%.
Importance in Investment Analysis
The arithmetic average return is an essential tool for investment analysis as it provides investors with an easy-to-understand metric for evaluating the performance of an investment over a certain period. It is particularly useful for evaluating the performance of investments with a short to medium-term horizon, such as stocks or mutual funds.
However, it is important to note that the arithmetic average return does not take into account the volatility of an investment. Therefore, it may not provide an accurate representation of the investment's performance over the entire period. For this reason, it is often used in conjunction with other metrics, such as the standard deviation or the Sharpe ratio, to provide a more comprehensive analysis of an investment's performance.
In summary, the arithmetic average return is a useful metric for evaluating the performance of an investment over a certain period. While it may not provide a complete picture of an investment's performance, it can be used in conjunction with other metrics to provide a more comprehensive analysis.
Calculating Arithmetic Average Return
Identifying Relevant Cash Flows
Before calculating the arithmetic average return, it is important to identify the relevant cash flows. These cash flows can be in the form of dividends, interest, or capital gains. For example, if an investor holds a stock for five years, they will receive dividends and may also experience capital gains or losses. It is important to include all relevant cash flows when calculating the arithmetic average return.
Summing Periodic Returns
Once the relevant cash flows have been identified, the periodic returns must be calculated. This involves subtracting the initial investment value from the ending investment value and dividing by the initial investment value. This will give the periodic return for each period.
Dividing by the Number of Periods
After the periodic returns have been calculated, they must be summed and divided by the number of periods to get the arithmetic average return. This will give a single figure that represents the average return over the investment period.
Overall, calculating the arithmetic average return requires identifying the relevant cash flows, summing the periodic returns, and dividing by the number of periods. By following these steps, investors can accurately calculate the average return on their investment.
Examples of Arithmetic Average Return Calculations
Single Investment Example
Suppose an investor invests $10,000 in a mutual fund and holds it for five years. The annual returns for the five years are 5%, 8%, -2%, 12%, and 9%. The arithmetic average return can be calculated by adding up all the returns and dividing by the number of years:
Arithmetic Average Return = (5% + 8% + (-2%) + 12% + 9%)/5
= 6.4%
Therefore, the arithmetic average return for the investment is 6.4%. If the investor reinvests all the returns, then the investment value after five years will be:
Investment Value = $10,000 * (1 + 6.4%)^5
= $13,567
However, the arithmetic average return suggests that the investment value will be $14,509. This is because the arithmetic average return assumes that the returns are compounded annually, which is not always the case.
Portfolio Example
Suppose an investor has a portfolio of three stocks: A, B, and C. The returns for the three stocks for the past year are as follows:
| Stock | Return |
|---|---|
| A | 10% |
| B | 5% |
| C | -2% |
The arithmetic average return for the portfolio can be calculated by adding up the returns for each stock and dividing by the number of stocks:
Arithmetic Average Return = (10% + 5% + (-2%))/3
= 4.33%
Therefore, the arithmetic average return for the portfolio is 4.33%. If the investor reinvests all the returns, then the portfolio value after one year will be:
Portfolio Value = $10,000 * (1 + 4.33%)^1
= $10,433
However, the actual portfolio value after one year will depend on the weights of the stocks in the portfolio and the actual returns of each stock.
Limitations of Arithmetic Average Return
Ignoring Volatility
One of the main limitations of the arithmetic average return is that it ignores volatility. The arithmetic average return only takes into account the average return over a period of time, but it does not consider how much the returns vary from year to year. This can be a problem because an investment with a high average return may have a lot of volatility, which can make it riskier than an investment with a lower average return but less volatility.
To illustrate this point, consider two investments with the same average return of 10% over a five-year period. Investment A has returns of 20%, -10%, 20%, -10%, and 20%, while Investment B has returns of 10%, 10%, 10%, 10%, and 10%. Although both investments have the same average return, Investment A is much riskier than Investment B because of its volatility.
Not Reflecting Compound Interest
Another limitation of the arithmetic average return is that it does not reflect compound interest. Compound interest is the interest earned on both the initial investment and the accumulated interest from previous periods. Because the arithmetic average return only takes into account the average return over a period of time, it does not reflect the effects of compound interest.
To illustrate this point, consider two investments with the same arithmetic average return of 10% over a five-year period. Investment A earns simple interest, while Investment B earns compound interest. After five years, Investment A has earned a total return of 50%, while Investment B has earned a total return of 61%. Although both investments have the same average return, Investment B has earned a higher total return because of the effects of compound interest.
Overall, while the arithmetic average return is a useful measure of investment performance, it has its limitations. Investors should be aware of these limitations and use other measures, such as the geometric average return, to get a more complete picture of their investment performance.
Comparing Arithmetic and Geometric Averages
When calculating investment returns, there are two types of averages that investors commonly use: arithmetic and geometric. The arithmetic average is also known as the simple average and is calculated by adding up all the returns and dividing by the number of periods. The geometric average, on the other hand, takes into account the compounding effect of returns over time.
One way to understand loan payment calculator bankrate the difference between the two is to imagine two investments, A and B, with the following returns:
| Period | Investment A | Investment B |
|---|---|---|
| Year 1 | 10% | 10% |
| Year 2 | -10% | 50% |
| Year 3 | 20% | -30% |
The arithmetic average return for Investment A is 6.67%, while Investment B has an arithmetic average return of 10%. However, when calculating the geometric average return, Investment A has a return of 0%, while Investment B has a return of 10.41%. This shows that the geometric average return provides a better representation of the actual return earned over the investment period.
Investors should use the geometric average when calculating returns over multiple periods, especially when returns are volatile. The arithmetic average can be misleading in such cases, as it does not take into account the compounding effect of returns. However, the arithmetic average can be useful when calculating returns over a single period, such as a year.
In summary, while both arithmetic and geometric averages are useful tools for calculating returns, investors should be aware of their differences and use them appropriately. The geometric average is better suited for long-term investments, while the arithmetic average is better suited for short-term investments.
Applications of Arithmetic Average Return
Performance Measurement
Arithmetic average return is a commonly used metric to measure the performance of an investment portfolio or a single asset class. It provides a simple and intuitive way to understand the average performance of an investment over a certain period of time. The metric is particularly useful when evaluating the performance of investments with a short to medium-term horizon.
Investors can use arithmetic average return to compare the performance of different investments or asset classes. For example, an investor can compare the average returns of two mutual funds over a five-year period to determine which fund performed better. The metric can also be used to compare the performance of a single asset class, such as stocks or bonds, against a benchmark index.
Financial Forecasting
Arithmetic average return is also useful in financial forecasting. It can be used to estimate the expected return of an investment over a certain period of time. For example, an investor can use the arithmetic average return of a stock over the past five years to estimate the expected return of the stock over the next five years.
The metric is particularly useful when forecasting the returns of investments with a short to medium-term horizon. However, it should be noted that arithmetic average return may not be an accurate predictor of future returns, especially for investments with a long-term horizon.
Overall, arithmetic average return is a useful metric for performance measurement and financial forecasting. However, it should be used in conjunction with other metrics and analysis to make informed investment decisions.
Best Practices in Reporting Average Returns
When reporting average returns, it is important to follow best practices to ensure accuracy and transparency. Here are some tips to keep in mind:
1. Clearly Define the Time Period
It is important to clearly define the time period over which the average return is being calculated. This allows investors to understand the historical performance of an investment and make informed decisions about future investments. It is recommended to use a standard time period, such as one year or five years, to ensure consistency across different investments.
2. Use Appropriate Methodology
There are different methodologies for calculating average returns, such as arithmetic average return and geometric average return. It is important to use the appropriate methodology for the type of investment being analyzed. For example, arithmetic average return is suitable for analyzing stocks, while geometric average return is more appropriate for analyzing mutual funds.
3. Include Standard Deviation
In addition to reporting average returns, it is recommended to also include standard deviation. Standard deviation measures the volatility of an investment and provides a better understanding of the risk involved. Including standard deviation allows investors to compare the risk and return of different investments and make informed decisions.
4. Avoid Misleading Reporting
It is important to avoid misleading reporting of average returns. For example, reporting only the best performing year or cherry-picking a time period can distort the overall performance of an investment. It is recommended to report average returns over a longer time period to provide a more accurate picture of historical performance.
By following these best practices, investors can make informed decisions based on accurate and transparent reporting of average returns.
Frequently Asked Questions
What steps are involved in calculating the arithmetic average return using Excel?
To calculate the arithmetic average return using Excel, one needs to follow these steps:
- Enter the individual returns in separate cells in an Excel spreadsheet.
- Use the formula "=AVERAGE(cell range)" to calculate the average of the individual returns.
- The result will be the arithmetic average return.
How does the formula for geometric average return differ from the arithmetic average return?
The formula for geometric average return is different from the arithmetic average return because it takes into account the compounding effect of returns over time. The formula for geometric average return is:
[(1+r1) * (1+r2) * (1+r3) * ... * (1+rn)]^(1/n) - 1
Where r1, r2, r3, ..., rn are the individual returns for each period, and n is the total number of periods.
Can you explain the difference between the arithmetic mean and geometric mean with examples?
The arithmetic mean is the simple average of a set of numbers, while the geometric mean is the nth root of the product of n numbers. For example, if we have the following set of numbers: 2, 4, 6, 8, the arithmetic mean is (2+4+6+8)/4 = 5, while the geometric mean is the fourth root of (246*8) = 4.89.
In what scenarios is the arithmetic mean higher than the geometric mean?
The arithmetic mean is higher than the geometric mean when the individual returns are positive and vary widely from period to period. This is because the arithmetic mean gives equal weight to each period, while the geometric mean gives more weight to the periods with higher returns.
What is the correct formula to use when aiming to calculate the average real return?
The correct formula to use when aiming to calculate the average real return is:
[(1+nominal return)/(1+inflation rate)] - 1
Where nominal return is the return on an investment before adjusting for inflation, and inflation rate is the rate of inflation during the investment period.
How can one determine the average rate of return from a given data set?
To determine the average rate of return from a given data set, one needs to:
- Add up all the returns in the data set.
- Divide the result by the total number of returns in the data set.
- The result will be the average rate of return.