What Is the Arithmetic Mean?
Let me tell you about the arithmetic mean—it's the simplest and most common way to find an average. You just add up a group of numbers and divide that sum by how many numbers there are. For instance, take the numbers 34, 44, 56, and 78; their sum is 212, and dividing by four gives you 53.
You might hear about other means too, like the geometric mean or harmonic mean, which pop up in financial calculations. There's also the trimmed mean, used for things like the Consumer Price Index (CPI) or Personal Consumption Expenditures (PCE).
Key Takeaways
- The arithmetic mean is the simple average, or sum of a series of numbers divided by the count of that series of numbers.
- In the world of finance, the arithmetic mean is not usually an appropriate method for calculating an average, especially when a single outlier can skew the mean by a large amount.
- Other averages used more commonly in finance include the geometric and harmonic mean.
The Arithmetic Mean in Finance
You see the arithmetic mean used in economics, finance, and other fields for data analysis. Even though it's not always reliable in some financial spots, it's still a go-to tool. For example, when you're looking at mean earnings estimates for a stock covered by 16 analysts, add up their estimates and divide by 16—that's your arithmetic mean.
The same goes for a stock's average closing price over a month with 23 trading days: sum the prices and divide by 23. It's straightforward, and most people can do it. Plus, it gives a solid measure of central tendency, even with big sets of numbers.
Limitations of the Arithmetic Mean
But watch out—the arithmetic mean isn't perfect, especially if there's an outlier that throws everything off. Say you're estimating allowances for 10 kids: nine get $10 to $12 a week, but one gets $60. The mean jumps to $16, which doesn't really represent the group. In that case, the median might be better.
It's also not great for investment portfolios with compounding, like reinvesting dividends. Analysts avoid it for present and future cash flows because it leads to misleading figures.
Important Note
Remember, the arithmetic mean can mislead with outliers or historical returns. The geometric mean is more suitable for series with serial correlation, particularly in investment portfolios.
Arithmetic vs. Geometric Mean
For those scenarios, turn to the geometric mean—it's calculated differently and fits series with serial correlation, like in investments. Returns in finance, such as bond yields or stock returns, are often correlated, and over longer periods, compounding matters more, making the geometric mean essential.
It uses the product of the numbers raised to the power of one over the series length. You can do it easily in Excel with the GEOMEAN function. Unlike the arithmetic mean, it factors in period-to-period compounding, so investors see it as more accurate for returns.
Example of the Arithmetic vs. Geometric Mean
Here's an example: a stock's returns over five years are 20%, 6%, -10%, -1%, and 6%. The arithmetic mean adds them up and divides by five, giving 4.2% average return per year.
But the geometric mean multiplies (1.2 × 1.06 × 0.9 × 0.99 × 1.06) and takes the fifth root minus one, resulting in 3.74%. Notice how the geometric mean is always smaller and more accurate here.
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