Statistics
Three statistics metrics that you likely remember from school are mean, median, and mode. Mean is the average value amongst the sample, median is the middle value, and mode shows the most repeating value. These are some of the most basic statical measures we’ve learned about and are still used in financial calculations today. Most frequently, we hear of mean or average values when measuring the returns of a portfolio, but has your advisor discussed the geometric mean with you? In today’s article, we’ll discuss how both measures are used to calculate your investment returns and which is most appropriate when looking at your data.
Mean and Geometric Mean
I feel the best way to explain these two metrics is to look at an example. Consider the following table, which showcases a hypothetical investor’s portfolio starting with a $100,000 investment.
| Year 0 | Year 1 | Year 2 | Year 3 | Year 4 |
Portfolio Value | $100,000 | $594,000 | $380,000 | $194,000 | $99,000 |
YoY Return |
| 494% | -36.06% | -48.95% | -48.97% |
Portfolio value = Dollar value at the end of the year
YoY return = Year over Year return
This portfolio assumes no cashflows in or out
Simply looking at the starting and ending balance, deducing a loss of $1,000 would be easy. However, when you take the arithmetic mean of these values, the number may surprise you. The arithmetic mean of the returns above is calculated by adding the returns and dividing by the number of years (periods or n – which you will see as you read on). The calculation would be as follows:
(494+[-36.06]+[-48.95]+[-48.97])
4
The calculated arithmetic mean shows a return of 90.01% during this 4-year period. It sounds counterintuitive that a portfolio with a 90.01% average return over four years has an ending balance that is less than what was invested. Odd, but this is precisely why we recommend working with your advisor to understand these metrics and when they should be used. Though arithmetic mean is an important statistical measure, let’s look at how geometric mean calculates return and why this metric is important to understand.
Geometric Mean
The geometric mean reports the returns as an average of the sample. However, this metric also considers the compounding occurring within the portfolio. We all want our investments to compound every year, and the geometric mean provides visibility as to what the net compounding of the returns looks like. To calculate the geometric mean, we use the formula:
Source: www.financeformulas.net
As shown in the image above from Financeformulas.net, the calculation for geometric mean seems much more complicated. Let’s calculate this together:
[((1+4.94)(1-.3603)(1-0.4895)(1-.4897))1/4 ] -1 = -0.25%
A quarter of a percent loss in the four years is much more palatable and accurate when looking at the data.
Key Takeaways
The calculated geometric mean will be lower than the arithmetic mean when the number of periods is more than two and returns from each period differ. In the examples above, we assume an initial investment without further contributions or withdrawals. Most investors will likely add or take funds out of their accounts over time. We use the dollar-weighted return or internal rate of return (IRR) metric to calculate accurate returns while accounting for cash flow. We’ll save that metric for another discussion so we can dive deeper into the associated metrics and calculations.
Financial metrics can get complicated, and as mentioned in previous posts, it isn’t best to only focus on one metric when making decisions. As you learn more, keep in mind that our team of expert financial advisors at Whitaker-Myers Wealth Managers is available to discuss any financial planning needs or questions you may have. Schedule a time to meet with them and help answer your questions!
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