“Whenever the market has volatility we lose money. We call this ‘volatility drag.’”
“The more volatile our year-to-year returns, the less money we actually have. . . . We call this the ‘volatility drag.’ I also like to call it the volatility tax.”
— Creekside Partners
Scary stuff! But reading these articles, I found myself wondering, is it actually true? Like so many myths, there is a kernel of truth. But the interpretation that volatility is an active force, “pulling” down returns and costing you money, is simply not correct.
In Part 1, we will explore the crux of the issue, understanding the geometric mean. In Part 2, we will apply this understanding to arguments for volatility drag.
Where—Force Art Thou?
Remember free-body diagrams from physics class, the drawings of an object with arrows representing the forces? Drag was a common force, present when an object moved through a medium like air or water. So where does the “volatility drag” force come from? What medium is it that prices move through?
The proposition is that the difference between the geometric mean and the arithmetic mean of a series of returns represents “drag.” Let us revisit the geometric mean, and perhaps we can find a force. (The geometric mean is often encountered in the form of compound annual growth rate (CAGR). CAGR is a special case of geometric mean, useful when the initial value and ending value for n periods are known.)
To motivate the discussion, let’s look at an example of past performance data on a mutual fund prospectus that makes use of the geometric mean to calculate the “average annual total return.”
Average Annual Total Return
If you have read a mutual fund prospectus, then you have seen a chart similar to the following one, showing the annual total returns for the previous 10 years.
Annual Total Returns — Vanguard Extended Market Index Fund Institutional Shares
The percent returns are the year-over-year numbers and are straightforward. These charts are accompanied by a table that includes average annual total returns for one, five, and 10 years.
Average Annual Total Returns for Periods Ended 31 December 2013
Here we must be a little cautious: This use of average is not the most common usage. In most cases, when we see the term average, we add up the numbers and divide the total by the number of elements. A quick check with the five-year return before taxes, calculating the usual average, is 23.75%. But the table says 22.68%. That is because there is more than one type of average, or mean, and in this case the geometric mean is the appropriate one to use. So why is it “appropriate”?
Means: A Quick Refresher
The arithmetic mean is the one with which we are most familiar. It is a property of sums: 2 + 8 is a sum of two elements. The one value that relates the number of elements to the sum of the elements is the arithmetic mean.
2 + 8 = 10 and the arithmetic mean is 10/2 = 5
The geometric mean is the analogous property for products. 2 * 8 is a product of the same two elements. The value that relates the number of elements to the product of the elements is the geometric mean.
Yes, and we can find it with the square root. √16 = 4. This is the geometric mean.