The equation shown in this blog subtracts
half of the square of some
variance (of what, it doesn't say). Volatility is often taken to mean standard deviation, and variance is the square of standard deviation. Thus according to the blog's equation (shown below) drag equals half the
fourth power (variance squared) of standard deviation, i.e. "volatility".
It cites as its source a
paper by Robert Becker, whom it calls Robert Decker. The expression there is correct. It's that equation that MJG has in mind, not the one in the page he linked to.
This blog also flails at simple things, like defining geometric mean: "Geometric mean is defined as the value
of a set of numbers by using the product of their values."
What "value" is that? (Rhetorical question - it's the nth root of the product, where n is the cardinality of the set.)
All this quibbling aside about how this blog page can't quote its way out of a paper bag, the real problem is that that it never defines volatility. Papers that the blog cites, both the Becker page above and
one by Tom Messmore discuss standard deviations of returns, but don't say that's what volatility means. AFAIK, they never mention the term "volatility".
In very simple form, all that these papers are saying is that if something goes up by 10% and then down by 10%, you don't break even.
(1 + 10%) x (1 - 10%) = 1 - 10% of 10% = 99%
When one gets to volatility, it is important to answer the question I alluded to at the start: variance (or standard deviation) of what? If one is going to equate volatility to standard deviation, this seems like a pretty important question.
The most obvious answer, given that we're talking about multiplicative (not additive) compounding, is to use the standard deviation of the
log of returns. Logarithms transform multiplication into addition. For example, if one charts prices logarithmically over time, one gets a fairly straight line (assuming a fairly constant rate of return).
In fact,
M* calculates historical return volatility using logs.
There's no "harm" per se in volatility; the "drag" is merely a computational artifact of simplistic calculations.
Here's a two part column on "The Myth of Volatility Drag" explaining this in more detail. FWIW, it's from CFA Institute (the organization that brands "CFA").
https://blogs.cfainstitute.org/investor/2015/03/23/the-myth-of-volatility-drag-part-1/https://blogs.cfainstitute.org/investor/2018/07/25/the-myth-of-volatility-drag-part-2/That's not to say that the term "volatility drag" is completely devoid of meaning. Kitces has a column where he explains how volatility drag causes Monte Carlo simulations to underestimate performance unless the software explicitly accounts for the "drag's" arithmetic effect.
The good news is that some Monte Carlo software tools, recognizing that most financial advisors report returns using the industry-standard geometric averages, already adjusts advisor-inputted return assumptions up to their arithmetic mean counterparts. However, not all Monte Carlo software automatically makes such adjustments.
https://www.kitces.com/blog/volatility-drag-variance-drain-mean-arithmetic-vs-geometric-average-investment-returns/
