Is Arithmetic Return Bias Basis of Low Vol Anomaly?

Question

An observation in capital markets is that the connection between return and risk (measured as volatility) is not that straightforward (at least not as modern portfolio theory assumes). One interesting instance is the so called low-volatility anomaly:

It turns out empirically that stocks that exhibit low volatility show higher returns than high-volatility stocks.

I stumbled upon some articles which try to explain this anomaly away with the simple relationship between geometric and arithmetic means with continuous compounding:$$GM=AM-\frac{\sigma^2}{2},$$ see e.g. here and here.

My question
Can it be that easy? It looks almost insultingly simple to use this well known identity as the basis for the anomaly (which wouldn't be an anomaly after all). Do you know of any low-vol studies that control for that effect?

Answer 1

No, the "low-beta" anomaly is not the result of the difference between arithmetic and geometric mean returns.

Statistical tests verifying the existence of the anomaly rely on models employing the arithmetic mean returns, $$\mu_a = \mu_g + \frac{\sigma^2}{2}$$, hence the penalty excess volatility incurs when compounding returns over time does not explain the difference.