The author is making very valid points.

It is key to understand the meaning of arithmetic and geometric average returns, and when they should be used - and this may depend on the nature of the investment, and the investment strategy you use.

For example take a zero coupon bond trading at 50 cents on the dollar. It will be redeemed at par in 20 years. Your strategy is to buy and hold to maturity. The geometric growth rate is 3.53% per annum. The arithmetic average return is 5% per annum.

So fine, geometric growth rate is below the arithmetic. But then again, so what? How does the arithmetic mean help you? You can't invest at that rate.

And in this case, volatility doesn't even matter if you hold to maturity. Regardless of what the volatility is, high or low, your geometric growth rate will always be 3.53% with that investment using that strategy.

If anything, volatility affects the arithmetic average, not the geometric. Will, "volatility inflation", good point!