The author's argument is really a pseudo-argument about semantics. Yes, the geometric mean will always be less than the arithmetic mean, unless the returns are exactly the same year after year. Then, your equity "curve" is not a curve but a straight line with volatility=0. If the returns are NOT the same year after year, there will be poor years and losing years. The higher the volatility, the greater the chance of a large drawdown in capital. Say you take a 25% haircut during a bear market. You then need a 33% gain to get back to even, so that your return would be zero. This is unlikely and thats why high volatility portfolios perform poorly over the long term.