As Spitznagel wrote: It is well known that steep portfolio losses crush long-run compound annual growth rates (CAGRs).
Standard quantitative finance assumes that a portfolio’s net asset value changes follow a geometric Brownian motion (and thus are log-normally distributed) with arithmetic average return (or “drift”)
[5]) The mathematics behind the volatility tax is such that a very large portfolio loss has a disproportionate impact on the volatility tax that it pays and, as Spitznagel wrote, this is why the most effective risk mitigation focuses on large losses: We can see how this works by considering that the compound (or geometric) average return is mathematically just the average of the logarithms of the arithmetic price changes.
It is the key to the kingdom, and explains in a nutshell Warren Buffett’s cardinal rule, ‘Don’t lose money.’”[7] Moreover, “the good news is the entire hedge fund industry basically exists to help with this—to help save on volatility taxes paid by portfolios.
The bad news is they haven't done that, not at all.”[6] As Nassim Nicholas Taleb wrote in his 2018 book Skin in the Game, “more than two decades ago, practitioners such as Mark Spitznagel and myself built our entire business careers around the effect of the difference between ensemble and time.”[8]