Volatility of volatility may seem an esoteric concept — the second moment of the second moment of a return distribution. But it can have real world consequences for portfolios, says Tim Choe, a quantitative analyst at Fidelity Canada Institutional.

He uses a simple illustration to show its significance. Take a $100 portfolio that averages 5% annually over 30 years, with 10% volatility and a payout of 4% each year. A Monte Carlo simulation suggests that the portfolio will sustain itself 92% of the time.

But that assumes constant volatility.

**Ups and downs **

If the volatility is varied, say by increasing it when markets goes down — as actually happens — then the 92% success rate diminishes, at times down to 50%, despite a constant mean return.

Volatility of volatility simply means incorporating more non-linearity into returns — the real-world case, says Choe. It becomes a drag because of the loss of 4% of the portfolio each year — the required payout acts as a fixed negative return.

Choe proposes two solutions. One is the straightforward approach, which is to target constant volatility through futures and options markets. Still, it is almost impossible to get volatility of volatility to zero, “because you have to predict 100% of the time what volatility will be in the future,” he says. This is, of course, impossible.

A second solution “requires a little more creativity,” he adds, and it uses low-volatility instruments — those whose beta is less than that of the market. If low volatility strategies are simply beta-adjusted arithmetic returns of the market, then the more volatility of volatility in down markets, the more alpha these strategies produce through geometric compounding.

It’s a novel approach — and one investors can use in today’s increasingly volatile investment space.