Volatility Targeting: Why Your Index Isn't as Stable as You Think

Volatility-targeting indices systematically deliver more volatility than their advertised target, so they should be treated as leveraged volatility-management strategies rather than low-risk instruments.

• The strategy dynamically adjusts exposure to a risky asset and holds the remainder in cash, reducing leverage when volatility rises and increasing it when volatility falls; targets such as 10% annual volatility are intended to smooth returns and risk.
• Nomura analyzes the limit as rebalancing intervals approach zero and derives the exact limiting distribution using a central limit theorem for dependent random variables.
• Two multiplier functions, U(λ) and V(λ), determine the bias, and both exceed 1; with a commonly used decay parameter λ = 0.9, V(λ) is approximately 1.1 or higher, implying at least a 10% underestimation of true volatility.
• The study identifies a competing effect between the historical-variance estimation window and rebalancing frequency, meaning that increasing rebalancing frequency does not make realized volatility converge to the stated target.
• It also derives a vega-conversion formula linking volatility sensitivity in the underlying asset to interest-rate sensitivity in the limiting diffusion, addressing the pricing and hedging of options on these indices.

Takeaway: Risk managers should adjust reported risk upward, while derivatives traders and index providers should incorporate the vega correction and the interaction between estimation windows and rebalancing frequency; the framework also extends to leverage caps and fees.