Inverse-volatility Weighting of Volatility Assets

Can long volatility investors improve performance of their portfolios by scaling positions inversely to some measure of volatility? In his March 2024 paper entitled "Volatility-Managed Volatility Trading", Aoxiang Yang tests volatility risk premium (VRP) timing strategies that hold a volatility asset and a risk-free asset, with the weight of the former inverse to some measure of volatility. He considers three volatility assets that are each month:

1. Long a 1-month variance swap contract, held to maturity (with prices sometimes approximated using VIX-squared).
2. Long a 1-month constant-maturity VIX futures portfolio (ignoring both a margin requirement and frictions required to maintain constant maturity).
3. Short a 1-month constant-maturity S&P 500 Index at-the-money (ATM) straddle (including a margin requirement of 100% of selling proceeds plus 20% of current S&P 500 Index level, but ignoring frictions required to maintain constant maturity).

Each month, he weights each asset by one of four measures related to stock market volatility:

1. Inverse of realized volatility.
2. Inverse of implied volatility (VIX).
3. Inverse of an autoregression forecast of next-month volatility.
4. Forecast of next-month VRP (which has an inverse VIX term) from a vector autoregression of realized volatility and VIX.

For each measure of volatility, he multiplies by a scaling constant that makes the respective long volatility portfolio have the same standard deviation of monthly returns as the S&P 500 Index. His benchmark portfolios hold the same assets with constant weights. He further analyzes performance of volatility portfolios during times of high volatility (highest 20%) and low volatility (lowest 80%). Using estimates for actual monthly prices for variance swaps during 1990-2023 (and actual prices for recent subperiods), for a constant-maturity VIX futures portfolio during 2004-2023 and for a constant-maturity S&P 500 Index ATM straddles portfolio during 1996-2022, he finds that: