VVIX/VIX as a Return Indicator?

Is the ratio of implied volatility of implied volatility (CBOE VVIX Index), interpretable as a measure of changes in investor fear level, to the CBOE VIX Index itself a useful indicator of future stock market returns? To investigate, we relate monthly VVIX/VIX and monthly change in VVIX/VIX to monthly SPDR S&P 500 ETF Trust (SPY) total returns. Using end-of-month levels of both VVIX and VIX and dividend-adjusted monthly SPY closes during September 2006 (limited by VVIX) through March 2025, we find that:

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