I performed correlation analyses between the monthly implied volatility of the S&P 500 (VIX) and the SPDR S&P 500 ETF Trust (NYSEARCA:SPY). I used 20 years of historical data for these analyses.
The correlation between the daily change of the VIX and the daily change of the SPY is -0.72. This is not a surprise. The implied volatility tends to increase when stock prices drop. The VIX tends to mean revert to 20. This is an indication that the SPY also has mean reverting characteristics.
The correlation between the VIX level and the next day return of the SPY is 0.03. This is an indication, although weak, that the expected daily returns of the SPY increase when the VIX increases.
The average of the VIX is 21 and the average actual volatility of the SPY is 20. This is an indication that implied volatility is slightly overpriced.
The correlation between the VIX level and the difference between the VIX and the standard deviation of the next day price change of the SPY is 0.06. This is an indication, although weak, that the difference between implied volatility and actual volatility increases during falling markets.
The analyses above confirm the assumption that expected returns of stocks and of short put options increase when the VIX increases. It also confirms the assumption that implied volatility is slightly overpriced in general.
Disclosure: I am/we are short SPY, SVXY.