The correlation between S&P 500 as PE IRR (1994-2019) of negative 0.15 is misleading.
An LP invests in PE for 'realized' and 'not accrued' uncorrelated returns. In other words, the relevant correlation for an investor is between S&P and 'realized' PE IRR. Do PE Funds create monetization when equity markets are down?

In 2021, PE funds 1731 deals aggregating to $854 billion (S&P up 27%). PE equity exits aggregated $361 billion and $326 billion in 2020 and 2019, respectively (S&P was up 16% and 22% during this period).

PE realizations coincide with buoyant equity markets, and it appears that the relevant correlation between S&P 500 and 'realized' PE IRR is not negative but positive.