Coinmetrics has some interesting charts to see the correlation between the prices of two different assets. Most are crypto related, but there are a few traditional assets such as Gold and S&P. The latter is the most approximate entry to compare to, of those available.

In order to see the correlation factor at work, I’m comparing BTC/S&P and BTC/ETH on the same chart:

https://coinmetrics.io/correlation-charts/#assets=btc-s&p,btc-eth

The chart shows a strong positive correlation of between BTC and ETH, even more so since April 2018 with a value of around 0,8 (maximum is 1 on the scale).

On the other hand, the hypothesis of the OP should show a significant negative correlation between BTC and S&P, meaning that when one goes up the other goes down and vice-versa. The closer the correlation to the value of -1, the more negative correlated they are. Nevertheless, the correlation factor between BTC and S&P flips positive and negative, with values within +/- 0.2, which is a weak to negligible correlation with variable direction.

At least with S&P, the hypothesis does not seem to stand as valid.

Additional: https://coinmetrics.io/correlation/