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One theory is that many small business owners are using their PPP loan money to invest in the market. This is local restaurants with millions of dollars in the bank that can't really invest in their own business due to slow business. If they are fearful of going out of business then taking a shot in the stock market doesn't seem all that risky.

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PPP loans have go be used for employee retention.

https://www.sba.gov/funding-programs/loans/coronavirus-relie...

"Forgiveness is based on the employer maintaining or quickly rehiring employees and maintaining salary levels. Forgiveness will be reduced if full-time headcount declines, or if salaries and wages decrease."

Interesting theory. Is there a way to quantify how evenly investing, say $200B, across the S&P would affect the index's price?

It wouldn't be evenly distributed. It would disproportionately be invested in well know consumer brand as these would be novice investors.

So they pay it back into the economy, because quarantine restrictions prevent them from producing their own economic activity. Now that's stimulus.

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