not buying equities. accepting certain equities as collateral.
The fed usually posts all purchases and sales on the internet, sometimes in nearly real time, particularly with Treasuries I have found. I think the Dodd Frank rules require posting within two years.* They typically identify exactly what they bought or sold and how much. So far as I'm aware they have never bought equities. They did act as an intermediary in the purchase of GM stock during the financial crisis. The stock was transferred to the Treasury within 24 hours.
*Significant parts of the Act were repealed in 2017. Don't know if disclosure was affected. The Bernanke fed was especially transparent re bond transactions.