The CEO of BP said in an interview this week that the Green New Deal was "unrealistic," while the outgoing CEO of JPMorgan took aim socialism.
"The subject of these tweets has increasingly turned toward market-moving topics, most prominently trade and monetary policy."
The banking news raised eyebrows in the context of the Cambridge Analytica data misuse scandal.
The hacking compromised information in 83 million household and small business accounts.
Authorities in the United States and Europe have fined seven banks over $10 billion.
The cyberattacks may have been fueled by sanctions in the escalating conflict between Ukraine and Russia
JPMorgan admitted that it had failed to raise the alarm about Madoff's activities to a bank regulator, even though employees had identified inconsistencies in Madoff's fund's returns.