Most people who have pondered this question do not expect bitcoin to have any effect on the stock market.
Today I will explain why this expectation is based on a false premise.
The stock market is the place where public companies go to obtain capital. They exchange their shares at a certain price determined by the market.
However, with bitcoin as money it is difficult to see how the company, in its present form, would survive.
Companies and firms need the government in order to survive.
But as I have explained in previous posts, I do not expect governments to survive when we adopt bitcoin as our currency.
So no governments - no companies, no companies - no stock market.
Even if companies were to survive, it is difficult to see the stock market surviving. Could you imagine bitcoin holders investing their accumulated bitcoin in stocks and shares?
The Decentralized Autonomous Organisation (DAO for short) was invented in 2016 but it doesn't seem to be gaining a foothold. The first DAO ended in acrimony after a hacker made off with its funds.
There will be no companies and there will be no stock market in a bitcoin economy.