Even in the days before perestroika, socialism, was never a monolith, within the Communists countries, the spectrum of socialism range from the quasi -market, the great expert on the economics of socialism, at what point on this spectrum of stat-ism would he designate a country as "socialist" or not. At that time, I was sure that any definite criteria existed to make that any sort of clear cut judgement.
So i was pleasantly surprised at the clarity and decisiveness of Moses answered. A stock market is crucial to the existence of capitalism and private property, For it means that there is a function market in the exchange of private titles to the means of production.
There can be no genuine private ownership of capital without a stock market. there can be no true socialism if such a market is allowed to exist. Exchange also act as the clear for each transaction, meaning that they collect and deliver the shares, and guarantee payments to the seller of security. this eliminates the risk to an individual buyers or seller that the counterpart could default on the transaction.