You can be registered on more than one exchange. In the US alone you can be dual listed. It’s pricey to be listed in multiple exchanges so not really worth it (plus depending, you may run into conflicting listing requirements issues). But ownership and all that has nothing to do with being listed on exchanges. Think of a private company. Same mechanics apply to public companies in terms of capital structure and so on. Exchanges are just a regulated marketplaces to make the stock liquid.
A company may offer 100 shares, each owner possesses 1% of the company. Once those 100 shares are sold, if I didn’t buy one but want to, then I have to buy a share from someone who previously bought a share and still owns it.
I could meet that person in an alley and buy that share, but for very good reasons we make laws to make that very difficult to become profitable for me.
A stock exchange (NYSE, NASDAQ, etc) are like a farmers market for shares. The buyers and sellers meet there to trade their shares for cash. The people who operate each ‘farmers market’ want to keep things fairly civil and fair-use, so they only allow shares of certain companies to be traded in their exchange market. Those companies have to prove they aren’t lying about their financials and are generally obeying the laws of the land. Keep in mind that at this point of our story, the company is not selling shares in that ‘farmers market’. It is just a safe place for an owner and a buyer to meet to exchange items. Similar to police stations for Facebook Marketplace transactions: people are there to protect both the buyer and seller.
So a company pretty much needs to put in the resources and time to have their shares acceptable for trade in at least one exchange. Once they are ‘listed’ at one exchange, all sellers and buyers can meet there for their transactions of shares of that company. But sometimes the company has their own reasons to offer a second safe place for transactions of their shares. It might be difficult for certain buyers to get to one exchange, so they want to buy shares at an exchange closer to home, or one that provides specific rules to ensure more fairness or profit or safety for their purchase. The company has to invest resources and time to have their shares allowed in each additional exchange. But they gain more exposure to more market action, which can help support the company’s strategic goals. If I can’t buy a share of a company in my neighborhood ‘farmers market’, how willing am I to support that company as a customer or supplier or regulator?
So allowing shares to be traded in multiple places and under multiple sets of rules that make sense to multiple cultures… means the company needs to be listed in the exchanges in those multiple places.
Tldr: being listed is like creating a safe space for trade. The more safe spaces you allow your stuff to be traded, the more effort it takes from you to keep those safe spaces available. But it also means the more buyers you can attract.
Besides what’s already been said – the prices on the various markets will always be pretty much identical. Because otherwise there would be the possibility to buy the stock at one exchange and sell it on another at the same time and generate a risk free profit (also known as “free lunch”). Such a constellation would immediately be exploited by the market participants and the prices would again align.
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