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I wanted to ask how a stock, listed in different exchanges, in different countries and different currency operates.

Say a stock is listed in Nasdaq, and the same company has a stock listed in Tsx. Does the Nasdaq price affect the Tsx price as trading commences?

If a trader buys from one exchange, will it affect the price of the other?

Are there any benefits to being listed in two exchanges?

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Say a stock is listed in Nasdaq, and the same company has a stock listed in Tsx. Does the Nasdaq price affect the Tsx price as trading commences?

Not directly. Basically, an exchange is a market, and the price is defined only by supply and demand in that market. However, any substantial price differential for a commodity traded in multiple market creates an arbitrage opportunity, and there are many traders whose job it is exactly to find and use such opportunities. Their activity in turn has the effect of reducing the price differentials to the point where transaction costs make them unprofitable.

With high-frequency traders around, the time for a price differential to disappear is nowadays measured in milliseconds.

If a trader buys from one exchange, will it affect the price of the other?

Only through the mechanism mentioned above.

Are there any benefits to being listed in two exchanges?

It increases the liquidity of a stock.

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