How to determine whether a business is carried on in Hong Kong?

The question applies also to a trade or a profession likewise.

Once we have established that there is a business, the next question is: Is it carried on in Hong Kong? If no, then no profits tax is payable, unless the income is deemed to be chargeable under Section 15 of Inland Revenue Ordinance.  

Trading with Hong Kong should be distinguished from trading in Hong Kong --- vide UK court case Grainger & Son versus Gough 3 T.C. 467. The former (trading with Hong Kong) does not give rise to any profits tax liability; but the latter (trading in Hong Kong) does. 

Setting up a buying office in Hong Kong does not by itself make it chargeable to Profits Tax. For example, foreign supermarkets may send purchasing officers to Hong Kong to buy goods --- generally this is no trading in Hong Kong. But if a permanent establishment is set up in Hong Kong to buy and sell goods, the permanent establishment will be liable to pay profits tax.