Origins
The word 'stock' is native English, descended from Old English 'stocc' (tree trunk, stump, post, log, block of wood), from Proto-Germanic *stukkaz (a trunk, a stick, a stump), from PIE *stew- (to push, to stick, to knock, to beat). The same root produced Old Norse 'stokkr' (trunk, log), German 'Stock' (stick, rod, floor of a building), Dutch 'stok' (stick, cane), and the English verb 'stoke' (to push fuel into a fire).
The semantic history of 'stock' is among the most intricate in English. The word has accumulated meanings over a thousand years, each one a metonymic extension of the last. The core sense — a piece of wood, a trunk, a fixed post — gave rise to: 'stocks' (the wooden frame in which prisoners' feet were locked), 'stock' (the wooden body of a rifle, to which the barrel is attached), 'stock' (the main stem of a plant onto which a graft is made, hence 'rootstock'), 'stock' (a line of descent, as in 'of good stock,' because family lineage was imagined as a tree trunk from which branches grow), 'stock' (a store of goods, because supplies were stored on or around wooden posts and shelves), 'stockpile' (a pile of stored goods), 'stocking' (a covering for the leg, originally knitted on a wooden frame or 'stock'), and 'livestock' (living stock, animals held as property).
The financial sense is the most consequential extension. In medieval England, the Exchequer recorded debts and tax payments using tally sticks — wooden rods notched to indicate the amount owed. The stick was split lengthwise: the longer piece, called the 'stock,' was kept by the creditor (the person owed money), and the shorter piece, called the 'foil' or 'counterfoil,' was kept by the debtor. These wooden 'stocks' were transferable — a creditor could sell or trade his stock to another party, creating a primitive form of negotiable financial instrument. This practice, well documented from the 12th century, is the direct ancestor of the modern concept of 'stock' as a financial share.
Later History
The Bank of England, founded in 1694, issued 'stock' — certificates of ownership in the bank's capital. The 'stock exchange' where these certificates were traded (the London Stock Exchange was formally established in 1801) took its name from the instruments being traded. 'Stockholder,' 'stockbroker,' 'stock market,' 'stock option,' and related terms all preserve the connection between a piece of wood and a share in a corporation.
The compound 'livestock' preserves the older commercial meaning of 'stock' as property or goods. Broth made by simmering bones and vegetables is called 'stock' because it serves as a foundational supply (a 'stock' of flavor) for other dishes. In every case, the thread runs back to the same Old English word for a tree trunk: something solid, fixed, and foundational from which other things grow or derive.