In their strictest financial senses, stock is a mass noun (meaning it can’t be plural), and share is a count noun (it can be plural). Shares are units of stock. These writers, for instance, abide by this distinction:
Last year, Quest repurchased about 15 million shares of common stock for $750 million. [Dow Jones Newswires]
President & CEOÂ Oleg Khaykin sold 6,870 shares of IRF stock on 12/01/2010 at the average price of 28.77. [Guru Focus]
Nektar Therapeutics Inc. sold 19 million shares of stock, which brought it $220.4 million in net proceeds after paying its underwriter. [San Francisco Business Times]
But stock can become plural when used synecdochically to refer to a stock market, a portfolio, or a segment of a market—for example:
Japanese stocks fell for the first time in three days. [Bloomberg Businessweek]
Stocks are falling amid a slew of earnings from Verizon, 3M, DuPont and others, and ahead of tonight’s State of the Union speech. [MarketWatch]