Yes, since shares of joint stock are considered merchandise since they were purchased with the intent to sell them at a greater price. They are to be calculated at their current market value on the day Zakah is due. For example, if I purchase $1,000 of Apple Computer stock with the intention to sell them after a few years when the value increases, I will pay on the market value every year.
However, if you are actually a real partner of a company or purchase stocks with the primary purpose of acquiring a dividend from the profits of the company, then the share is not considered an article of trade but rather a portion of ownership in the company. Therefore, you will pay Zakāh on merchandise for sale, raw materials, and cash equivalents but not on assets such as machinery, furniture, and buildings.
[Shaykh] Mustafa Umar