I asked this question when I worked at Google, and the answer was that our legal department thought it was a bad idea for two reasons.

Reason one is insider trading. The information Google has is aggregated from many sources, including insiders. If Google trades on that information they risk violating insider trading laws.

Reason two is privacy. The laws here vary a lot from country to country and Europe is generally the strictest. But the summary is that there are privacy laws which say it is okay to use some types of personal information as long as it is only used to improve a service being provided. Trading wouldn't fall into the category of allowable use.