Facebook's 40% plunge from its initial-public-offering price of $38 in May has millions of investors asking a single question: Is the stock a buy? The short answer is "No." After a recent rally, to $23 from a low of $17.55, the stock trades at high multiples of both sales and earnings, even as uncertainty about the outlook for its business grows.

The rapid shift in Facebook's user base to mobile platforms—more than half of users now access the site on smartphones and tablets—appears...