Yes, a stock can have a negative price-to-earnings ratio (P/E). 

The P/E ratio provides the market value of a stock compared to the company's earnings. The P/E ratio shows what the market is willing to pay today for a stock based on its past or future earnings. A high P/E typically means a stock's price is high relative to earnings, while a low P/E indicates a stock's price is low compared to earnings. The P/E is calculated by dividing the current price by the current earnings per share or EPS

Investors use the P/E ratio to determine if a stock is overvalued or undervalued. However, investors also use the P/E to gauge market expectations for future earnings growth. A high P/E might be due to investors expecting earnings growth in the coming quarters, and as a result, investors have been buying expecting the stock price to appreciate.  

A negative P/E ratio means the company has negative earnings or is losing money. Even the most established companies have had times when they've lost money, but companies that have consistently had a negative P/E ratio are not generating enough profit and run the risk of bankruptcy.

A negative P/E may not be reported. Instead, the EPS might be reported as "not applicable" for quarters in which a company reported a loss. Investors buying a company with a negative P/E should be aware that they're buying shares of a company that is losing money and should be mindful of the risks.

However, there are sectors with companies that have negative P/Es when the companies are just starting out. Pharmaceutical companies that invest billions of dollars in drug research may report a loss for years before turning a profit. Also, technology companies may post a loss, yet the stock price may rise significantly due to market expectations of positive earnings growth in the years to come. As with any financial metric, it's important to compare the P/E ratio with companies in the same industry.

For more on P/E ratios, please read "How to Use the P/E Ratio and PEG to Tell a Stock's Future."