Despite the market's strong showing so far this year, PayPal (PYPL 2.90%) hasn't experienced the same success. It's down about 17% versus the S&P 500's 19% rise. That's a drastic underperformance and might trigger investors to take action with the stock.

However, the stock price movement doesn't tell the full story, and there is a bull case to make. What should you do with PayPal stock? Let's find out.

Sell: PayPal hasn't captured the market share it needed to be successful

PayPal's payment processing business hasn't grown at lightning-fast speeds over the past year, posting high-single-digit percentage revenue growth. There are some questions about why PayPal isn't growing faster, and some investors believe it is outdated in a world with so many payment options. It has also failed to establish a strong in-person presence, as the phone makers have championed their own apps (like Apple and Google Pay) over third-party ones like PayPal.

Unfortunately, it's probably too late for PayPal to reverse this trend, making the company a ticking time bomb as it concedes market share in its primary offering.

Another factor is PayPal's tumbling gross margin. PayPal's cost of goods sold is basically the price of making a transaction, which has consistently risen over the past decade, causing its gross margin to fall off a cliff.

PYPL Gross Profit Margin Chart

Data source: YCharts

None of these trends bode well for the company, and may be a reason to get out of PayPal stock before things get worse.

Buy: The new CEO thinks he can make PayPal more efficient

On the flip side of PayPal's falling gross margin has been its rising profit margin. This metric took a significant dip last year, and through various efficiency efforts, PayPal has returned it to previous levels.

PYPL Profit Margin Chart

Data source: YCharts

But it's not done yet. New Chief Executive Officer Alex Chriss cast this vision for PayPal: "We will become leaner, more efficient, and more effective, driving greater velocity, innovation, and impact for customers." It's clear that Chriss thinks he can squeeze more profit out of the business, which would further help the buy side, especially if revenue isn't going to grow in the double-digit percentage range.

Another reason to buy the stock is how cheap it is. The market doesn't like PayPal stock, which has caused it to become incredibly cheap.

PYPL PE Ratio Chart

Data source: YCharts

At less than 17 times trailing and 11 times forward earnings, PayPal's stock is almost too cheap to ignore. Previous management took advantage of this by instituting a share repurchase program, which was smart.

With a new CEO and a bargain bin stock price, PayPal's stock has nowhere to go from here but up, making it a buy.

Hold: A reason to ride it out 

The hold side of the argument is essentially a combination of the buy and sell side. New CEOs (especially inexperienced ones like Chriss) can be great or struggle. No one knows how Chriss will do, so it may be a good idea to wait for a few quarters and see if he can turn around PayPal's business.

Additionally, selling shares at an all-time low valuation isn't wise. Buying high, selling low is a surefire way to destroy long-term returns.

PayPal is a damaged stock, not a damaged company, and the original investing thesis hasn't changed much. When purchasing a stock, you should be committed to holding it for three to five years. Those holding periods must sometimes be extended due to business success or market disdain for the stock.

So, where do I sit? I think PayPal shares are firmly between the buy and hold camps. I already own a decent amount of PayPal stock, so I don't need any more exposure. But if I didn't own any, I'd consider taking a small position due to the incredibly cheap stock price. PayPal is a sleeping giant, and eventually the stock will awaken and provide a strong recovery, although it may not regain previous highs.