A Square system. Image source: Square.

In its relatively short history as a publicly traded company, payments processor Square (NYSE:SQ) has largely been a disappointment. Since it made its market debut last November, shares have been volatile, but have mostly trended down. That's been great for short sellers, who have targeted the company aggressively, but not for investors: If you purchased Square shares on its first day of trading, you may have lost upwards of 27%.

Still, there are plenty of reasons to like Square. The following charts provide a snapshot of the trends affecting the company's business.

Square is processing more and more payments

Square's partners process billions of dollars worth of goods and services each and every quarter, and Square provides this metric to investors in the form of its gross payment volume (GPV). Last quarter, Square's partners used its credit card readers to accept $10.3 billion from their customers, a 45% increase from the first quarter of 2015. GPV growth has begun to slow, but remains strong. Very little of this money actually goes into Square's coffers, but it underscores the strength of Square's business. The more money Square processes, the more companies derive value from its products.

Image source: Q1 2016 shareholder letter.

Square's share of those payments has remained relatively flat

Last quarter, Square collected 2.92% of every dollar it processed. Most of that went to credit card companies, but it was able to keep some of that as transaction profit. Square's transaction revenue and transaction profit as a percentage of GPV has remained steady in recent quarters. It declined slightly last quarter, but that was largely due to the rollout of Square's new reader. "If you exclude out the promotional credit for the new chip and EMV reader, [transaction revenue as a percentage of GPV] was 2.95%," Square's CFO Sarah Friar explained on the company's May earnings call.

Image source: Q1 2016 shareholder letter.

Larger sellers are using Square

Square's credit card readers appeal mostly to small businesses. But Square's small business partners vary in size quite drastically. Square tracks and categorizes its partners by their GPV, putting them in categories based on the amount of transactions they process, projecting their sales out for a given year. Over time, larger sellers have grown to represent a more significant share of Square's partner base.

Image source: Q1 2016 shareholder letter.

Retailers are buying Square's new reader

In December, Square began selling its latest reader -- a credit card processor that's capable of accepting both mobile payments and chip-enabled cards. Square's new hardware has been popular with a wide variety of its partners, but retail, services, and health and beauty have generated the most demand. Although this represents only those Square sellers that have purchased its latest reader (those who have not purchased it do not show up in the data), it provides some insight into the makeup of Square's overall base of partners.

Image source: Q1 2016 shareholder letter.

Square's revenue is growing at a rapid pace

As it processes more payments and sells more hardware, Square is seeing its revenue surge. Last quarter, Square's adjusted revenue rose 64% on an annual basis. Square's management prefers to highlight its adjusted revenue, as it excludes revenue related to the transactions it currently processes for coffee giant Starbucks. Square's relationship with Starbucks is set to end later this year.

Image source: Q1 2016 shareholder letter.

Service revenue is surging, but remains relatively small

The single most important aspect of Square's business may be the demand for its services. Square can profit by expanding its base of sellers, processing more payments, and collecting a modest cut, but Square's real potential may lie with its services, including Square Capital and Square Customer Engagement, as they offer greater margins. So far, demand for Square's various services has been modest, but sales are rising rapidly. 

Image source: Q1 2016 shareholder letter.

This article represents the opinion of the writer, who may disagree with the “official” recommendation position of a Motley Fool premium advisory service. We’re motley! Questioning an investing thesis -- even one of our own -- helps us all think critically about investing and make decisions that help us become smarter, happier, and richer.