Robinhood Markets (HOOD -0.76%), whose online brokerage helped democratize investing while fueling the meme-stock trading frenzy that persists today, went public recently to great fanfare. Its debut was initially greeted with a collective "meh" -- shares opened for trading at $38 but closed out their first day below $35, an 8% drop.

Since then, the stock has whipsawed a bit, surging 50% one day only to tumble over 25% the next. At Thursday's prices, Robinhood sits around 25% above its IPO price, which leads to the question of whether stock traders will fully embrace the platform the way they did to boost shares of AMC Entertainment Holdings and GameStop by 1,000% or more.

There's certainly potential for Robinhood to gain meme stock status, but it's just as possible the online brokerage could be eventually shunned by those same traders.

Day traders watch their screens.

Image source: Getty Images.

Robinhood's meme stock potential

The online brokerage is growing fast. Monthly active users surged from 11.7 million at the end of last year to 22.5 million today. Robinhood itself says its growth has been because its business went viral, allowing 80% of its new accounts to join organically or through its referral program, which rewards investors with stock for referring someone to the platform.

More than half of its new customers are first-time investors. That's partly a result of Robinhood's technology making investing accessible to broad swaths of the public. By eliminating transaction fees for buying and selling shares, it has made it easy and frictionless for investors to get into the stock market with very little money.

Indeed, the average Robinhood investor is 31 years old and has an account balance around $4,500, according to the company. In comparison, the average account size at the biggest discount broker, Charles Schwab, is over $100,000.

The online brokerage sought to reward retail investors for their support of its app by reserving between 20% and 35% of its IPO shares for users of its platform. Typically, retail investors get less than 10% of an IPO. Similar to how AMC Entertainment CEO Adam Aron offered free perks at the concession stand to engage with the retail investors who boosted the theater operator's stock, Robinhood was looking to bring those who used its app into the fold. The Wall Street Journal reports it ended up selling shares to 300,000 of its users, or about 1.3% of the total accounts.

Person using mobile stock trading app.

Image source: Getty Images.

Factors arguing against it

Yet skepticism about Robinhood remains, with many traders still believing the brokerage operates in league with hedge funds.

When the trading frenzy broke out earlier this year and hedge funds were piling up massive losses as the shares of heavily shorted GameStop soared in value, Robinhood slammed the brakes on trading in the stock (and on a few others, too). First, traders were not able to buy any of its stock, only sell it, and then buying was restricted to just a handful of shares.

The restrictions sucked the wind out of the sails of the GameStop rally, and while a number of short-sellers still suffered significant losses, they were eventually able to unwind their positions, something that would likely not have happened had Robinhood not limited trading in the stock.

Yet Robinhood CEO Vlad Tenev said the hold was done to comply with Securities and Exchange Commission capital requirements. Because its separate Robinhood Securities division is required to make deposits with clearinghouses to cover the trades, and virtually all of the trading being done on the platform was occurring in just a couple of stocks, Robinhood was forced to limit buying until it could raise enough capital.

Still, the episode left a bad impression with many traders.

Does it matter?

Regardless, the Robinhood platform remains popular, and its future looks bright. If it can keep most of its customers until they retire (or convert them to other types of accounts, such as credit cards or micro payments, as it says it wants to), the value can expand greatly over time.

Robinhood also just acquired Say Technologies, a platform to connect shareholders with the companies they invest in. AMC Entertainment used Say's services on its most recent earnings conference call to field questions from retail investors, who dominated the call. In fact, only one Wall Street analyst was given time to ask a question.

With its shares now trading above their IPO price, there's certainly support for Robinhood Markets stock, but the online brokerage that enabled retail investors to create so-called meme stocks in the first place doesn't seem to possess the same qualities around which traders can rally.

It seems well on its way to democratize finance, but it's not likely Robinhood will become a meme stock itself.