• Joe Moglia, former CEO of online trading platform TD Ameritrade, issued a stern warning Thursday about using leverage to try to outsize returns in meme stocks.
• "My biggest concern is what's going on with the individual investor" using borrowed money to trade more than they have, Moglia told CNBC's "Squawk Box."
• Brokerages, particularly those catering to individual investors, need to do a better job of educating their clients, he added.

Joe Moglia, former CEO of online trading platform TD Ameritrade, issued a stern warning Thursday about using leverage to try to outsize returns in meme stocks.

"My biggest concern is what's going on with the individual investor" using borrowed money to trade more than they have, Moglia told CNBC's "Squawk Box," as AMC Entertainment shares whipsawed in early trading and dropped as much as 30%. Shares turned positive in the afternoon, before dipping once more to close down nearly 18%.

The stock's year-to-date gain, despite Thursday's earlier sharp pullback, was more than 2,300%. AMC shares nearly doubled in the prior session.

Another Reddit favorite, BlackBerry, soared Thursday before cutting those gains after closing up nearly 32% in the prior session. Shares returned to positive territory in the afternoon and were up 4.1% at the end of the day.

Bed Bath & Beyond, also caught up in the meme stock mania, closed down 27.8% on Thursday. It soared 62% on Wednesday.

"They got to be able to understand when they use leverage what that really means. Leverage on the way up is a great thing. Leverage on the way down can rip your arms off," added Moglia, currently chairman of Capital Wealth Advisors.

The wild swings in AMC on Thursday started after the movie theater chain filed to sell 11.55 million shares "from time to time." As a disclosure, the company said, "We caution you against investing in our Class A common stock, unless you are prepared to incur the risk of losing all or a substantial portion of your investment."

On Thursday afternoon, the movie theater operator announced it completed the share offering and raised $587.4 million.

AMC revealed Tuesday in a securities filing that it raised $230.5 million in a stock sale to depressed debt firm Mudrick Capital Management, which reportedly sold those new AMC shares immediately for a profit.

With meme stock prices and headlines about the companies' businesses moving quickly, brokerages —particularly those catering to individual investors — need to do a better job of educating their clients about the risks of what seems like an easy way to make money and when to sell, Moglia said.

"For example, if you bought AMC at $10 and its goes to $20, is that not enough of a profit? If it goes to $30, $40, at what time do you start to trim that position or in effect get rid of that position altogether. We have to do a better job with the day traders," he added.

Disclosure: The $22 billion Charles Schwab-TD Ameritrade merger closed in October 2020.