Allianz Technology Trust (ATT) doesn’t hold heavy positions in many FAANG stocks, senior portfolio manager Walter Price told CNBC on Friday, partly because he prefers opportunities elsewhere, but also because he doesn’t see massive growth ahead.

FAANG refers to a basket of high-technology growth stocks — Facebook, Amazon, Apple, Netflix and Google — that have led the bull run of the last nine years. Those five stocks now represent 50 percent of the market cap of the Nasdaq 100 index.

“We have very small positions in Google and Facebook and many of the FAANGs — because we think there are great opportunities elsewhere, and it’s really hard for us to rationalize a stock that’s worth $500 billion to a trillion going up another 50 or 100 percent. I think that would be very improbable,” Price told CNBC’s “Squawk Box Europe.” Price also serves as a managing director with Allianz Global Investors.

For the first time in history, investors are anticipating a public company reaching a market value of $1 trillion, and analysts are putting their bets on Apple to win that race. And investors seem happy to keep in bidding up these tech stocks — only on Thursday did the Nasdaq briefly dip back from record levels.

But many now question the logic of buying some of these tech stocks and whether their valuations are justified. Some investors doubt the ability to still get bang for your buck, with one wealth management fund manager calling them “hideously overvalued.”

Price points to earnings as motivation for investors to stay in the game, despite the slew of negative headlines in recent months as major tech companies come under fire for personal data mismanagement and other unscrupulous practices.

“Maybe I’d put a little lower PE on the stock because of this regulatory risk and potential governments scrutinizing the company,” Price said. PE stands for price-to-earnings ratio, which is one of the most common tools used for stock selection. It’s found by dividing a stock’s current market price by its earning per share (EPS).

“I think there are also limits to the business — they have 50 percent of the advertising business already, and the advertising business is only growing a few percent a year,” Price said, referring to online ad behemoths Google and Facebook. “So I think they’re going take a lot more of the advertising business, but there is a limit to their growth.”

Not all investors subscribe to the “overvalued” argument. “A lot of these FAANG stocks, with the exception of Amazon support, very very reasonable valuations relative to their growth rates,” Leon Cooperman, chairman and CEO of Omega Advisors, told CNBC in May. Amazon’s stock price has grown a whopping 510 percent from 2013 to today.

Carol Pepper, chief executive of asset management firm Pepper International, would disagree with Price’s assessment. She told CNBC in April that stocks like Amazon and Facebook were the ones to hold onto for the next 10 and 20 years, saying that leading tech stocks are where “all the profit is migrating.”

Between 2013 and 2017, Facebook’s revenue grew from $7.87 billion to $40.7 billion, ranking first in social media company revenues. Pepper owns stock in both Facebook and Amazon, professionally and personally.

Since the start of 2018, all of the FAANG stocks have grown, but some have eclipsed others. Facebook and Google parent company Alphabet are up more than 6.6 percent and 8.9 percent, respectively, while Amazon has jumped 44 percent this year and Netflix has soared 88 percent.

Still, Allianz’s view is that there are other companies with fewer limits to their growth over next five years, Prince said. He pointed to media-related tech companies and sub-sector leaders like Nvidia and Intel, as well as those beyond U.S. markets.

“The leader in memory is clearly Samsung, leader in foundry is clearly TSMC (Taiwan Semiconductor Manufacturing Company),” he added, highlighting the value in Asian tech stocks. “I think it makes sense for investors to consider them as part of their portfolio.”

— CNBC’s Tae Kim contributed to this report.