Technology stocks had another scorching weeklong run last month, capped off by Amazon’s startling decision to buy Whole Foods for $13.4 billion.

And like many stock pickers these days, the portfolio managers at Parnassus Investments, a mutual fund company that invests mostly in large American companies, were at their wits’ end as they gathered for the firm’s weekly investment committee meeting.

“These stocks are hitting highs — again,” said Todd Ahlsten, who oversees the firm’s $15.6 billion core equity fund, pointing out that even low-risk exchange-traded funds were piling into the likes of Facebook, Apple, Google, Netflix and, yes, Amazon.

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The explosion in low-cost, index-tracking ETFs and soaring technology stocks is generating existential angst among portfolio managers working in traditional mutual fund companies.

Products of a culture where fame and fortune have accrued to those with the skills to pick stock market winners — foremost among them Warren Buffett and Peter Lynch at Fidelity — these brainy stock experts are now finding it harder than ever to fulfill their core function: investing in stocks that beat the broader market.

That is largely because a torrent of money has been pouring into machine-driven tracking funds, which allocate money to stocks like Facebook, Apple, Amazon, Netflix and Google’s parent Alphabet — known as Faang stocks — on the basis of how big they have become and where they rank in an index.

For stock pickers like the ones at Parnassus, who pride themselves on their ability to zig where others zag by uncovering undervalued gems, such follow-the-crowd investing is anathema — and it is showing up in the numbers.

According to S&P Dow Jones Indexes, 88 percent of mutual funds that invest in large capitalization stocks trailed their benchmark over a five-year period ending last year.

This period of underperformance has been most acute in the last 12 months, a period when the Faang stocks have outpaced the market by a large measure.

Value-oriented investors who screen out companies that do not meet strict social standards, Ahlsten and his team have, over the last year, generated a respectable 14 percent return in their core equity fund where they have large stakes in Apple and Google.

But the positions are not nearly enough to keep pace with the 18 percent return of the Standard & Poor’s 500 index, within which six of the 10 top components are now technology stocks.

Making matters even more stressful, Amazon, which they do not own, just agreed to buy Whole Foods — a deal that sent its stock even higher and could threaten a number of companies in the Parnassus portfolio.

“This is giving me a flashback ... with all this correlation,” said Benjamin Allen, Ahlsten’s partner on the fund, recalling the lemming-like behavior of investors that led to the collapse of Long Term Capital Management in 1998. “It is just mindless buying of these technology names.”

Over the past year through May, $263 billion has exited actively managed mutual funds that invest in U.S. stocks while $308 billion has poured into ETFs and index funds. Vanguard and BlackRock have vacuumed up just about all of this cash, according to Morningstar.

This wave of money, combined with the slack performance of its old-style equity funds, prompted Laurence Fink, the CEO of BlackRock, to shake up his stock-picking ranks this spring.

Funds were revamped, managers were let go and, in so doing, Fink questioned whether, in light of technological advances and the spread of information, stock experts could actually add value when it came to assessing widely followed companies in the S&P 500 index.

More than $5 trillion remains invested in active-oriented funds, according to FactSet, a data provider. It is still early to determine if Fink is describing a trend that will eventually reach its limits or whether a more fundamental, longer-term reordering of the stock-picking process will take place.

The Parnassus portfolio managers are not alone in their fears. Of late, the argument has been made that the rise of machines and passive investing is distorting the broader market.

And last week, a Bank of America report called it the “ETF-ization” of the S&P, warning that passive mutual fund assets in the United States have doubled to 37 percent today since 2009.

For the moment, though, be it hedge funds that refuse to chase Amazon because it disdains showing a profit, or value investors who blanch at the thought of buying Netflix at a price-to-earnings multiple of 360, the frustration is beginning to boil over.

Compared with many of its peers, Parnassus has held up fairly well in terms of outflows.

The company was founded in 1984 by Jerome Dodson on the notion that buying companies that respect the environment, cultivate harmony in the workplace and have sound governance policies would generate decent investment returns in addition to making investors feel virtuous.

It has been a well-timed strategy, one that kicked into high gear after the financial crisis as investors embraced both the fund’s philosophy and its performance.

Assets under management shot up to $25 billion today from $1.8 billion at the end of 2008.

Still, as technology stocks have skyrocketed, the returns of Parnassus’ bellwether fund have lagged. Some 80 percent of the fund’s peer group has done better over the past year.

Over the longer term, however, the Parnassus results are better. For 10 years, the core equity fund handily beats its benchmark — 9 percent compared with 7 percent, a record that outpaces 98 percent of the competition.

But at a time when investors are transferring cash from pricey mutual funds to lower-cost — and to date, better-performing — exchange-traded funds falling back on 10-year performance figures has become a less reliable defense.

Through the first five months of the year, according to Morningstar data, the core equity fund has experienced outflows. They are small — $150 million out of a $15 billion fund — and they come after five consecutive years of inflows.

Nevertheless, they have been enough to concentrate minds at Parnassus.

“It’s stressful — we are competitive people,” Allen said. “I don’t like calling my clients up every quarter and saying ‘Sorry.’”

Embracing a deep-value style of investing, Parnassus is no momentum investor. And Allen, who was appointed president this year and is expected to succeed Dodson in running the firm, has made it clear to fund holders that his ultimate aim is to outperform when stocks are tanking — as core equity did in 2008 — as opposed to running ahead of a bull market.

So instead of chasing Amazon and Facebook, Allen and team have been betting big on health care stocks like Gilead Sciences.

“There is a herd mentality out there,” he said. “People are buying stocks irrespective of valuations — if we can’t do the math, we are just not going to own it.”

Parnassus has a quirky culture. Turnover is low and just about all of its investment professionals start as summer interns, an approach that exposes potential employees to a three-month period of scrutiny.

As per the orders of Dodson, men must wear ties — in the office and on the road — a sartorial demand that stands out in San Francisco’s ultra-casual workplace culture.

To foster togetherness, at the end of each investment committee meeting, participants are asked to offer up a personal tidbit about how they spent their weekends.

Deep-value stock pickers often exhibit idiosyncratic qualities, and that is true here. Allen, for example, keeps his desk virtually clutter-free, to encourage lean, disciplined thinking. And Ahlsten, to keep his own mind clear, limits himself to one hour of screen time (phone, computer or any other device) per day.

Lately, it has been Amazon filling up their brains, and following the investment committee meeting, the two portfolio managers huddled in Ahlsten’s office.

At its current valuation, they agreed, the stock was too expensive to buy.

But the Whole Foods transaction poses a potential threat to at least five companies that Parnassus owns — from Sysco, the food distributor, to CVS, the pharmacy chain.

All five have trailed the index over the past year, and the worry is that the Amazon deal could put further pressure on them.

“The threat to these companies has increased,” Allen told his colleague. “It reveals what Jeff Bezos’ ambitions are, which are to disrupt and be part of everything. But the reality is that Amazon is not going to take over the entire world.”

At least they hope not.

Landon Thomas Jr. is a New York Times writer.