When stocks are trading near their all-time highs, especially amid a recession, it can be risky to hang on to them. If there's a market crash, investors typically shed their portfolios of their most expensive holdings and look for cover in safer stocks that aren't trading at sky-high prices. Below are three alarmingly expensive stocks that investors should think long and hard about keeping in their portfolios.

1. Quidel 

Quidel (NASDAQ:QDEL) shares are up a staggering 220% since the beginning of 2020, while the S&P 500 is flat. The diagnostics and research company's been on fire since the U.S. Food and Drug Administration (FDA) granted emergency use authorization (EUA) for its Lyra SARS-CoV-2 Assay, a rapid point-of-care test, on March 17. Then, on May 8, the FDA issued another EUA for the company's Sofia 2 SARS Antigen FIA, which can help detect SARS-CoV-2 and generate results in as little as 15 minutes.

A yellow road sign with the word "overpriced" on it

Image source: Getty Images.

With more than 3 million coronavirus cases in the U.S., there's a significant need for testing across the country. Although Quidel's not the only company offering coronavirus testing, it was one of the first to receive an EUA from the FDA for one of its tests, and the stock's been soaring ever since.

On July 6, the company announced that its second-quarter revenue will be between $201 million and $202 million -- a year-over-year increase of at least 86%. But even with all that growth, the stock's still an expensive buy.

Shares of Quidel are trading at more than 100 times their earnings, and even with the increase in revenue, the company's stock will still be at a multiple of more than 15 times sales.

Those are some incredibly high valuations, making the stock high risk for correction should there be a market crash.

2. Veeva Systems

Veeva Systems (NYSE:VEEV) has also been a hot commodity since the coronavirus outbreak. Up 74% year to date, shares of Veeva are trading around their all-time highs.

The company's cloud-based products, Veeva Vault and Veeva Commercial Cloud, help healthcare companies manage their data and customer relationship management systems. With people working remotely and needing more flexible, cloud-based solutions, it's easy to see why Veeva has been a hot buy this year.

The company released its first-quarter results for fiscal 2020 on May 28. Revenue of $337 million was up 38% from the prior-year period. Veeva's profit margin also continues to be strong, coming in at 26% in Q1. Although that's down from the 30% profit margin it recorded a year ago, it's still a very healthy percentage of revenue that's flowing through to its bottom line.

In the earnings release, Veeva also noted several new ways it's helping clients during the pandemic, such as offering remote meetings free of charge, providing telehealth metrics, processing drug sample requests online, and supporting remote monitoring and review of documents. These are great examples of the growth opportunities the company's been undertaking and the value it's adding for its clients, which could lead to even stronger sales numbers in the future.

While Veeva's doing a lot of good, this unfortunately doesn't change the fact that the stock is extremely expensive. Like Quidel, shares of Veeva are trading at more than 100 times earnings, and its price-to-sales multiple is higher than 30. Veeva wasn't a cheap stock to begin with -- it was trading at similar multiples a year ago -- but now it's even more expensive.

3. Zoom

Zoom Video Communications (NASDAQ:ZM) stock is the highest performer on this list, up about 270% year to date. Although the stock's been falling in recent days, it's still not far from its all-time high of $281. Zoom's been synonymous with remote work as offices around the world have been able to stay connected using the company's video chat software. Its ease of use makes the software appealing; with the click of a link, even a novice computer user can quickly connect to a virtual meeting.

On June 2, the company released its first-quarter results for fiscal 2020, in which its sales of $328 million were up an amazing 169% year over year. Management expects sales to reach as high as $500 million in the second quarter. The tech company reported a profit of $27.1 million in Q1, up from just $2.2 million a year ago.

The challenge for Zoom is that it's facing lots of competition. From Microsoft Teams to Facebook Rooms and Google Meet, there are plenty of options out there for businesses to keep in contact using video. And that competition makes it all the more difficult to justify Zoom's mammoth price-to-sales multiple of more than 90 and its price-to-earnings ratio of nearly 1,500.

What should investors with these stocks do?

If I were holding any of these stocks, I'd be selling them today. For one reason, their valuations are through the roof; for another, I'd probably have some terrific profits to cash out if I bought them weeks or months ago. They are all good businesses to invest in, but their stock prices are just too expensive, especially with a possible market crash right around the corner.

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.