• Arm Holdings jumped another 6% at market open on Friday.
• Arm began trading Thursday with shares in its blockbuster IPO priced at $51 each, valuing the company at about $54.5 billion.
• A lot of focus this week has been on some of the risk around the company including its exposure to China and rising competition from a rival semiconductor architecture, backed by some of Arm's biggest customers.

Arm Holdings jumped another 6% on Friday at the market open, but those gains cooled off some in its second day of trading after its Nasdaq debut Thursday.

The British chip designer's shares were trading at just more than $67 around the market open, implying a valuation of more than $72 billion. Arm shares were even higher earlier in premarket trading but pared some of those gains.

It comes after Arm shares rallied nearly 25% on the company's first day of trade on Thursday. Shares for its blockbuster IPO were originally priced at $51 each, valuing the company at about $54.5 billion.

With the rally ongoing, Arm continues to trade at a premium to chip giant Nvidia, even as its faces headwinds to its growth. Some analysts have expressed concerns over the valuation.

"The pricing is expensive … I think a lot of investors are thinking on the sidelines … and waiting to see how they execute on those drivers," Ben Barringer, equity research analyst at Quilter Cheviot, told CNBC's "Squawk Box Europe."

SoftBank, which acquired Arm in 2016, floated about 10% of the company, with the Japanese giant holding on to 90% ownership.

SoftBank has faced criticism about its investment strategy with its massive Vision Fund tech investment arm posting a significant loss in its last fiscal year. This has been enough to put off some investors from the Arm IPO.

William de Gale, portfolio manager at BlueBox Asset Management, said he did not invest in ARM.

"In the end, we decided that we were too worried about corporate governance with SoftBank still controlling the company with a questionable record for asset allocation," de Gale told CNBC's "Street Signs Europe" on Friday.

"So we wanted to watch from the sidelines for a bit to watch how the company operates as an independent business."

Still, there was huge demand for shares, with several reports this week ahead of the initial public offering suggesting the listing was multiple times oversubscribed.

Arm, whose chip architecture is in 99% of the world's smartphones, managed to get strategic investors including Apple and Nvidia to buy shares in the listing.

A lot of focus this week has been on some of the risk around the company including its exposure to China and rising competition from a rival semiconductor architecture, backed by some of Arm's biggest customers.

For it's part, Arm CEO Rene Haas told CNBC on Thursday that the company's China business is "doing well" with strong potential in data center and automotive applications.

Arm's strength has typically been in smartphones and other consumer electronics. But the company is now looking to new areas including artificial intelligence to grow its business.

"We diversified our business. We've got significant growth in the cloud data center and in automotive," Hass said.