Shares of Intel (INTC -0.69%) continued to retreat today after an initial pop following the exit of CEO Pat Gelsinger. Intel added new members to its board this morning, but a picture of a chaotic search for a new CEO is emerging as well.

As a result, the stock was down 4.3% as of 11:15 a.m. ET.

A tweezer holding a computer chip.

Image source: Getty Images.

Did Intel make a mistake?

It's rare for a company to push out a CEO without a replacement ready or a clear strategy for finding one, but it seems like that's what Intel has done.

Since the board pushed Gelsinger into retirement, the company has reportedly contacted everyone from Marvell CEO Matt Murphy to former Cadence Design Systems CEO and former Intel board member Lip-Bu Tan as well as several executives from Taiwan Semiconductor Manufacturing.

Intel also presented at an investor conference, facing a number of questions from puzzled analysts about the CEO situation, and investors seem to be unsatisfied with the responses. While the stock underperformed under Gelsinger's tenure, he also seemed to have an ideal resume for the job as the former chief technology officer of the company and CEO of VMware for several years.

The timing is also odd as Gelsinger had just announced a massive restructuring in August, and Intel's foundry is set to roll out its 18A (18 angstrom) process, meaning the decision looks highly disruptive to the company's near-term priorities.

Intel also named former ASML CEO Eric Meurice and Steve Sanghi, the interim CEO of Microchip Technology.

What's next for Intel

It's unclear how long the CEO search will drag out, but the longer it goes on, the worse it will likely be for the stock and the company. Its foundry strategy now appears to be in limbo as well, as presumably, Gelsinger was ousted because of the challenges at the foundry division.

The company reaffirmed its guidance at the investor conference, but the chip stock could easily drift lower as questions about the hole in its leadership continue.