Investors who own 5.4 percent of First California Financial Group’s shares have joined the ranks of disgruntled stockholders after the bank snubbed a buyout offer from Los Angeles-based PacWest Bancorp.

A letter dated May 23 from Loeb Offshore Management out of New York came through in the bank’s regulatory filings on May 29. Addressing Westlake Village-based First California’s board, the investors say they “wish for the company to be sold to the highest bidder as soon as possible and we would be sorely disappointed if the board were not to make this happen right now.”

First California CEO and President C.G. Kum could not immediately be reached for comment for this story.

First California has been under pressure to change course after investors have watched the stock trade at low prices despite the bank’s strong deposit base and aggressive acquisition strategy.

Los Angeles-based PacWest, a major player in the Tri-Counties, made public its unsolicited $7.25-per-share buyout offer for First California on May 9. Its offer represents a 32 percent premium over First California’s share price before the proposal.

“We’ve made this disclosure reluctantly, and only after First California summarily rejected our proposal and ignored our previous efforts to engage with them in discussions. Given the significant premium we have offered, we wanted to make sure all [First California] constituents are aware of this attractive proposal,” PacWest CEO Matt Wagner said in a release. “We are excited about the prospects for a combination of PacWest and [First California] and plan to work diligently toward a transaction.”

In an interview on May 9, First California chief executive Kum told the Business Times that PacWest’s offer was rejected because the Los Angeles lender wanted an exclusivity agreement that would have precluded him from talking to other potential buyers.

Kum told the Business Times his company received the offer on May 3 with a deadline to reply by May 8. He said he asked PacWest officials for more time. “I called the CEO [Matt Wagner] and asked him for a one-week extension to process this request properly. I was summarily rejected,” Kum told the Business Times. “The phone conversation ended with him saying either you sign by the deadline or we’re going to go public. … It’s a pressure tactic.”

By forcing PacWest to go public with its $7.25 offer, an asking price is now in full public view as a floor. “It’s a two-edged sword for them,” Kum said in the May 9 interview. First California’s shares have climbed 22.1 percent to $6.85 since PacWest broadcast its proposal.

Loeb becomes the fourth major investor group to publicly pressure the bank to improve the outlook for shareholders. New York-based Basswood Capital Management, the Pohlad banking family of Minnesota and Boston-based Castine Capital Management have also been leaning on the bank’s leaders to consider all options, including a sale. Together, the four groups own more than 16 percent of First California’s common stock.

In its May 23 letter, Loeb Offshore Management said it is “troubled” by First California’s formal response to PacWest’s offer. “While we are not able to decipher exactly what caused PacWest to ‘go public,’ we nevertheless are concerned that a buyer with a premium bid felt it necessary to go to shareholders with a ‘bear hug strategy,’ ” Loeb wrote. “If a formal process were in place in which potential buyers were accessing a data room as part of a normal auction process, then we doubt things would have eventuated in such a messy fashion. We can only hope the board of FCAL’s denial of exclusivity to PacWest was for a good and sufficient reason, all to do with maximizing value from a different bidder.”

Earlier this month, New York-based Basswood Capital Management wrote a letter to First California’s board, warning it would move to oust the directors if they didn’t consider a buyout offer. In its letter, Loeb warns that it, too, “will not hesitate to take vigorous action if we think the board is not engaged in a formal process to sell to the highest bidder.”