A California-based investment firm has called on MicroStrategy to remove longtime chief executive Michael Saylor, buy back $455 million in stock and reinstitute quarterly investor calls after a nine-year hiatus as a way to boost the Tysons Corner-based company’s stock price.

The suggestions were made in a critical letter that Apex Capital sent to MicroStrategy’s executives and board of directors this week. The letter also was filed with the U.S. Securities and Exchange Commission on Monday.

“This is, frankly, a highly unusual situation where the company’s conduct is sufficiently egregious to have earned it pariah status,” Gil Simon, Apex Capital’s portfolio manager for technology and entertainment, said in a telephone interview Tuesday.

MicroStrategy spokesman Warren Getler said the company had no comment.

Apex Capital holds 467,100 shares of MicroStrategy stock, according to the letter. That represents 5.15 percent of MicroStrategy’s outstanding Class A shares. Apex has been an investor in MicroStrategy for two years, Simon said.

MicroStrategy creates software and mobile applications that other companies use to crunch their data and make more informed business decisions. Recently, it has expanded into office security with the creation of identification software called Usher that gives approved employees access to buildings and computer networks.

The letter calls for Saylor to be removed as Microstrategy’s chief executive because of Apex’s concerns that he no longer remains focused on the company’s core business after 24 years at the helm. Instead, Apex cited Saylor’s recent appearances on Fox Business News in which he touted his book and the firm’s Usher product, as well as Twitter photos of his yacht in Saint Lucia and Grenada, as signs that his commitment has lapsed.

However, Apex recommends in the letter that Saylor remain the company’s chairman and praised his “vision and execution” since the company’s creation.

“At this critical stage in the company’s life cycle, we believe that his skills and expertise are best suited for a chairman or advisory capacity,” the letter states. “There is ample precedent where successful technology company founders — among them Bill Gates at Microsoft and Sergey Brin at Google — made a natural progression into these types of roles.”

Saylor “seems to spend more of his time as a technologist than engaged in the day-to-day responsibilities of running the company,” Simon said in the interview.

As a result of what it calls poor communication, Apex contends there is little insight into MicroStrategy’s long-term direction and financial goals, stunting the growth of its stock price.

“It’s really the workings of the chief executive officer and the board who have decided to take on a strategy of non-communication, which makes it nearly impossible for any investor who comprehends the concept of fiduciary responsibility to take this company seriously,” Simon said in the interview.

MicroStrategy’s stock price closed at $124.09 Tuesday, up 68 cents, or a half-percentage point, compared to the day before. Tuesday’s closing price is nearer the high end of its range over the past year, which saw the price dip as low as $82.72 and climb as high as $134.

Simon believes the stock could triple if Apex’s suggested changes are followed.

“We get paid to make money for our investors and we like the company,” Simon said. “We like the product. They’re a leader in their field, the business model is sound and the opportunity for capital return is phenomenal.”