One of an investor’s most challenging decisions is how to handle the news that a former chief executive officer returns to power. Buy or sell or hold? The development should prompt several timely questions.

Professional investors often gauge a company's fortunes by measuring the CEO's individual experience, strategy and frame of mind. After all, this top executive will call the shots on a company's strategy when it comes to such critical management decisions as making acquisitions, rolling out new products and adding branch offices around the world.

Assessing a CEO’s value and potential can be particularly thorny when the leader returns to the company that he or she had previously run. As mutual fund literature invariably reminds us: Past performance is not always indicative of future results. 

For example, A.G. Lafley came back to run Procter & Gamble (NYSE:PG) last May 23. On Aug. 1, a Reuters article proclaimed:  "P&G Appears Back on Track with CEO Lafley's Return," referring to a favorable 2014 forecast for P&G. Yet the company's stock has slightly lagged the benchmark Standard & Poor's 500 Index by a few percentage points since his return.

Granted, it is too soon to reach any conclusions about P&G. But given how widely respected Lafley is, the data underscores just how challenging it is even for a very well regarded chief, such as Lafley, to impress Wall Street right from the get-go.

U.S. corporate annals are filled with high-profile examples of CEOs who returned to glory. The roster includes Lafley, Mike Ullman of J.C. Penney, Charles Schwab of the brokerage firm bearing his name, Howard Schultz of Starbucks, Michael Dell of Dell Computers and Steve Jobs of Apple.

Here are five questions investors should ask when a CEO returns:

1. What is the state of the company that the CEO is taking over?

Exactly how is the company doing? If an entity is utterly downtrodden, no leader can work miracles, no matter how glowing the track record or promising the stated growth strategy.

“Investors must ask if the company has greatly suffered or has it been on the rise?” says Betsy Billard, a private wealth adviser at Ameriprise Financial. “Visionaries really are few and far between so investors have to take each example on a case-by-case basis.”

The condition of a company is crucial because it will give a hint as to how long it may take the returning CEO to put his or her stamp on a company. “I would want to know if the company is innovating. Or, is it hiring and therefore expanding?” Billard points out.

2. Why did the CEO leave in the first place?

As Sam Hill, a CEO consultant and the author of “Radical Marketing: From Harvard to Harley, Lessons from Ten That Broke the Rules and Made It Big,” said in an interview: “CEO gigs are the modern equivalent of dukedoms, extremely privileged positions. Typically, people leave them for a small handful of reasons, one of which is they’re exhausted by the job. Whenever a CEO returns, I’d like to make sure she or he has the energy and enthusiasm to take the job back on.”

Long-term investors in particular may want to monitor some aspects of the incoming CEO. “That’s particularly true when the CEO is older, like A.G. Lafley is now,” Hill noted. “As much as I respect Procter and the incredible job (that) A.G. did the first time around, I’d be watchful this time. He’s a 66-year-old man who left the position to write books and give speeches. Is he back enthusiastically or reluctantly?”

3. How has the returning CEO exhibited personal or professional growth in the time away?

The most famous case of a CEO returning to the old stomping grounds involved Steve Jobs coming back to Apple (Nasdaq:AAPL). His case is worth examining because, given his notoriety over the years, he can serve as the totem for returning CEOs. Upon his return, he demonstrated self-awareness and maturity, factors that would encourage even skeptical investors to conclude he has grown.

Jobs co-founded Apple, driven by a vision for changing the world through computers. This was the message he conveyed to John Sculley, then of Pepsi-Cola (NYSE:PEP) when he beseeched Sculley to be CEO of Apple. But when the two leaders engaged in a power struggle, the Apple board sided with Sculley and Jobs left the company as a defeated man.

Jobs founded NeXT Inc. in 1985, with $7 million. It was not a noteworthy success partly because the NeXT computers carried huge price tags. He also acquired The Graphics Group, later called Pixar, from Lucasfilm for $10 million. The first movie he rolled out was "Toy Story," a big success that spawned sequels and changed the animation-movie scene.

But what Jobs learned about life and himself proved to be even more important. When Jobs addressed Stanford University in 2005, he acknowledged this. He told his audience that getting fired was the best thing that might have happened to him. He said, "The heaviness of being successful was replaced by the lightness of being a beginner again, less sure about everything. It freed me up to enter one of the most creative periods of my life.”

What he learned about himself helped to pave the wave for Apple’s remarkable growth in the 21st century. “I’m pretty sure,” Jobs said in the speech, “none of this would have happened if I hadn’t been fired from Apple. It was awful-tasting medicine, but I guess the patient needed it.”

4. Do you trust the incoming CEO’s growth strategy?

Ultimately, you have to go with your gut when you’re investing your money. You have to feel assured that the individual has the experience, savvy and understanding of the marketplace to do whatever will be required.

One returning CEO who changed the company’s fortunes for the better was Howard Schultz of Starbucks (Nasdaq:SBUX). “When Schultz came back to Starbucks (in January 2008), he revived the company,” says Anton Bayer, the chief executive of UpCapital Management, a registered investment advisor in Granite Bay, California.

Schultz, upon his return, worked to revitalize the “experience” of going to a Starbucks shop. He had disapprovingly noted in a memo in February 2007, a full year before he came back to the company, that Starbucks had experienced a “commoditization” of its brand by creating “efficiencies.”

He instilled a sense of purpose in the company’s 10,000 store managers by bringing them to New Orleans for a meeting. He also innovated smartly with technology by employing social media as a way to further Starbucks’ branding efforts.

Schultz also instituted e-payments, allowing customers to send one another e-gifts. When you walk into a Starbucks these days, you can’t help but notice how many people pay for their coffees with nifty apps on their iPhones. This makes the payment process more convenient for customers and advances Starbucks’ image as a company that is in tune with the attitudes of its young customers.

As a corollary to the question of what to do when a CEO returns, how should investors deal with the development when a CEO comes in from outside the cocoon?

Sometimes, as it turns out, the devil you know is ultimately better than the one you don’t. Look at what happened at the giant retailer J.C. Penney (NYSE:JCP).

The company hoped to shake up its stodgy image by recruiting Apple veteran Ron Johnson, who was widely praised as the architect behind the successful Apple-store concept. In November, 2011, Johnson succeeded Ullman as J.C. Penney’s CEO.

But Johnson turned off long-time Penney customers who had grown accustomed to such practices as heavy discounting and welcomed those coupons and sales. He exited unceremoniously last April and was replaced by Ullman, his predecessor.

“Ron Johnson made a lot of changes without making any tests,” Hill says. “In retail, you can test everything, such as a store layout or even the hours it is open. Maybe at J.C. Penney, maybe he felt he a sense of urgency and didn’t have time to test. Sometimes these changes take time.”

5. Do institutional investors trust the CEO’s strategy?

No matter how successful or charismatic a CEO has been, he or she will need to have professional investors, who often determine the direction of a company’s shares.

“You want to have the assurance that the institutional managers are confirming the incoming CEO’s strategy,” Bayer said. “They sit down with the CEO and we (investors) don’t get a chance to do that. A company can’t hide from how the stock is doing and what the institutional buyers are doing. No CEO can hide behind a ‘great story’ if those investors are running away.” 

I asked Bayer how his investment firm conducts research into a company before he buys its shares of stock. “We look at annual reports and company announcements. Then, we combine the fundamental analysis with technical analysis.”

The Bottom Line

Clearly, the return of a CEO brings formidable investment challenges. It helps to check the investment research that is readily available. It is wise to consult a professional investment strategist. But ultimately, it’s your money and you have to trust your gut. As Bayer succinctly put it about a returning CEO’s arrival: “Do you believe in the story? If so, invest in the company.”