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It is rare, but some new chief executives fail early — just after they begin their new jobs. That leaves boards with impossible decisions. How will the stock market react to the admission of a mistake? Or, is the matter more simple than an error in judgement? Some companies will do poorly no matter who is in charge.

Yahoo! (NASDAQ: YHOO) had a change forced on it. Whether Scott Thompson, who was chief executive for four months, would have done well as a new leader of a troubled company will never be known. There is at least a chance he might have succeeded, if the scandal about his resume had not occurred. The board of Yahoo! did not get the opportunity to evaluate his tenure because he had none.

Two examples of CEOs who have been hired and supported by their boards despite very poor results are Ron Johnson of JCPenney (NYSE: JCP) and Stephen Elop of Nokia (NYSE: NOK). Elop has run the large handset company since September 2010. Johnson has only run Penney for a little longer than a quarter.

Elop followed Olli-Pekka Kallasvuo as chief executive. Kallasvuo was blamed because he could not transform Nokia into a successful manufacturer of smartphones. He may have stayed with the Symbian operating system, which lost popularity as Google’s (NASDAQ: GOOG) Android and Apple’s (NASDAQ: AAPL) iPhone gained market share. Elop, the Nokia board reasoned, could rely on his years as a the head of Microsoft’s (NASDAQ: MSFT) business division, although the link between that job and being the head of a handset company is difficult to understand.

Johnson’s promise as a turnaround CEO for JCPenney at least had a foundation in the success he had in his former job as head of Apple’s retail division, although some critics believe that Apple would have done well in retail no matter who was in charge. The demand for Apple products assured that. But JCPenney had been nearly ruined by former CEO and chairman Myron E. Ullman III. His strategy to make the retailer a better competitor to companies such as Macy’s (NYSE: M) and Nordstrom (NYSE: JWN) did not advance JCPenney. The company’s board gambled that Johnson could do better.

Elop made one bet on a turnaround of Nokia, and it may have been his best and only chance. He tethered his company’s success to that of Microsoft and its troubled Windows Mobile OS. At least Microsoft had the cash and marketing muscle to press its software into the market, although those efforts have been failures in the past. Elop’s decision did almost nothing for Nokia, at least based on the results from the last year. Nokia’s revenue collapsed along with its market share in smartphones. Microsoft was no help at all. The Nokia board is left to decide whether Elop made the wrong decision, or whether Nokia is doomed along with other companies that have been crushed by Google and Apple: Sony Ericsson, LG and Motorola. Nokia’s future may have been set long before Elop joined. There is no reason to replace him. Who can do any better?

Johnson’s situation is another matter. He decided that JCPenney could only do well if he utterly and completely changed how the retailer brought in customers and turned them into buyers. He rebranded the retailer “JCP.” JCPenney now has three basic tiers of pricing, which are supposed to make it easier for shoppers to decide the value of products sold by the company. The results of the most recently reported quarter show the strategy has not paid off. JCPenney’s same-store sales fell an astonishing 20% and online sales dropped more than 27%. If the results for the current quarter are similar, it will be clear that Johnson’s plan has failed, or that JCPenney has been a failure for some time. The board will have to face the fact that it picked the wrong candidate or that JCPenney cannot survive in its current form in competition with several other larger retailers and e-commerce firms led by Amazon.com (NASDAQ: AMZN). As with Nokia, the battle may have been lost long before the new CEO took up the reins.

The boards of Nokia and JCPenney may as well be passive as their new CEOs preside over companies that continue to fall apart. Neither had any chance of succeeding no matter who was put in charge.

Douglas A. McIntyre