When a crisis occurs and your company is responsible, what's your first move? If you think it is to push blame onto someone else, you have the wrong job.

Lauren Leader-Chivée, an adviser to companies on leadership issues, says that as a CEO, you need to own company crises when they happen--whether you are personally at fault or not.

A study Leader-Chivée coauthored in 2010 with the Center for Talent Innovation examined "the intangibles of leadership"--the ways in which CEOs show their leadership capabilities and their power to influence their staff. The study found that leaders need to possess three characteristics to be seen as a "true leader."

"First, they must have 'grace under fire'--the ability to stay calm and coolheaded in any crisis. Indeed, this calm emerged as fundamental to leader credibility," Leader-Chivée writes in the Harvard Business Review. "But also, our research found that leaders must stand for and by a clear set of values which define them. Finally, they must have integrity, constantly speaking truthfully."

Leader-Chivée's study made clear that while "crises are inevitable ... leaders are made by the way they handle them." A prime example of a leader owning a crisis, she writes, is General Motors CEO Mary Barra, who has taken responsibility for the company's recall of 1.6 million cars due to a faulty ignition switch. GM's cars included in the recall have been tied to 26 deaths.

"By taking responsibility, demonstrating her values, and speaking honestly and forthrightly, Barra has shown stronger, not weaker leadership," she writes in HBR. "Had she not done this, or simply blamed others … she would have inevitably faced withering and justified criticism."

On the other end of the spectrum is New Jersey governor Chris Christie, who has not taken ownership of the infamous "Bridgegate" scandal, Leader-Chivée writes. Christie has denied all responsibility for the September closure of ramps onto the George Washington Bridge, which created a four-day traffic jam and is allegedly tied to a political payback scheme.

"Christie's passionate refusal to take any responsibility for the actions of his team was a bad miscalculation and made him look weak, self-serving, and desperate," Leader-Chivée writes. "The public has not forgiven him. His approval ratings are at an all-time low, and his national aspirations are clearly unattainable."

The lesson here is that leaders sacrifice themselves for their employees. If you're a leader, your job is to take ownership of everything your company does--good, bad, and ugly.