Among survey respondents, only 7 percent believe that their stressed leaders effectively lead their teams and only 11 percent of employees with stressed leaders are highly engaged at work.

"Companies often focus on fixing individual employees to help them be less stressed and therefore more engaged. Yet, our study found that employee engagement was better predicted by the leader's ability to manage stress than the employee's current stress level," said Kenneth Matos, psychologist and Vice President of Research for Life Meets Work, which conducted the study. "A leader's inability to manage stress ripples through the entire organization in a negative way."

According to the study, when leaders do not manage stress effectively, more than 50 percent of their employees believe their leader is either harmful or irrelevant to their job and the organization's performance. Yet when leaders are adept at managing stress, only about 10% of their employees harbor such negative opinions.

The study also found that when employees see their leaders as unable to manage stress, they report lesser ambitions to advance in their organization. While 79% of employees with resilient leaders wanted to have a more senior role in their organization, only 55% of those with a leader who is less capable of managing stress felt the same.

"This finding should make employers ask themselves an important question, 'Are stressed leaders corroding my talent pipelines by being unattractive examples of leadership in the company?'" said Matos.