The best-paid CEOs tend to run some of the worst-performing companies and vice versa—even when pay and performance are measured over the course of many years, according to a new study.

The analysis, from corporate-governance research firm MSCI, examined the pay of some 800 CEOs at 429 large and midsize U.S. companies during the decade ending in 2014, and also looked at the total shareholder return of the companies during the same period.

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