Yeah well this entire study is invalidated by using stock performance as the lazy way to measure CEO performance.
Expensive CEOs are typically expensive, because they're hired to fix a company that everyone knows is going down. The riskier the company, the more the stock is expected to go worthless, the more you get paid in cash for taking on the job.
So it's expected that if you look for expensive CEOs you'll be seeing stock/accounting performance going down in short to mid term, because recoveries, whether successful or not, take time. They take years.
Also are you honestly counting CEOs who get millions in stock and $1 pay as... just getting $1 in pay? How stupid are you.