Just to be clear, the NY Times piece saying his compensation was $378 million last year is quite misleading. As Fortune writer Philip Elmer-Dewitt explains:
"Although the text of the article correctly reports that Cook's annual salary last year was a relatively modest (by CEO standards) $900,000, the lead sentence -- and the graphic -- make the same mistake the Associated Press and other publications made in January when Apple (AAPL) issued its 2012 proxy statement.
"To collect the full 1 million shares of Apple stock (technically, restrictive stock units, or RSUs) Cook was granted in 2011, he has to stay at the company for 10 years. The proxy statement is quite clear on this."
"The SEC requires a company to book a share grant's value in the year it is awarded, however, which is why Equilar included the grant in Cook's 'total compensation package.' But Tim Cook didn't pocket a penny of it in 2011, never mind $1 million a day."
So, obviously he's very well paid, but his take home pay that went into his back account in 2011 was considerably less than many CEOs. He has to stay at the company for 10 years in order to exercise this one-time large stock award; and obviously the value of the stock will vary greatly throughout the course of the next 10 years. Thus, clearly, his compensation is heavily tied to how the company's stock performs after the next decade.
Still, good to see a Duke grad lead the largest company in the world!