“It simply stumps me,” said Charles Skorina, an executive recruiter in San Francisco who specializes in endowments and foundations. “Any board that sets substandard benchmarks ought to take a hard look at their investment goals.”

Paul Andrew, a Harvard spokesman, declined to discuss compensation. Mendillo, who left Harvard Management Co. at the end of last year, declined to comment through Andrew.

Texas surpassed Yale last year to become the second biggest endowment, with $25.4 billion in assets, after Harvard’s $36.4 billion. The pool grew as the state funneled more than $5 billion in revenue from oil and gas wells it owns into the system’s fund over the past 10 years. Zimmerman, who ranks No. 6 in pay among endowment chiefs, also manages some of Texas A&M University’s money.

Zimmerman said his 2013 pay was the result of an “extraordinary event,” the decision to defer his entire 2012 bonus because of a loss that year. He also said the fund’s performance was weighed down by a decision to have less equity exposure than other universities to reduce risk.

Superior Returns

Some top-paid managers had superior returns. Notre Dame, which had an 11.9 percent gain over three years, ranking 13th among those surveyed, gave Scott Malpass a 10 percent raise to $3.9 million, second-highest in the survey. Columbia, which had a three-year average return of 12.1 percent, ninth best, boosted Nirmal Narvekar’s pay 9 percent to $3.7 million, according to tax filings. He was No. 3 in the pay ranking.

Narvekar, a former equity-derivatives trader at JPMorgan Chase & Co., was hired by Columbia from the University of Pennsylvania in 2002.

“His compensation reflects a level of endowment performance that is at the top of our peer group over the past decade,” Scott Schell, a Columbia spokesman, said in an e-mail.

Swensen Raise

To find the highest-paid endowment managers, Bloomberg made public-records requests to state universities and examined tax filings of dozens of the largest college endowments for 2013, the latest data available. Bloomberg corrected for inflated figures in Internal Revenue Service filings by subtracting previously reported deferred compensation.