Goldman Sachs removed Disney from its "conviction buy" list on Thursday, citing a run-up in the shares since early last year, rising sports-rights costs, and new competition from News Corp.'s upcoming sports channel, Fox Sports 1.

Analyst Drew Borst maintained his target price of $70 in the coming 12 months, but downgraded his rating to "neutral."

Disney shares fell 3.65 percent to end at $61.98 Thursday, amid a broad market sell-off. Markets worldwide fell Thursday following comments by the Federal Reserve that it will pare back its easy money policies starting this year if the economy continues to improve.

The Walt Disney Co.'s ESPN sports network, which accounts for about 45 percent of the company's operating income, is likely to see decreased profit margins starting next year because of renewed rights deals for pro football, baseball and college sports, according to Borst. Also, Fox Sports 1, which launches in August, will likely become a fierce bidder for sports rights going forward, either raising ESPN's costs or snatching rights away from it.

ESPN's contract to carry certain NBA games live expires after the 2015-2016 season, and its contract to carry NASCAR auto races expires next year.

"FS1 will be competing for sports viewers and advertising dollars and this could hamper ESPN's advertising growth," Borst writes in a research note published Thursday.

He sees Disney's cable networks operating income growth slowing from 12 percent in fiscal 2013 to 7 percent in fiscal 2014 and to 4 percent in fiscal 2015. Disney's fiscal 2013 year ends around the end of September.

He also said that Disney's share price growth is starting to decelerate. Since adding Disney to its conviction list in late February 2012, the stock is up 55 percent, compared to a rise in the S&P 500 of 19 percent. However, in the past 12 months, Disney shares rose 35 percent compared with the S&P's 20 percent gain.