After last year's rout, emerging markets have charged ahead recently, but Morgan Stanley expects the rally will run out of steam as soon as earnings season strikes.

"Don't chase the rally," Morgan Stanley said in a note dated Wednesday. "We don't see top-down or bottom-up catalysts." It noted the MSCI Emerging Markets index's around 10 percent rally since early February means it's now nearing its 12-month target of 1050. The index ended at 1009.22 on Thursday.