China’s richest man, Wang Jianlin, has just signed a deal to buy U.S. Legendary Entertainment and boasts a raft of property projects abroad. But headwinds at home could put a dent in his ambitions.

Two ratings firms in the past two days downgraded bonds issued by Dalian Wanda Commercial Properties Co. Ltd., the real estate arm that Mr. Wang controls, on expectations that falling sales revenue in 2016 and 2017 will not be sufficient to support the firm’s spending plans.

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