SHANGHAI — Index provider MSCI Inc. said it would quadruple the contribution of mainland Chinese companies’ to its benchmarks, a move that makes shares in Shanghai SHCOMP, +0.16% and Shenzhen 399106, +0.82% all but unignorable for many international investors.

While many asset managers own stakes in Chinese companies listed in Hong Kong or New York, such as Alibaba Group Holding Ltd. BABA, +0.80% or PetroChina Co. PTR, -0.22% , global investors have far less exposure to stocks listed on the mainland.