A holding is China Mobile (CHL), a telecom company that serves 700 million customers. "This is a dominant provider that has been able to increase its dividend payout over time," says Harriss.

While the overall China markets have stagnated, e-commerce stocks have soared. That has provided a boost for Oberweis China Opportunities (OBCHX), which focuses on small- and mid-cap growth stocks. During the past year, Oberweis returned an eye-popping 50.8%.

Portfolio manager John Wong says that e-commerce currently accounts for 6% of all retail sales in China. The figure will climb to 10% by the end of next year as more consumers in rural areas come to rely on the Internet. Wong holds Vipshop (VIPS), a discount online retailer that sells apparel and cosmetics brands. "The e-commerce growth rates will continue to be strong for the next couple years," says Wong.

Fidelity China Region seeks modestly priced stocks with above-average growth prospects. Portfolio manager Robert Bao often favors rock-solid businesses. "We emphasize companies with strong balance sheets and superior cash flows," he says.

During the past five years, Fidelity returned 20.1% annually, outdoing its average peer by 3.8 percentage points. In 2013, the fund scored big gains with Tencent (TCEHY), an Internet giant. The company provides messaging services and social networks.

For a broader Asian fund, consider Wells Fargo Advantage Asia Pacific, which has 19% of assets in China. Portfolio manager Anthony Cragg favors growing companies that sell at reasonable prices. He takes stocks of all sizes. During the past five years, the fund returned 15.9%, outdoing its average peer by half a percentage point.

Cragg is willing to take contrarian positions. At the moment he has a stake in Industrial and Commercial Bank of China (IDCBY), which has a price-earnings ratio of 5. Investors have fled Chinese banks because they worry about debts in the country's shadow banking system. Cragg argues the fears are overdone. "The Chinese government is coming to grips with the banking problems," he says.

At the time of publication the author had no position in any of the stocks mentioned.

This article represents the opinion of a contributor and not necessarily that of TheStreet or its editorial staff.

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