Shares in the property market, another set of old-economy companies, have also climbed, even though not all stocks in the sector have experienced the same boost.
Share prices of property developer Vanke spiked 23.14 percent from Jun. 1 until Thursday, after mostly stagnating in the first four months of the year. Poly Real Estate has risen 11.68 percent from Jun. 1.
"Up until the beginning of this summer, the main driver of emerging markets, it was quite a narrow recovery. It was very much in tech or the internet, and now we're beginning to see that widening out ... across many markets," Sean Taylor, Asia-Pacific CIO of Deutsche Asset Management, told CNBC's "Squawk Box" on Thursday.
Taylor appeared confident that the widening recovery would continue.
"People are still very underweight China internationally, but we are going for a much broader portfolio than we had at the beginning of the year, which was probably more new economy and tech-oriented," Taylor said.
Leung said he believed there was room for further upside for Chinese shares, pointing to how valuations on the Hang Seng China Enterprises Index — shares of Chinese companies listed in Hong Kong — were still cheap and continued to underperform the Hang Seng Index.
"Our call has always been that there will be a reverse in the second-half where HSCEI will play catch up, with the mostly old economy constituents there likely to pick up steam," he added.
Leung also highlighted improvements in the real economy as being responsible for driving the recovery in Chinese markets.
"People were previously focusing on new economy sectors because earnings in those sectors are relatively immune to what's happening in the real economy. But now that the real economy is confirmed to be picking up, people are revisiting," he explained.