SHANGHAI/HONG KONG, Aug 21 (Reuters) - China and Hong Kong stocks fell on Monday, as regulators' support measures and a fresh cut in the benchmark lending rate disappointed, even as listed firms and fund managers rushed to unveil share purchases.

Shanghai's blue-chip index and Hong Kong's Hang Seng Index both dropped to nine-month lows, underwhelmed by a package of measures China's securities regulators announced on Friday aimed at boosting investor confidence.

Investors were also let down by Monday's smaller-than-expected rate cut. China lowered its one-year benchmark lending rate, but surprised markets by keeping unchanged the five-year rate - on which mortgage rates are based.

"If you don't address the property debt problem, it won't help the sentiment much," said Steven Leung, executive director of institutional sales at UOB Kay Hian in Hong Kong.

"Technically Hong Kong and China markets are oversold, but confidence remains very weak, no one really wants to come back to the market."

The onshore yuan eased roughly 0.3% in morning trade to about 7.3066 per dollar, compared with the previous close of 7.2855.

Analysts say the modest rate cut shows authorities are concerned about the risks of a major yuan sell off and capital flight, with any easing likely to widen the yawning gap between interest rates in China and its major trading partners.

Those worries could limit the scope policymakers have to loosen monetary settings, which would only add to investor disappointment about Beijing's response to the current economic slowdown.

"Probably China limited the size and scope of rate cuts because they are concerned about downward pressure on the yuan," said Masayuki Kichikawa, chief macro strategist at Sumitomo Mitsui DS Asset Management. "Chinese authorities care about currency market stability."

Investors were already unenthused even as dozens of China-listed companies outlined plans over the weekend to purchase their own shares in answer to regulators' call for share buybacks.

More than 30 companies including chipmaker Loongson Technology Corp and Xian Manareco New Materials Co have said since Friday that their controlling shareholders had proposed buying back shares because of confidence in the companies' future development and value.

Other companies that have announced share buyback plans include Shenzhen Kiwi Instruments Co and Chengdu Screeen Micro Electronics Co.

Meanwhile, at least eight asset managers, including E Fund Asset Management Co and China Asset Management Co said they would use their own money to buy into equity funds.

Other measures unveiled by the China Securities Regulatory Commission (CSRC) on Friday include cutting trading costs, encouraging long-term investment and studying plans to extend trading hours. (Reporting by Samuel Shen and Winni Zhou in Shanghai and Summer Zhen in Hong Kong. Additional reporting by Kevin Buckland in Tokyo. Editing by Sonali Paul and Sam Holmes)