* China stocks open up over 2 pct but end morning down over 3 pct
* Investors shrug off cbank easing, still unwinding leverage bets
* Regional markets down on China uncertainty, looming Grexit
* Highlights risk of c.bank monetary policy in equity markets
By Pete Sweeney and Samuel Shen
SHANGHAI, June 29 (Reuters) - Chinese stock markets showed no signs of relief on Monday after a surprise double-barrelled policy easing by the central bank, with indexes ending a wild roller-coaster morning session down more than 3 percent.
The People's Bank of China (PBOC) said one of the goals of the weekend policy adjustments, which included simultaneous cuts to interest rates and a targeted reduction to some banks' reserve requirements, was to calm stock market fluctuations.
Instead, Chinese bourses saw one of their most volatile trading sessions to date, with major benchmarks see-sawing in and out of positive and negative territory over the course of minutes.
The CSI300 index fell 3.4 percent to 4,190.30 points by the end of the morning session, while the Shanghai Composite Index lost 3.8 percent to 4,035.48 points.
The losses pushed China stocks deeper into correction territory, after a slump of over 20 percent in the last two weeks, fueled in large part by fears of a growing regulatory crackdown on loans used to speculate in securities. The main indexes had more than doubled over the last year.
The small cap Chinext growth board, the erstwhile favourite of speculators, plunged 7.4 percent, dragged by stocks like Siasun Robot & Automation, which once boasted a price-to-earnings ratio of over 200 thanks to speculators betting on government subsidies for industrial automation.
China CSI300 stock index futures for July pointed to further losses, falling 2.6 percent to 4,136.8, some 53.50 points below the current value of the underlying index.
"The market is still fragile because the clean-up of gray-market margin financing is still going on, and last week's market tumble triggered some margin calls and some investors are under pressure to sell," said Samuel Chien, partner of Shanghai-based hedge fund BoomTrend Investment Management Co.
"It's very natural, but many fund managers in China haven't experienced this kind of volatility in a highly-leveraged stock market, so they're at a loss."
Economists and analysts also expressed scepticism that the latest easing move would provide a durable floor under the market, given how sharply and quickly it had risen - in particular small cap stocks - and the lack of fundamental justifications for valuations.
"Short-term bounce aside, we doubt that the latest cuts will trigger any sustained rally," wrote Bank of American Merrill Lynch analysts in a research note, noting that the recent series of rate cuts have resulted in steadily weaker stock market reactions.
In Hong Kong, the Hang Seng index dropped 2.78 percent, while the Hong Kong China Enterprises Index lost 3.6 percent.
Sam Chi Yung, a strategist at Delta Asia Securities Ltd. said that Hong Kong was reacting to negative developments in Greece as well as China. Asian investors moved toward safe haven currencies and assets on Monday as Athens faced a debt default.
While stocks floundered, Chinese money market rates dropped sharply, due both to the easing move and to the end of cyclical cash pressure at the end of the first half reporting period.
The benchmark seven-day bond repurchase contract dropped to 2.69 percent from 2.9292 percent previously. The loan prime rate and key interest rate swaps (IRS) also declined.
The yuan, however, remained steady, with traders saying the central bank is holding it stable as it tries to position the currency for inclusion in the International Monetary Fund's currency basket.
However, some warned that the collapse in stock markets might negatively impact China's IMF application.
"We believe that PBoC prefers to see a strong A-share market, so capital doesn't take flight, leading up to the SDR vote in October," wrote the BofA analysts.
"As a result, if the market continues to be under pressure, it may do more."
Editing by Kim Coghill