86%: Increase in foreign banks’ lending to China in 2010.

The world’s banks are betting China is the place to put their money. That could complicate Chinese officials’ efforts to cool down the country’s economy and real-estate market.

During 2010, banks that report their holdings to the Bank for International Settlements plowed an exchange-rate-adjusted $77 billion into China, increasing their exposure by 86% from the end of 2009 and bringing the country’s share of global cross-border lending — while still small at 1.1 % — to its highest level on records going back to 1977.

The shift represents a vote of confidence in China, as banks pulling out of financially troubled European countries such as Greece, Portugal and Ireland send more money east. But it also underscores the pitfalls of China’s efforts to find its own solution to a fundamental problem of international finance, the so-called “trilemma”: While countries may want to maintain stable currencies, run an independent monetary policy and keep their borders open to foreign capital, they can do only two of the three.

China has chosen the first two. It tightly controls the yuan’s exchange rate, in part to stimulate its vast export sector. It’s trying to run its own monetary policy, raising interest rates and ratcheting back bank credit to curb inflation. But that choice requires the country to keep out the foreign money that its relatively high interest rates would typically attract. Otherwise, the inflow of cash would either push up the yuan’s exchange rate or stoke the inflation China’s policy makers are trying to rein in.