Seoul shares rally to over 4-month high after Fed

* KOSPI jumps 2.17 pct on Fed stimulus

* Investors snap up beaten-down shares such as steel, chemicals

* Brokerages among best performers

SEOUL, Sept 14 (Reuters) - Seoul shares surged to their highest levels in more than four months on Friday after the U.S. Federal Reserve launched another aggressive programme to stimulate the U.S. economy.

The Korea Composite Stock Price Index (KOSPI) was up 2.17 percent at 1,993.02 points at 0046 GMT, its highest level since May 3.

"Less risk and more liquidity are driving higher beaten-down cyclicals such as steel and chemicals firms," said Chun Jong-kyu, an analyst at Samsung Securities.

"But any additional rises will be limited after the KOSPI reaches the 2,000-point level as the rally is driven by policy hopes in the United States and Europe, but economic uncertainty still lingers in China," he said.

Foreigners continued their buying spree for a sixth consecutive session, while institutional buying kicked in again.

Brokerages were among the best performers, with Daewoo Securities jumping 6.8 percent and Woori Investment & Securities gaining 6.1 percent.

Steel firms and chemical companies also gained ground, with top steelmaker POSCO climbing 2.6 percent and LG Chem jumping 3.2 percent. (Reporting by Hyunjoo Jin; Editing by Joseph Radford)