* KOSPI holds firm after setting over 3-mth highs     * Won inches down, but analysts have upbeat outlook      By Jungmin Jang     SEOUL, April 15 (Reuters) - Seoul shares held firm after touching their strongest level in more than three months on Tuesday morning after gains on Wall Street, but investors remained cautious on uncertainty over global economic and policy prospects.     The Korea Composite Stock Price Index (KOSPI)  
  .KS11
   was up 0.1 percent at 1,998.90 points as of 0240 GMT after touching an intraday high of 2,009.04, its highest since Jan. 2.     "The sentiment remains quite fragile as questions regarding local corporate earnings and policy prospects in the euro zone and China are still up in the air," said Kim Yong-goo, an analyst at Samsung Securities.     Reflecting the fragile sentiment, local institutional investors were quick to lock in profits, selling a net 133 billion won ($128 million) worth of KOSPI shares in the morning. Foreigners picked up a net 36 billion won worth.     Cosmetics stocks gained on upbeat earnings outlook, with AmorePacific Corp  
  090430.KS
   and Cosmax Inc  
  192820.KS
   rising 3.7 percent and 2 percent, respectively.     In contrast, a grim earnings outlook dragged down shipbuilders as Hyundai Heavy Industries Co Ltd  
  009540.KS
   fell 1.6 percent and Samsung Heavy Industries Co Ltd  
  010140.KS
   dropped 2.2 percent.     In the foreign exchange market, the won  
  KRW=
   inched lower on dollar demand from foreign share investors converting their dividends paid by South Korean companies.     The local currency  
  KRW=KFTC
   was quoted at 1,040.7 against the dollar as of 0240 GMT, down 0.2 percent from Monday's onshore close at 1,038.9.     Despite a lacklustre trend this week, analysts said the won's outlook was firm, with investment bank ING saying in a client note on Tuesday that it may cut the year-end target for the dollar/won pair from the current 1,060 won.                        0240 GMT    Prev close  Dollar/won            1,040.7       1,038.9  Yen/won           10.2140/189       10.2021  *KTB futures           105.72        105.75  KOSPI                1,998.90      1,997.02  * Front-month futures on three-year treasury bonds ($1 = 1038.8500 Korean Won)   (Editing by Choonsik Yoo and Eric Meijer)  ((jungmin.jang@thomsonreuters.com)(822 3704 5643)(Reuters Messaging: jungmin.jang.thomsonreuters.com@reuters.net))  Keywords: MARKETS KOREA/