Why does investor/speculator/fund chase after already very high stock market? Risk of sharp correction?

Referring to STI index, is this a sign of bear trap?

There is always a risk of a sharp correction in a strong bull market. However a correction implies that the long-term trend is still positive. A bear market is where the long-term trend is negative. To answer your specific question, you should see if the P/E ratio has increased significantly in the recent run up.
If the P/E ratio of the index has soared then the market is in trouble because it means buyers are paying more than before for the same earnings. If the P/E ratio has not moved higher the market may not be overvalued.

Finally, the trend around the world is for interest rates to rise so this doesn't help stock markets but there is, apparently, boatloads of cash searching for investments so around the world, stock markets are still strong. This will change very quickly if there is an unexpected "event" that destroys this global complacency.

Right now - I don't think you will miss much if you sit on the sidelines - but that is my opinion.

Yes an attack on Iran would hit all markets - oil would increase and that damages the anti-inflation stance of world banks. Report It

Good question. Greed and Fear. AS LONG AS the liquidity in stock markets is healthy, you should have no fear to invest. In modern investing theory, the government can 100% own its stock market by issuing unlimited money. The correction will be temporarily as world central banks act together to provent any stock crash.

The smart investors will hold precious metals like gold and silver to diversify the risk of hyperinflation may occur in case the central banks own the stock market 100%. The consequence is the currency will be worth less like a real paper.

So far, the public still trust their governments and feel there is a "need" for a central bank. Therefore, no fear to invest...