NEW HAVEN, Connecticut — The sharp drop in the world's stock markets on Aug. 9 — after BNP Paribas announced that it would freeze three of its funds — is just one more example of the markets' recent downward instability or asymmetry. The markets have been more vulnerable to sudden large drops than they have been to sudden large increases.

Daily stock price changes for the 100-business-day period ended Aug. 3 were unusually negatively skewed in Argentina, Australia, Brazil, Canada, China, France, Germany, India, Japan, Korea, Mexico, the United States and Britain.

In the U.S., for example, the Standard and Poor's 500 index in July recorded six days of declines and only three days of increases amounting to more than 1 percent. In June, the index dropped more than 1 percent on four days, and gained more than 1 percent on two days. Going back further, there was a gigantic one-day drop on Feb. 27 of 3.5 percent, and no sharp rebound.