Costs to protect against losses in developing-nation stocks posted the biggest weekly increase in more than four years.

The Chicago Board Options Exchange Emerging Markets Volatility Index rose 51 percent in the week ended Jan. 8. That was second only to the 57 percent surge in the five days through September 23, 2011 amid a slump triggered by the euro-area debt crisis and the downgrade of U.S. credit rating by Standard & Poor’s.

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