Greenspan's remarks came at an emerging- and frontier-markets-themed event filled with private equity fund managers and their investors.
Greenspan said it's human nature to be overly fearful of such countries, making for investment opportunity.
He recommended buying and holding securities in such developing countries for the long term as part of a broader portfolio, even if there was still risk.
That, he said, reflected his overall views on how most people should invest in stocks.
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"The best strategy for equity investment has always been buy and hold, and forget it," he said.
"Once you start to try and trade the market. I don't care how good you are, how smart you are, you will not beat an index fund."