Robert Shiller: Stocks pricey—here's what to do

The U.S. stock market is one of the most expensive in the world right now, Nobel Prize-winning economist Robert Shiller warned Wednesday.

Measuring valuations with his cyclically adjusted price-to-earnings index—which is price divided by 10-year average earnings—the Yale University professor said, "My CAPE index ... is higher than it's been, except 1929, 2000 and 2007," ominous years for the market.

Despite the high valuations, Shiller told CNBC's "Squawk Box" that he does have personal investments in U.S. stocks, but warned of being too overexposed. "Some people are not very diversified internationally. This is a good time to rethink that."

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He stopped short of calling a bubble in the U.S. stock market, but said, "The public [also] worries that the stock market is overpriced."

"Their confidence in the level in the market is at its lowest since 2000," said Shiller—referring to his research into investor expectations.

He did acknowledge that sometimes investor sentiment can be a contrary indicator—citing the late 1990s leading up to the dot-com crash as an example. Bubbles can be formed "when people think it's time to get in, even though it's overpriced."

'Diminishing momentum' in housing

Moderate increases in home prices may continue for a year or so, said Shiller. "[But] I don't think this is a flaming bubble."

In fact, "the housing market has had diminishing momentum," the economist told CNBC on Wednesday, a day after his namesake S&P/Case Shiller index showed home prices in 20 big cities rose 4.9 percent year over year in April.

"It's down to just kind of average performance," he said. "We saw a bottoming out of the housing market in most U.S. cities around 2012. And then we saw really rapid increases ... [which are] starting to fade."

One of the factors supporting home prices is the lack of supply, Shiller added. "Construction is still not very high."

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