After beginning Wednesday in the red, thanks, ostensibly, to a below-expected revision in the first-quarter GDP reading, U.S. stocks managed to power ahead for a winning day, with the benchmark S&P 500 and the narrower Dow Jones Industrial Average (DJINDICES:^DJI) up 0.5% and 0.3%, respectively. The technology-heavy Nasdaq Composite Index (NASDAQINDEX:^IXIC) gained 0.7%.

With that established, let's move from short-term observation to some (very) long-term thinking –--which is actually the most appropriate kind when you're discussing the stock market. Professor Robert Shiller of Yale, who shared the most recent Nobel Prize in Economics, said today in an interview with Yahoo! Finance's Daily Ticker that he is concerned about the medium-term prospects for U.S. stocks. The good news: He has two key recommendations for investors.

Source: Wikipedia.

Normally, I wouldn't give much weight to an academic's hand-wringing regarding the stock market, but Shiller has, in my opinion, the best grasp on stocks of any prominent economist. He is empirically driven, has taken a deep look at U.S. stock market data, and uses just enough quantitative analysis so that it does not crowd out common sense.

Shiller's concern is based on his observations with regard to a valuation he has named the cyclically adjusted price-to-earnings ratio, or CAPE. The "cyclically adjusted" part refers to the use of a trailing-10-year average of inflation-adjusted earnings per share in deriving the ratio, rather than trailing 12 months' earnings per share or the next 12 months' EPS estimate. Right now, Shiller points out, the CAPE, at 26, is near historic highs:

I'm definitely concerned. I have a plot on my website [the link will download Shiller's Excel spreadsheet, which contains the graph] showing the CAPE ratio all the way back to 1881, and I'm looking: When was it higher than it is now? I can tell you: 1929, 2000, and 2007. I think that's about it. It was close in the late '60s; it got up to something like 24 -- I don't remember exactly. But that's about it, so we are kind of at a historically high market right now -- in the United States, not so in other parts of the world.

(Incidentally, if you're wondering, the late 1960s ultimately gave way to a horrific stock market crash in 1973-4.)

Multiple brokers, including Bank of America Merrill Lynch, Goldman Sachs, and Citigroup, in a bid to reassure their clients that they can keep buying stocks, have tried to address this argument, explaining that a historically high CAPE simply reflects historically low interest rates. But Shiller doesn't believe that counterargument offers any protection from the valuation risk stocks now present (emphasis mine):

The very low interest rates are a sign that maybe you want to keep more invested in the [stock] market now rather than getting nothing [in bonds.] So [low interest rates] ought to help explain the high CAPE. That doesn't mean that the high CAPE isn't the forecast of bad performance. When I look at interest rates in a forecasting regression with CAPE, I don't get much additional benefit from looking at interest rates. But yeah, right now, if you're forming a portfolio, the fixed-income market just doesn't look very attractive, so that certainly has to help you put more into the stock market than you would just based on the CAPE.

In other words, stocks are simply a less ugly alternative to bonds -- which is pretty well the main argument brokers and strategists have been advancing for the past several years. It's not a particularly reassuring line of thinking. So what are investors to do? Shiller has two main recommendations:

We don't know what [the stock market] is going to do. There could be a massive crash like we saw in 2000 and 2007, the last two times it looked like this. But I don't know. ... I think, realistically, stocks should still be in one's portfolio -- maybe lighten up. And also: more abroad than usual, because the U.S. is really high relative to other countries.

I will add a third: Keep investing continually, both in yourself (i.e., in the skills you bring to the job market) and in stocks. The benefits of the former ought to be obvious; with regard to the latter, regular saving and stock purchases will enable you to smooth out your cost basis over time.