U.S. stocks closed at yet another record high yesterday, but the indexes are edging lower this morning, with the S&P 500 (SNPINDEX:^GSPC) and the Dow Jones Industrial Average (DJINDICES:^DJI) down half a point and five points, respectively, at 10:05 a.m. EDT.

Can "record high" and "cheap" coincide?
Stocks have enjoyed a great run so far this year, setting record high upon record high and gaining 15.7% as of yesterday's close (based on the S&P 500). That has some investors a bit nervous, but Fernando Duarte and Carlo Rosa, two economists at the Federal Reserve Bank of New York, think the good times could continue. In "
Are Stocks Cheap? A Review of the Evidence," published a week ago, they write: "We surveyed banks, we combed the academic literature, we asked economists at central banks. It turns out that most of their models predict that we will enjoy historically high excess returns for the S&P 500 for the next five years."

Let's be clear about what they mean by "excess return." The "equity risk premium" is the expected future return of stocks minus the risk-free rate over some investment horizon. In other words, Duarte and Rosa assert that these models predict that stocks will beat bonds by a historically wide margin over the next five years. However, that has more to do with the dreadful prospects for bonds than it does with outstanding stock fundamentals:  

"Why is the equity premium so high right now? And why is it high at all horizons? There are two possible reasons: low discount rates (that is, low Treasury yields) and/or high current or future expected dividends. ... We find that the equity risk premium is high mainly due to exceptionally low Treasury yields at all foreseeable horizons. In contrast, the current level of dividends is roughly at its historical average and future dividends are expected to grow only modestly above average in the coming years."

"Max," one of the smartest money-managers I've come across on Twitter, tweeted this morning (SPX is one of the tickers for the S&P 500 Index):

SPX is AAPL before AAPL lost 37% from its peak. No one thought AAPL would go down either. Buy some cheap puts* (*not financial advice)

-- Max (@_CB01) May 15, 2013

With the VIX Index (VOLATILITYINDICES:^VIX) closing at 12.77 yesterday, those puts are indeed remarkably cheap (the VIX Index is derived from the implied volatility of short-dated options on the S&P 500). Not that I'm recommending that individual investors follow Max's not-financial advice. I think equity investors need to accept volatility -- and not the kind that only goes one way. Right now, central banks' actions have levitated asset markets worldwide. Investors need to make sure their portfolios are anchored to fundamentals as well.