Just how overvalued are stocks? Depends on which Ivy League economist you ask

The unwinnable debate rages on.

With the S&P 500 Index closing in on record highs this week, the question of how richly stocks are valued looms large in the market conversation—and well-known academics Robert Shiller and Jeremy Siegel have very different answers.

What's clear is that the recent rally has come largely on the back of rising valuations; the S&P's forward price-earnings ratio has risen from 16.4 just before the election to 18.1 as of Friday's close, according to data from S&P Capital IQ. The current earnings multiple is just a touch below the 13-year high of 18.4 it set at the beginning of March.

Other methods of analysis suggest even more anomalous levels of valuation. In a Wednesday interview on CNBC's " Trading Nation, " Shiller, a Yale University professor of economics, said that the market "hasn't been this overvalued except for a couple times in history—around 1929, around 2000."

Shiller is referring to the cyclically adjusted price-earning (or CAPE) ratio, which he helped develop and popularize. The CAPE ratio compares the current level of the market to the last 10 years' worth of reported earnings adjusted for inflation; the idea is to consider corporate earnings power across the breadth of the business cycle. After all, most companies aren't actually valued based on what investors think they will do in the next year alone.

Of course, this doesn't necessarily suggest that a market plunge is around the corner. As Shiller also pointed out, the CAPE ratio was about the same in 1998, but it continued skyward as the dot-com froth escalated into a full-fledged bubble.

"We could go back up there, and we're in an oddball enough mood that we might," Shiller said this week. "So I'm not saying pull out of the market — I'm saying that it looks dangerous now, but it could keep going up."

Not everyone is buying the "dangerous" descriptor, however. In fact, Jeremy Siegel, a professor of finance at the University of Pennsylvania's Wharton School and a longtime sparring partner (as well as personal friend) of Shiller's, says the CAPE ratio is now giving off a false signal.

For starters, the past 10 years of earnings currently include the massive profit decline seen during the financial crisis era of late 2008 and 2009. In the three quarters beginning in the third quarter of 2008, the S&P 500 actually saw total net income of approximately $0 — in contrast to the $76 per share seen in the last three quarters of 2016.

"I consider that a once-in-a-50-year event, or even a 75-year event, that's not going to be repeated." The fact that Shiller's ratio treats them as a once-in-a-decade event "is why he gets a very low earnings base," Siegel said on "Trading Nation" this week.

Second, "he uses GAAP earnings, which are very conservative" and "have become much more conservative over time. That's another reason why it looks like the ratio is high."

Siegel's third, and perhaps most cutting, gripe is that Shiller's "valuation statement takes no account of returns elsewhere in the asset markets, it takes no account of where interest rates are, where real estate are, where anything else is; it says there's one right price for equities, and the average from 1871 through, let's say, 2000 should be that average."

"We are not in that world," Siegel continued. "We are in a low interest rate world. We shouldn't use a 10-year lagging average now, especially with the growth that we're seeing."

Given these factors, "I do not share Bob's high concern for this market," said Siegel, "which, by the way, Bob has voiced for a long time."

Siegel added that Shiller "always tempers [his calls] at the end with, 'Doesn't mean it's not still going to go up.' And it still goes up. So I think even he realizes there's another dynamic at work here."

Shiller was not immediately available to respond to Siegel's comments.

As the debate between the two esteemed financial minds makes clear, whether stocks are expensive or not remains an open question.

Given this uncertainty, the fact that valuation is roundly considered a poor predictor of short-term moves can serve as a source of solace. Whether an investor goes to sleep with their head resting on Shiller's "Irrational Exuberance" or on Siegel's "Stocks for the Long Run," the basics of good money management remain the same.

For starters, a sound diversification strategy, which can mitigate risk without dragging on potential reward, is key.

"Right now is a good time to look at one's portfolio and ask if it's diversified enough," Shiller said.

This is a good idea even for those who think stocks are cheap—or in "a Goldilocks situation," as Siegel does. That's because the big rally in U.S. stocks compared with nearly every other asset class could well have morphed a once-balanced portfolio into a big bet on the S&P continuing its run.

After as sizable a rally as we've seen, even the biggest bulls might see fit to act like squirrels.