Math is hard. Just ask Bill Gross, managing director of fixed-income giant Pacific Investment Management Co. LLC (PIMCO), who was criticized in August for his claim that future real (i.e., inflation-adjusted) returns on stocks will fall well short of long-term averages.

The most highly criticized aspect of Gross’ argument was his claim that over the long term, stock returns cannot exceed gross domestic product (GDP) growth. This is a remarkable assertion, because from 1929 through 2011, real returns on U.S. stocks have exceeded GDP growth by an average of 2.6 percent per annum. So what’s up? Gross says that stockholders have earned outsized returns for decades by appropriating them from three groups – laborers, lenders and the government. Going forward, he expects those groups to push for higher wages, higher loan rates and higher taxes. As their shares of GDP growth rise, he reasons, returns on stocks will fall.

What’s more, Gross expects slower GDP growth in the years ahead. Combined, the net result is dramatically lower stock returns. Gross takes to task Wharton finance professor Jeremy Siegel’s work identifying a persistent 6.6 percent real return on stocks (aka, the “Siegel constant”).

Says Gross, “The Siegel constant … is an historical freak, a mutation likely never to be seen again…”

Stock mavens don’t like it when bond guys get into their business. And so Jeremy Siegel promptly went on CNBC to explain that Gross “got the economics wrong.” Where Gross went wrong, said Siegel, is expecting total stock returns to be bounded by GDP growth. The reason stock returns have consistently exceeded GDP growth is dividends, which in fact account for the majority of total stock returns over time.

Gross’ reply was less diplomatic, saying Siegel “belongs back in his ivory tower.”

A number of investment luminaries have since weighed in, and the clear consensus is that Gross got the math wrong. GDP growth does not cap stock returns. As Yogi Berra reportedly once said, “In theory there is no difference between theory and practice. In practice there is.”

So Gross got this wrong. Why should we care about a rather esoteric debate between investment gurus? Simple: Because if one has money to invest, it matters immensely whether real returns from stocks are 6 percent or 2 percent. If returns are lower, most of us will need to save more for a longer period of time to achieve our goals.

On Aug. 10, Ben Inker, the head of asset allocation for GMO LLC, published a white paper titled, “Reports of the Death of Equities Have Been Greatly Exaggerated: Explaining Equity Returns.” In it, Inker takes Gross’s argument head-on, demonstrating convincingly that there is no relationship between stock returns and GDP growth.

According to Inker, stock returns are driven not by a titanic struggle between labor and capital, but by investor demand. And, because stocks have a strong propensity to lose money at the worst possible times (i.e., when the rest of the economy is weak), investors should and do demand higher returns from stocks than less risky instruments. In Inker’s view, given the pain equity investors have endured recently, they will insist upon higher returns from stocks going forward.

But here’s the interesting part: Both Gross and Inker expect lower returns from stocks in the near term. Gross links his argument for lower stock returns to a battle among competing groups for a share of slower GDP growth. Inker foresees lower corporate earnings and a depressing effect on stock prices as new investors look to earn higher forward-looking returns.

The takeaway for investors from August’s mildly amusing tempest among the financial titans is this: However you piece the puzzle together, recovery from the 2008 financial crisis may well depress stock returns for quite some time, particularly given present levels.

Stocks could still remain attractive relative to other investments (we think they will), but lower real stock returns nevertheless exact real pain on investors.

And that is just simple math.