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They may be “paper losses,” but the hurt is real.

And the losses may well be real too.

After another rough week, the Dow Jones industrial average stands at its lowest level since the downturn of 2002. Stocks have plunged roughly 50 percent from their peak in October 2007.

That’s right: We’ve been halved.

Every investor knows those losses aren’t realized unless the positions are closed out.

Just hang in there, the thinking goes, and maybe the market will take off again, restoring lost gains: After all, what goes up must come down, then go up again.

Dream on, said Jeremy Grantham, a legendary money manager who sounded a warning about overpriced assets a couple of years before the bubble burst.

In Grantham’s opinion, the gains of the recent past were the product of active imaginations.

“You shouldn’t view them as paper losses. You never really had them,” he said. “You’re giving back the paper gains. Ninety percent of what we’ve lost was an illusion.”

Grantham has some grim calculations about how much of America’s wealth will vanish in “the terrible recession.” Using round numbers, he figures that stock and real estate holdings amounted to $50 trillion at the market’s top. Private debt stands at about $25 trillion.

Grantham reckons that with U.S. stocks down 50 percent, housing 35 percent and commercial real estate as much as 40 percent from their peaks, $20 trillion in “perceived wealth,” as he calls it, has disappeared.

If stocks and real estate have yet to hit bottom — which “you should more or less count on,” he said — that $50 trillion shrinks to $25 trillion, an amount equal to debt.

What to do about it?

How much time have you got?

“We’re not going back to $50 trillion anytime soon,” he said. “If you come back in seven years we will have awoken from a terrible nightmare.”

Over time, Grantham predicts, stock and real estate values will rebound at least a little from the bottom. He’s also counting on inflation, which makes it less burdensome to pay back a fixed amount of debt.

The passage of time will help, too, because he expects the economy to grow at a modest pace in the long run.

None of those factors can make all the difference, however. Sooner or later, lenders will recognize that an estimated $4 trillion in loans won’t be paid back, forcing a “bitter” reckoning, Grantham said.

Naturally, the loss of perceived wealth tends to accelerate the recession’s downward spiral. There’s nothing like the cold realization that you’re not as rich as you thought to discourage spending and investment.

The good news, as he sees it: No one blew up the factories. The homes are still standing. The capacity to work remains. And the developing world is positioned for relatively healthy growth, which helps every global citizen.

At Chicago’s Wayne Hummer Investments, William Hummer thinks Grantham is on to something. Although Hummer sees bargain prices in the stock market, “as far as going back to where we were, the frenzy of 2007 won’t be revisited,” he said. “Or if it is, it will be a long time off.”

From his perch in the Loop’s financial district, Hummer said he feels less alarm than might be expected given the gloomy outlook. “At this juncture,” he said, “I think it’s resignation.”

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