The highly touted deal to solidify Greece’s finances doesn’t look so good in the naked light of day. It’s short on details and long on optimistic assumptions.

You know the story of the euro’s new clothes, right?

One day, the president of France, the chancellor of Germany, and other princes and princesses from countries no one could pronounce—so they all used initials like EFSF—declared that they had saved the euro. And they held a big parade in celebration.

All the people in the marketplace laughed and cheered—while eating and drinking more than was good for them. Except for one little boy, who tugged on his mother’s sleeve and said, “Mommy, don’t the people see? The euro has no clothes.”

The people standing nearby, especially those people who were selling things to the crowd, tried to shush the little boy. “Don’t worry,” they said. “We just don’t have all the details yet.”

Yes, as the crowd says, we don’t have all the details of the euro-debt grand plan announced October 27. But we do have enough to do some very basic math.

And the math shows that the deal leaves the euro very naked indeed.

The Bank Haircut Is Only a Trim
The markets can be excused for overlooking some of the math—the issues are esoteric, and the parties involved are far away from the center of the financial world.

For example, it looks as if the way that the European Banking Authority calculated how much additional capital European banks will have to raise wound up going easy on French and UK banks, and coming down hard on Swedish, Danish, and Norwegian banks.

That’s because the formula for calculating how much capital a bank needs looks at risk-adjusted capital, and the European Banking Authority apparently decided that mortgage-backed bonds are less liquid than government debt—you know, safe Greek and Italian debt—and therefore more risky.

Scandinavian banks have relatively large portfolios of mortgage-backed debt, so a bank like Svenska Handelsbanken (SVNLF) will have to raise $1.1 billion in new capital, while the five big United Kingdom banks will have to raise nothing at all.

This, even though the credit-default swaps market that insures against bank defaults says Svenska Handelsbanken is among the ten least risky big banks in the world. And even when you remember the size of the real-estate bubble and crash in the United Kingdom.

Some of the math is hard, but I suspect the real reason that no one is waving the numbers around is that it might blow up the politics of the whole debt deal.

The biggest example of math that no one wants to examine too closely is that of the much-trumpeted 50% cut to the value of their Greek government bonds. German Chancellor Angela Merkel and French President Nicolas Sarkozy are depicted as having forced European banks to (grudgingly) accept the cut.

Well, it’s already clear that if you keep score the way the banks do, the size of the haircut is going to be a whole lot less than 50%. There’s a good chance that the big bank concession to these tough negotiators is going to be close to the 21% haircut banks accepted in the original Greek debt plan in July.

The way to score this part of the deal is with a financial measure called net present value. Net present value takes into account the fact that money in your hand today is more valuable than money you’ll receive sometime down the road. ("I’ll gladly pay you Tuesday for a hamburger today," as Wimpy says in those Popeye comics.)

It’s more valuable because its purchasing power isn’t eroded by inflation, because money in hand is certain while promises of money aren’t, and because you can reinvest money in hand to earn what might be a higher return instead of waiting for those promises to come sailing in.

So, yes, those bankers will be forced—excuse me, “offered the voluntary opportunity”—to take a 50% reduction in the face value of their Greek government bonds. But if the new bonds that the banks receive in exchange for the old Greek bonds come with a shorter maturity—meaning the banks have to wait a shorter time for their money— the loss measured by net present value will be less than 50%.

If the bonds carry a higher interest rate, there’s again less loss when measured by net present value. If a sweetener to the deal gives banks some immediate cash payout when they sign up for their haircut, then the net present value loss will be less than 50%.

And one thing we know for certain is that Greek banks, which hold about $70 billion in Greek government bonds, will need about $40 billion to bail them out when the face value of the Greek government bonds they hold is cut by this deal. That’s about $14 billion more than the rescue package included in the July deal. (And we do know who will pay that, right? It’s not the Tooth Fairy.)

NEXT: Counting on a Booming Greek Economy

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Counting on a Booming Greek Economy
Still too peripheral for you?

Well, let’s go to the math at the heart of this deal—and the claim that a 50% writedown in the face value of what Greece owes will reduce Greek debt to a sustainable 120% of gross domestic product by 2020.

Oh, missed the “by 2020” part? It wasn’t exactly proudly emphasized when the grand plan was announced. That’s because if it had been, it might have produced some disconcerting questions about the economic assumptions behind that claim.

I’ve mocked the very idea that a debt-to-GDP ratio of 120% can be called sustainable. In their book This Time Is Different, on why it takes longer for economies to recover from a financial crisis than a run-of-the-mill recession, Carmen Reinhart and Kenneth Rogoff peg a 90% debt-to-GDP ratio as the make-or-break point.

After looking at 44 countries over 200 years, they conclude that ratios above 90% take—at the median—1 percentage point off the annual GDP growth rate. On average, a ratio above 90% takes 4 percentage points off the annual GDP growth rate.

Last I looked, Greece didn’t have 1 percentage point of growth—let alone 4—to give away. The International Monetary Fund projects that the Greek economy will shrink by 5.5% in 2011 and an additional 2.5% in 2012. Yeah, 120% is sustainable.

But if you look at the math that Eurozone leaders—or, more likely, the experts who advised them—used to get to that 120% ratio by 2020, there are even bigger problems than the sustainability of that ratio.

Like Greece won’t get to 120% by 2020 at all. No way. Betcha a million zillion drachmas.

To get to that 120% figure for 2020—indeed to get to any debt-to-GDP ratio that far down the road—the experts had to assume some growth rate for the Greek economy over that period. (Spoiler alert: Some of you, I’m sure, already know where this is going. Please don’t spoil it for other readers by shouting out the ending.)

And what growth rates did they plug into their formulas?

Greece, the country with the shrinking economy, will implement new austerity measures and still show enough growth that the government budget will achieve a 4.5% surplus in 2014, the math assumed.

This, mind you, when in October, Greece raised its estimate for its 2011 budget deficit to 9.5% of GDP, from an earlier estimate of 8.6%. The budget deficit is still going in the wrong direction, with the economy shrinking faster than the government can pass and implement deeply unpopular austerity programs.

But even that projection of a 4.5% budget surplus by 2014 isn’t the most amazing piece of math in the grand plan for ending the euro debt crisis. I’d have to give that award to the assumption that the Greek economy will be growing at an annual rate of 3% by 2016.

Hey, this is Europe, remember? European economies—even Germany’s economy—almost never break 2% annual growth.

And this is Greece, right? We’re talking about a country that has major productivity and efficiency problems that make many Greek products and services deeply uncompetitive in global markets. The country has run a trade deficit in every year stretching back to at least 2001.

Unit labor costs rose 40% in Greece between 2000 and 2009. In Germany, the increase was 7%. (Even Spain, at 31%, did better.)

NEXT: Default Is Still in the Cards

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Default Is Still in the Cards
It’s not that the situation can’t be turned around. It’s just that without massive, Argentine-style currency devaluation, the situation can’t be turned around quickly.

Argentina went off its peso/dollar peg in 2001, setting the exchange rate initially at 1.4 pesos to the dollar. The exchange rate rapidly climbed to 4 pesos to the dollar. The country moved to a trade surplus in 2001 and has run a surplus every year since.

(We won’t talk about the cost of being locked out of global capital markets or of inflation, though. The Argentine government recently made it a crime to publish inflation estimates that disagree with the official government inflation rate.)

But here we have the crux of the problem. As long as Greece is stuck with the euro, it can’t devalue. And as long as it is saddled with huge interest payments—under most scenarios, in the next few years, about 25% of the Greek government’s budget will go to interest-rate payments—the country will face a steady diet of new austerity measures that promise an additional decade of crisis.

One or the other has to go. I’d bet Greece winds up keeping the euro and defaulting on its debt. Leaving the euro is just too painful—for Greece and the rest of the Eurozone. Somehow the Eurozone will find a way to keep Greece as a member.

But because the latest euro debt solution doesn’t give Greece any hope of ending its crisis within a reasonable length of time—and because the deal doesn’t offer Greece nearly the debt relief that it seems to—Greece is still looking at default.

But not necessarily because it is financially inevitable. If the rest of Europe decided to carry Greece with cash payments indefinitely, then Greece wouldn’t need to default. If the Greeks were a nation of masochists who enjoyed fiscal pain, then Greece wouldn’t need to default.

But in these negotiations, the countries with the cash have made it clear that they aren’t willing to keep sending it to Athens. The Bundestag vote that gave Chancellor Merkel authority to negotiate the current deal, for example, came with a clear stipulation that Germany would not increase its contribution to the European Financial Stability Facility by a single euro.

And at some point, Greek politicians will do the math and conclude that—except for all those interest payments—the budget would be in balance. At that point, default becomes in Greece’s self-interest.

When I wrote about this in my September 22 column (“If Greece Defaults…Then What?”), I pegged that default to 2012. The most recent deal to save the euro and the tough time that Greece is having in reducing its deficit may have pushed that back to as late as 2013.

But whether it’s 2012 or 2013, my math still adds up to a Greek default. This grand plan hasn’t changed that, even if we don’t have all the details.

Full disclosure: I don’t own shares of any of the companies mentioned in this post in my personal portfolio. The mutual fund I manage, Jubak Global Equity Fund, may or may not now own positions in any stock mentioned in this post. For a full list of the stocks in the fund as of the end of June, see the fund’s portfolio here.