Ever since I showed that gold is wildly overpriced on a historical basis, I have been looking for ways to demolish the conclusion that we are in a gold bubble. Why? That way, I could either reject the notion or achieve greater certainty about it. Now, the ongoing turmoil in Europe has spurred my imagination into constructing a crisis scenario to try to justify today's inflated gold prices.

Turning somersaults
As the Greek debt crisis has continued to fester, European officials and bankers are coming up with contrived stop-gap plans to put off the day of reckoning. Slowly, ever so slowly, we appear to be headed toward a fork in the road: On one side is Greek default and an ignominious exit from the Eurozone; on the other, Greece becomes a permanent ward of the European Union/northern European nations.

Under a default scenario, the Greek banking system becomes insolvent and would require a recapitalization. As a result, National Bank of Greece (NYSE: NBG) shareholders would be wiped out. Not surprisingly, the huge ambient uncertainty has done nothing good for Greek citizens' confidence in the safety of their assets. On Monday, credit rating agency Moody's reported that Greek banks had lost 8% of their deposits since the beginning of the year.

The case of the vanishing bank deposits
Where are these deposits going? Roughly half of the drop is a response to declining incomes, but the other half is "confidence-sensitive depositors ... transferring funds abroad and converting their deposits into gold coins, while others have been placing their cash into bank safety-boxes."  (Emphasis mine.)

The U.S. is insolvent, too
Greece is emblematic of a wider problem: the massive accumulation of sovereign debt in many developed countries coupled with low growth prospects. Need I remind readers that the U.S. faces a debt crisis of its own? The uncertainty concerning the extension of the debt ceiling is the tip of the iceberg; once the total liabilities relating to Medicare, Medicaid, and Social Security are added to existing debt, the U.S. is technically insolvent. Despite the U.S.'s huge advantages, it's no longer possible to rule out a dollar crisis entirely, despite what our irresponsible politicians' behavior suggests.

In its annual report on U.S. economic policy released last week, the International Monetary Fund warned against the possibility of "a sudden increase in interest rates and/or a sovereign downgrade if an agreement on consolidation does not materialize or the debt ceiling is not raised soon enough." In that context, here are two possible scenarios for the U.S. and their potential impact on gold prices:

 

Scenario 1

Scenario 2

Description

Crisis

Mounting concern regarding the inability of the U.S. government to address the long-term sustainability of the country's finances reaches a tipping point. Concern gives way to fear, then panic, spurring a dollar crisis.

U.S. government bonds lose status as the global risk-free benchmark and the reserve asset of choice. Surplus countries and other investors reduce their exposure to the dollar, selling U.S. assets at an accelerating pace and driving Treasury yields significantly higher.

The U.S. banking system, including too-big-to-fail institutions like Citigroup (NYSE: C) and Bank of America (NYSE: BAC), comes under intense stress, and without a safety net this time (there is no lender of last resort).

Recovery/Muddle-through

U.S. government addresses its fiscal position to put it on a sound footing for the long term.

The U.S. economic recovery achieves "escape velocity," led by multinationals like Caterpillar (NYSE: CAT), Procter & Gamble (NYSE: PG), and Boeing (NYSE: BA). Employment improves, the housing market stabilizes, and consumer confidence improves.

China engineers a soft landing of its economy and allows the renminbi to appreciate. Global macroeconomic imbalances decline.

Hypothetical price impact on gold market

The price of gold explodes to $5,000 per ounce

Investors are desperate to own any asset regarded as a safe haven. Unprecedented demand overwhelms limited supply and the clearing price for gold shoots up to $5,000 per ounce.

Gold declines to $500 per ounce

The Fed raises interest rates, thereby raising the opportunity cost of holding gold.

As investors discount the possibility of another financial crisis as increasingly unlikely, they reduce their exposure to gold. The metal's price reverts back to its historical average price (approximately $500).

Probability

Unknowable/Small (but rising)

Unknowable

Now, for the sake of argument, let's assume we assign odds of 25% to Scenario 1 and 75% to Scenario 2. Under those assumptions, a fair price for gold is (.25)*(5,000) + (.75)(500) = $1,625, a slight premium to current prices. Let me emphasize that I have no idea what the price of gold would be in a crisis of extreme severity, but the number seems plausible and I'm not trying to predict what will actually occur. I constructed this very simple model to get a sense of the assumptions that are necessary to justify today's prices.

"Possible" doesn't equal "probable"
As the analysis shows, it is possible to justify $1,500 gold under a specific set of assumptions. In the follow-up article, I'll explain why I remain unconvinced and why investors who own bullion or gold-backed ETFs such as the SPDR Gold Shares (NYSE: GLD) almost certainly misunderstand the nature of their position.

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Fool contributor Alex Dumortier holds no position in any company mentioned. Click here to see his holdings and a short bio. You can follow him on Twitter. The Motley Fool owns shares of National Bank of Greece SA. The Fool owns shares of and has opened a short position on Bank of America. Motley Fool newsletter services have recommended buying shares of Procter & Gamble. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.