John Maynard Keynes famously observed that if you owe your bank a hundred pounds, you have a problem. But if you owe it a million, it has a problem. One has to wonder what he might have said of Greece and the European Central Bank (ECB), since Greece now owes the ECB a staggering 104 billion euros, or over 60 percent of that country’s GDP. This has to keep ECB President Mario Draghi awake at night, since he has to know that those loans dwarf the ECB's 10 billion euros in paid-up capital.

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Two slippery slopes have led the ECB to such imprudent Greek exposure. The first was through its secondary market purchases of around 27 billion euros in Greek government bonds at the height of the European sovereign debt crisis in 2011 and 2012. The ECB engaged in such purchases as market lending to Greek froze, which threatened to push Greece into default. Fearing that a Greek default might spawn contagion to the rest of the European economic periphery and might thereby precipitate a full-blown European banking crisis, the ECB found ways to get around its own constitutional strictures prohibiting it from the monetary financing of a member country's budget deficit.

The second and more pernicious way in which the ECB's Greek exposure has mushroomed has been through its lending to prop up the Greek banking system. The ECB has done so as the Greek banks have bled deposits in reaction to depositors' fears that Greece might be forced to exit the euro. The ECB has also done so despite the very poor quality of the collateral that the Greek banks have offered as security for those loans.

Recent Greek political developments underline the difficult position in which the ECB now finds itself. Over the past three months, against the backdrop of the election of a far-left Greek government opposed to austerity and structural reform, the Greek banks have lost over 25 euros billion in deposits or around 15 percent of the total. This has obliged the ECB to increase its support to the Greek banking system to 77 billion euros. It has also placed the ECB in the unenviable position of soon having to decide whether or not to double-up on its already very high Greek exposure should the run on the Greek banks continue.

There are many uncertainties surrounding the full ramifications of a Greek default on its official obligations. However, it would seem clear that were Greece indeed to default, the ECB would not be spared from sizeable losses on its Greek lending. Since, much as the ECB would like to enjoy the preferred creditor status customarily afforded to the International Monetary Fund (IMF), at more than 30 percent of the total, the ECB's relative exposure to Greece is too large to afford it that luxury.

Being forced to recognize large losses on its Greek lending would be politically very awkward for the ECB, since such recognition would threaten to more than wipe out the ECB's slender capital base. That in turn would oblige the ECB to have to seek a fresh capital infusion from its members. Needless to add, there has to be the real risk that having to admit to European taxpayers large losses on ECB lending might fuel the already strong anti-bailout sentiment in the euro's core member countries.

Since embracing full-bodied quantitative easing earlier this year, the ECB has faced strong opposition to its unorthodox policy approach, particularly in Germany, its main shareholder. At this delicate juncture for the euro, the last thing that the ECB now needs is a further erosion in political support as a result of Greek loan losses, since one has to expect that a Greek default would trigger a meltdown of the Greek banking system, which would in turn spread contagion to the rest of the European periphery's banking system. One would think that if Greece's financial instability is to be ring-fenced successfully, one would need an ECB about which there was no doubt about its ability to act as a decisive lender of last resort.

Sadly, the present buoyancy of the non-Greek European sovereign debt market has seemingly lulled many European policymakers into a false sense of complacency about the systemic consequences of a Greek exit from the euro. One must hope that before allowing themselves to be blinded by such complacency, those policymakers might give due consideration to the probable consequences of a Greek default on the ECB's room for policy maneuver. If they do so, they might not be so cavalier about the prospect of a Greek policy accident for the rest of Europe.

Lachman is a resident fellow at the American Enterprise Institute. He was formerly a deputy director in the International Monetary Fund's Policy Development and Review Department and the chief emerging market economic strategist at Salomon Smith Barney.