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You've heard the euro's nicknames: "Teflon euro," "safe haven euro," and "Draghi's euro."
They're referring to the persistent strength of the currency in the face of a slew of obstacles.
First, the euro zone faces stagnant or near-zero growth and an 11.6 percent unemployment rate—still close to the 12 percent post-crisis peak.
Consumer prices are barely rising: They're up only 0.5 percent, the lowest level in more than four years, and it's the ninth month where inflation has been running below 1 percent.
Then there's the banking system, with potential shocks lurking, such as a financially troubled parent company of one of Portugal's biggest banks.
Even with the European Central Bank's extraordinary easy policy—including the recently unveiled unprecedented negative deposit rates, near-zero interest rates and a fresh round of low-cost loans to pump up lending—the banking system is fragile.
While the euro has fallen recently from its May highs of 1.39 to 1.35, a drop of nearly 3 percent, it's still trading above its historical average. Market participants, economists and policymakers still find themselves scratching their heads about the remarkable resilience of the currency in the face of so many factors building against it.
Furthermore, when one of the world's most powerful central bankers wants a weaker currency, it's usually a sure bet that the currency will weaken.
And ECB President Mario Draghi has made it clear that's part of what he has in mind.
"In the present contact, an appreciated exchange rate is a risk to the sustainability of the recovery," Draghi told the European Parliament's Committee on Economic and Monetary Affairs in Strasbourg earlier this month.
So why does the currency remain stubbornly stronger?
Ask a European politician and you'll hear that it's the unwavering commitment to European integration and the steadfast political support and devotion to the European monetary union.
Market pros, however, point to the ECB.
A stronger euro started with the magic words uttered by Draghi in July 2012, when he vowed to do "whatever it takes" to save the currency.
Read MoreEurope's two 'weak links'-guess who?
It bottomed on that day at 1.20, has risen to nearly 1.40 by March 2014.
That marked the beginning of the paradox of the ECB.
That is, when Draghi promised to do whatever it takes—and then followed it up with easing measures to pump up Europe's economy (think LTRO, rate cuts)—not only did the euro bottom, but so did European stocks and bonds. In fact, with the promise of easy policy and cheap money, those assets became very attractive.
Money flowed in.
European stocks marched almost 50 percent higher from the day of the Draghi speech, hitting multiyear highs by the end of last month. Greek stocks leapt 100 percent, and Spanish stocks jumped 87 percent.
European peripheral bonds staged an even more remarkable comeback.
In Spain, the 10-year bond yield fell from 7.6 percent to below 2.6 percent now. Similar rallies pushed rates lower across Italy, Portugal, Greece, and Ireland as investors pounced on peripheral debt.
Herein lies the ECB paradox.
According to BlackRock chief investment strategist Jeffrey Rosenberg, "when they take actions to stabilize the euro zone (do whatever it takes), and that entails zero interest rates and flooding markets with liquidity and narrowing the peripheral to core country interest rate differentials…that might suggest a lower value of the euro." However, Rosenberg continues "that brings more demand for euro-denominated assets and hence more demand for the euro."
That idea turns the traditional thinking of what drives currencies on its head.
"The net impact of the ECB's actions are ambiguous on the value of the euro," said Rosenberg.
In other words, interest rate differentials typically serve as a primary driver of currency values. That explains why the consensus view going into 2014 was for the euro to weaken against the dollar because the Fed is in tightening mode while the ECB is firmly in easing mode. And historically, currencies do tend to follow relative paths of interest rates.
So how do you explain the stronger euro versus dollar earlier in the year (from 1.35 to 1.39) when the ECB was raising hopes of easy policy to fight inflation and boost growth?
Strategists say you can partly point to those rising European stocks and bonds, driven by easy policies of the ECB. But there was an added factor behind the currency's move: U.S. Treasury yields were falling as frigid winter weather took a bite out of U.S. economic growth and pushed back expectations of Fed tightening, boosting the dollar and further weakening the euro.
So while yields in the U.S. slumped to multimonth lows and pulled down the dollar, dovish easy ECB policy at the same time was boosting European assets and therefore the euro.
According to David Woo, head of global rates and currencies strategy at Bank of America Merrill Lynch, "with the euro area running a current account surplus, a precondition for a lower euro is increased purchases of foreign securities by European investors. So far this year, European investors have been happy to stay close to home—European fixed income assets have done very well this year, especially on a volatility-adjusted basis."
At the same time, "the consensus remains that a significant selloff in U.S. Treasurys has yet to come."
"By doing whatever it takes to support the euro zone, the ECB takes the tail risk out of the equation," said Rosenberg, referring to a potential euro zone collapse and breakup.
"That strengthens the euro. And that impact offsets the interest rate policies that may lead to a weaker euro. … In this line of thinking, currencies are not an asset class by themselves. Rather they are a means to owning an asset class, whether it be stocks, bonds, real assets, etc."
The next path for the euro could be determined by whether the voracious demand holds up for European stocks and bonds.
And watch whether U.S. Treasury yields stay historically low or start to creep higher on rising inflation expectations, higher interest rates or a better economy.
There's also the third factor to keep in mind—big money loves the euro.
"Reserve diversification into euros is strong. For each U.S. dollar of diversification our analysis of 87 reserve managers shows 67 percent bought euros versus the dollar," said Sebastien Galy, senior currency strategist at Societe Generale.
In Societe Generale's survey published this month, 11 percent of those dollars went to buying yen, 5.4 percent Australia's dollar and smaller amounts of British pounds and Chinese yuan.
Beyond the daily swings in European stocks and bonds, and shifting expectations for interest rates, inflation and economic growth, there is a fundamental bid and growing trust in the euro.
—By CNBC's Sara Eisen