LONDON (Reuters) - The euro’s downward momentum is gathering strength, raising the risk that the single currency overshoots estimates of fair value and hits parity with the U.S. dollar within the next year.

The euro last traded below parity in June 2002, before a period of sustained dollar weakness saw the single currency appreciate for six years to a lifetime high above $1.60 in 2008.

The subsequent reversal has taken it back to a four-year low at $1.2142. In 2010 alone, it has shed 17 percent from its January peak to its May trough, weighed down by negative factors stemming from the build-up of fiscal deficits in peripheral euro zone countries, primarily Greece.

Such concerns led euro zone governments to agree a 750 billion euro rescue package earlier this month to try to shore up confidence in bond markets, but the deal has provided little durable support for the ailing currency.

The euro downtrend has so far stalled at $1.2142, stopping well shy of the currency’s January 1999 launch rate at $1.1747, but analysts say currencies’ tendency to overshoot estimates of where they should be means further weakness is likely.

The $1.18 level is the single currency’s lifetime weekly average, said Jane Foley, Research Director at Forex.Com, adding that area that could be considered “fair value.”

“Historically currencies don’t stay around fair value for long. In the medium term I think there is a risk of overshoot which could take us down to the $1.15/1.10 area,” she said.

Foley did not rule out a long-term move toward parity with the dollar, but if that were to occur, she did not think it would stay around the $1.00 level for long before bouncing.

The euro has also moved toward levels associated with purchasing power parity, an economic theory that estimates the amount of adjustment needed in an exchange rate in order for it to be equivalent to each currency’s purchasing power.

BNP Paribas’s estimate of PPP in euro/dollar currently stands at $1.1370. The bank’s FX strategists expect the euro to drop to parity and possibly beyond by the first quarter of 2011.

They cite the historic tendency for the euro to overshoot PPP by at least one standard deviation, which measures variation from the mean.

Based on BNP Paribas estimates, a one standard deviation overshoot would put the euro down to levels around $1.03.

An overshoot by 2 standard deviations would take the euro to around $0.87, a level not seen since the first quarter of 2002, and not far from record lows of $0.8225 hit in October 2000.

“PPP gives you a framework as to where currencies are trading in the bigger picture. At the moment our PPP estimates suggests the euro is overvalued,” said Ian Stannard, senior currency strategist at BNP Paribas.

“Assuming an adjustment to one standard deviation below PPP, this provides a target of $1.03, which is consistent with our forecast of parity,” he said.

POSITIONING

The latest CFTC positioning data showed euro shorts being pared back slightly, though they remain close to record levels.

Analysts said that although there was little room for speculators to add to shorts, the increasing desire for reserve diversification would create the need for further euro selling.

“There’s still a lot of euro short positioning to be done from reserve managers, institutional investors and the corporate sector,” said Forex.com’s Foley.

“Any squeezes toward $1.26/1.27 will provide levels for them to sell.”

Technical analysts said there was a good chance the euro would get to parity.

Boris Simonder, certified technical strategist at Nordea Bank, put the chance at more than 50 percent.

“The trend here is that support levels are being taken out one by one, and that short-term rallies are being used as selling opportunities, and rightfully so. It’s hard to make the case for owning the euro, both technically and fundamentally.”