The U.S. dollar hasn’t been this strong against the euro in 20 years. Here’s what happened next.

The last time the dollar traded at parity with the euro was late 2002, two decades ago, and what happened afterward fits the contrarian narrative. Over the subsequent five years the dollar weakened considerably against the euro; by early 2008 it took more than US$1.50 to buy one euro, compared to US$1.00 in late 2002. Over this same period, the U.S. Dollar Index fell by 40%.

Not surprisingly, given that the dollar-denominated returns of non-U.S. stocks rise when the U.S. dollar weakens, the S&P 500 SPX, +1.92% seriously lagged the world stock markets over this five-year period. It lagged the FTSE World Ex-US index by almost five percentage points annualized, and the FTSE Europe Index by almost three percentage points.

This five-year period through 2008 represents just one data point. To develop a more comprehensive picture, I measured the correlation between the dollar and the euro going back to the late 1990s, when the euro first started trading on foreign exchange markets. I found that the correlation is inverse: 12-month periods in which the dollar was stronger than the euro were more often than not followed by 12-month periods in which the dollar was weaker — and vice versa.

This correlation was of only moderate statistical significance, so it would be risky to bet everything on it. The strongest conclusion you can draw is that you should by no means bet that the trend of the past 12 months will persist. A somewhat less strong implication is that the past 12 months’ trend may soon reverse itself.

There is a strong correlation between contemporaneous changes in the dollar-euro exchange rate, on the one hand, and the performance of the S&P 500 relative to that of the dollar-denominated return European stocks, on the other. The chart above shows the difference: In those months in which the dollar gained ground relative to the euro, the S&P 500 beat the Vanguard European Stock Index Fund VEUSX, +2.00% by an annualized 16.3%. In those months in which the dollar lost to the euro, in contrast, the S&P 500 lagged the Vanguard fund by 9.5% annualized.

U.S. versus European equities

Even if the euro isn’t stronger than the dollar anytime soon, contrarians would still bet that U.S. stocks will lag European equities. That’s because European equities trade at much lower valuations than their U.S. counterparts, so even if the dollar-euro exchange rate stays constant they offer better value. If the euro strengthens against the dollar, then the return these stocks produce for dollar-denominated investors will be even better.

One indication of how undervalued European stocks are, relative to U.S. stocks, comes from comparing their Cyclically-Adjusted Price-Earnings (CAPE) ratios. On this basis, according to Barclays Indices, European stocks as a whole currently are 31% more undervalued than the U.S. equity market (or 31% less overvalued, depending on your perspective).

If you want to bet on European equities, an index fund is the cheapest way to gain diversified exposure. The ETF in this space with the most assets under management is the Vanguard FTSE Europe ETF VGK, +1.92%, with an 0.08% expense ratio (or just $8 per $10,000 invested).

If you want to try individual stocks, below are the stocks of European companies that currently are recommended for purchase by top-performing newsletters that my auditing firm monitors:

Mark Hulbert is a regular contributor to MarketWatch. His Hulbert Ratings tracks investment newsletters that pay a flat fee to be audited. He can be reached at mark@hulbertratings.com

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