The dollar rally has room to run, and those who stand in its way risk getting bowled over by its unstoppable strength. That's the view of hedge funds and investment banks from New York to Melbourne, as a Bloomberg gauge of the world's reserve currency heads higher, breaking past its pandemic peak to a fresh record.

Potential catalysts are numerous and lie on both sides of the dollar smile argument—which suggests the U.S. currency can benefit in times of strong growth and during an economic slowdown. Investors say it may only be a matter of time before anything from a hawkish Federal Reserve to a global recession turbocharges the greenback higher.

"Don't fight it; it's not the right time to go against dollar strength yet," said George Boubouras, head of research at hedge fund K2 Asset Management in Melbourne, who sees the greenback rising against everything from emerging-market currencies to the euro. "You can't see a bottoming out of developed-market recession risks—it's too difficult to short the dollar anytime soon."