Whisk together 2/3 cup broth, soy sauce, brown sugar, ketchup, ginger, garlic, and vinegar and pour into a large sealable plastic bag.
Add tenderloin and seal bag, then marinate, chilled, turning bag over occasionally, 2 hours.
Bring tenderloin to room temperature, about 1 hour.
Put oven rack in middle position and preheat oven to 425°F.
Pat tenderloin dry and reserve marinade.
Heat oil in a 12-inch ovenproof skillet over moderately high heat until hot but not smoking, then brown tenderloin on all sides, turning with tongs, about 3 minutes total.
Transfer skillet to oven and roast pork until thermometer inserted diagonally into center of meat registers 155°F, 12 to 15 minutes.
Transfer to a cutting board and let stand, loosely covered with foil, 10 minutes.
While meat is roasting, pour marinade through a fine-mesh sieve into a small saucepan and boil until reduced to about 1/3 cup, 10 to 15 minutes. Stir in remaining cup broth and bring sauce to a simmer.
Serve slices of tenderloin with sauce.
Pork keeps, wrapped tightly in foil and chilled, 3 days.
