Kosmos Energy Ltd. is that rare bird, a publicly held pure-play on international exploration, nearly all offshore. If you like risk and lots of upside on the frontier, then this Dallas-based company is for you.

It has no cushy resource play back home to throw off cash flow to fund adventures in exotic places. But that doesn’t bother chief executive officer Brian F. Maxted in the least; in fact, he thrives on looking for elephants—or if you prefer, “accessing new petroleum systems based on new and existing themes and geographies.” ...