How did Apple Inc. do it? The high-tech company that couldn't do anything right in the mid-1990s has emerged as the world's most valuable company, with a stock-market capitalization of about $342 billion.

Apple's triumph happened this week amid extreme market turbulence. Shares of Exxon Mobil Corp., which had been number one in stock-market value, tumbled in tandem with falling oil prices. Apple didn't fall as much.

Stepping back, though, it's clear that Apple's rise to the top reflects its remarkable agility. Apple is dwarfed by Wal-Mart Stores Inc. in terms of revenue and employee headcount; it lags Exxon Mobil in annual net income. No other big company, however, comes close to Apple's ability to conquer new markets, one after another.

Just 14 years ago, Apple's business consisted almost entirely of a small and dwindling share of the personal computer market. Today, as Bloomberg's Adam Satariano points out, Apple gets two-thirds of its revenue from iPhones and iPads, two products that didn't exist five years ago. Apple keeps its growth-stock valuation because investors feel confident that the company hasn't run out of big ideas.

As rapidly as Apple retools its product line, it stays loyal to a few core values. It makes easy-to-use, elegant products. It charges premium prices for them. It has enough faith in its own engineering to leap ahead of what customers already like -- on the belief that it can correctly anticipate what they want next.

Apple won't always be blunder-free. Every company that becomes a market-cap leader eventually cedes that honor to a newer entrant or a resurgent rival. But Apple's advance should still be seen as a reminder of how much can be accomplished with ingenuity and conviction.

(George Anders is a member of the Bloomberg View editorial board.)