The Dow Jones Industrial Average (^DJI -0.98%) is famous for its resistance to change. The only change in the last four years was forced by former member Kraft Foods' splitting in half, with each half lacking the scale to keep a seat on the Dow. The member list has changed only 52 times in 128 years, or 25 times since it first became a 30-ticker list in 1928. Breaking into this exclusive club takes extraordinary qualities.

That's something Apple (AAPL 0.52%) has delivered in spades for the last decade or so. The pride of Cupertino is still the world's largest company by market cap, edging out oil giant ExxonMobil (XOM 0.23%) despite a horrific 29% plunge over the last 12 months. In a long-term perspective, the Dow and Exxon look like they're flatlining next to Apple's fantastic growth.

AAPL Chart

AAPL data by YCharts.

Apple also rules the roost in terms of trailing net income, where its $37.7 billion performance beats runner-up Exxon by nearly $2 billion. Its $43 billion in trailing free cash flows places Apple third in the world, losing out only to a pair of multinational banking titans. On this list, Exxon misses the top 10, with only $13.7 billion in free cash flows to its name.

That's an elite performance record, no matter how you slice it. And yet Apple has not been invited to the Dow. What would it take to get Cupertino into the market's oldest index?

The answer comes in two parts. For one, the Dow is a price-weighted index, meaning that stocks with high share prices automatically account for a larger portion of the Dow's value than lower-priced shares. Today, IBM (IBM -8.25%) has the honor of being the heaviest-weighted Dow stock thanks to a $183 share price. That's 50% more than the runner-up and more than 20 times the weight of Alcoa. If the aluminum producer doubled in price overnight, it would add about 60 points to the Dow. IBM would move the index 60 points with just a 4% price change.

And that's why Apple isn't particularly welcome, with share prices in the $500 neighborhood. That's more than twice IBM's price, and a fairly ordinary 1.6% price swing would hit the Dow as hard as Alcoa's doubling (or plummeting to zero).

Apple could overcome this obstacle by performing a simple share split, trading every current stub for something like five or 10 new shares. It's a common enough maneuver, and one that doesn't really change anything about the stock's total value or the underlying business. Apple hasn't done a split since 2005, but if the Dow's steering committee called Apple's board up with a tit-for-tat proposal, I'm sure Cupertino could break up its shares to fit better on the Dow.

But then there's the second half of the answer, which brings us right back to where we started: The Dow doesn't like change. Apple looks pretty awesome right now, but what if it's just a flash in the pan?

Sure, Apple has more than 30 years of operating history to fall back on. But only the last 10 years or so qualify as a Dow-style success story. And Apple works in a notoriously volatile industry. Less than five years ago, Canadian smartphone veteran BlackBerry (BB -3.14%) (nee Research In Motion) sported a market cap nearly the size of Apple's. But then Apple took off on the back of iPhones and iPads, while BlackBerry missed the boat, and the Canadians are now looking for an exit strategy.

AAPL Market Cap Chart

AAPL Market Cap data by YCharts.

Who's to say that this won't happen to Apple in the next unforeseen mobile revolution? This is the second, and probably more important reason why the world's biggest, baddest stock still isn't on the Dow. The uncertainty regarding CEO Tim Cook's ability to keep the creative juices flowing in Cupertino only add to the burden of proof.

If Apple can deliver some serious innovation under Cook and stay this big, this efficient, and this important for another five years or so, I'd wager that we'll see a quick stock split that lets Apple enter the Dow. But not now. Cook must prove that he and his company belong in the market's most elite club.