The Dow Jones Industrials (^DJI -0.11%) purports to provide a representative view of the U.S. stock market. Apart from its avoidance of transportation and utility stocks, given the fact that other Dow averages focus exclusively on those areas, the Dow chooses its 30 components in a way that tries to include companies from every major sector of the market.

Yet given the limitations of having only 30 stocks and the peculiarities of its price-weighted methodology, the Dow isn't able to give every sector of the market the representation it deserves. Let's look at two areas in which the Dow is particularly egregious in short-changing investors: gold and financial stocks.

The not-so-golden Dow
The Dow doesn't include very many basic-materials stocks of any type, and it has no direct gold exposure at all. DuPont technically counts as a basic-materials company, but its traditional emphasis on chemicals and its evolution toward greater exposure toward agricultural products keeps it well clear of the gold arena. The only metals producer in the Dow is Alcoa, and given aluminum's woes and the rock-bottom share price that Alcoa has, its influence in the Dow is minimal.

The main problem with gold stocks is that none of them as large as most typical Dow components. But arguably the best candidate is Freeport-McMoRan Copper & Gold (FCX 0.52%), which as its name suggests brings the combination of gold and copper production to the table. Its recent acquisitions of two energy-related companies make it a more diversified natural-resources company, but with just two energy stocks, the Dow could benefit from a different angle on oil and gas as well. With Freeport commanding twice the market cap of Newmont Mining and almost double Alcoa's market cap, Freeport is the more logical choice to replace Alcoa and give the Dow a more golden future.

Too few financials?
At first glance, the Dow doesn't seem to be struggling for financial exposure, with two big banks, a combination bank and credit card company, and an insurance giant. But even with those companies within the Dow, the sector carries less than half the weight of the S&P.

Here, the big problem is that share prices aren't reflective of market cap. The most egregious example is Bank of America (BAC -0.13%), whose market cap is double that of American Express yet carries only a fifth of AmEx's weight in the Dow because of its low price. Substituting in Wells Fargo (WFC -0.56%) or even former Dow component Citigroup would potentially address much of the problem, as their shares trade at least somewhat more in line with the other Dow financials. Barring that, a reverse share split for B of A would boost the Dow's exposure to financials quite nicely as well.

Looking for balance
The Dow doesn't have to match up with the S&P 500's sector exposure perfectly, as otherwise, there'd be no need to have both indexes. But with a big underweighting of financials and no gold exposure, the Dow misses out on some trends that the broader market offers to those investors willing to take advantage of them. By being aware of the Dow's gaps, you can consider whether you want to add your own individual stock exposure to fill out your portfolio.