Exchange-traded funds have become exceedingly popular, thanks to their ease of use and flexibility in helping investors meet their investing needs. But if you're not careful, it's easy to fall prey to a common trap that many ETF investors fall into: thinking that you own a diversified portfolio, when in fact you own many of the same stocks in different funds. That mistake in turn can cost you thousands in a bear market or correction.

The myth of diversification
The value of having a diversified portfolio is easy to understand. If you invest all of your money in a single stock, then your fortune is completely dependant on how that stock does. Pick wisely, and you can get rich. Pick poorly, and you can lose everything you have. Although some people have the fortitude to make big bets on investments they believe in, most of us can't afford to take that level of risk. That's why owning more than one stock makes sense; that way, even if one stock goes to zero, you'll still have money in other stocks to help you recover your losses over time.

Even a single ETF typically provides a great deal of diversification. Although sector-specific ETFs sometimes have only a handful of stocks, many broad market ETFs have hundreds or even thousands of holdings. In some cases, owning just one ETF can be all you need.

However, you can't assume that adding more ETFs will automatically make your portfolio more diversified. In fact, certain combinations of ETFs will actually give you less diversification.

Different ETFs, same stocks
Let's take a look at an example. Say you've already established a core ETF portfolio, which one might do with the ETF Vanguard Total Stock Market (NYSE: VTI). But to add some diversification, you decide you'd like to buy two other ETFs: a sector play on telecommunications stocks and an emerging-markets fund.

The emerging-markets fund does add to your diversification, because it's a completely different asset class. Neither iShares MSCI Emerging Markets (NYSE: EEM) nor Schwab Emerging Markets Equity has any duplication of stocks with Vanguard's total stock market ETF, because the former hold foreign stocks while the latter tracks a domestic-only index.

Most telecommunication stock sector ETFs, however, are not going to make your portfolio more diversified. That's because you're going to find a lot of the same stocks in there. For instance, if you buy the iShares DJ US Telecom (NYSE: IYZ) ETF, 25% of your assets will go toward shares of AT&T (NYSE: T) and Verizon (NYSE: VZ), while you'll also get decent-sized helpings of smaller competitors CenturyLink (NYSE: CTL) and Frontier Communications (NYSE: FTR). You'll also find those stocks in the Vanguard broad-market fund.

Now, that kind of duplication may be exactly what you want. After all, both Verizon and AT&T have strong footholds in the quickly growing smartphone market, and they're in position to reap the benefits of future advances in technology. Meanwhile, CenturyLink and Frontier may not have quite as glamorous prospects for the future, but their dividend yields give shareholders a big return on their investment, at least for now.

But duplicating stocks isn't diversification, it's concentration. By buying the telecom ETF, you don't broaden out the scope of your portfolio. Rather, you simply change the amount you have allocated to telecom stocks versus the rest of the broader market. Moreover, the more different sector ETFs you buy, the greater the likelihood that all you're doing is mimicking a broad-market ETF.

Stay safe
Diversification helped protect many investors from taking the full brunt of the bear market in 2008 and 2009. It's important for you to be aware of just how diversified your portfolio really is. Don't assume that just because you own a bunch of different ETFs, your portfolio is diversified. Only by taking a close look at the stocks your ETFs own can you be sure about whether you're increasing your diversification.

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Fool contributor Dan Caplinger loves the smell of a well-diversified portfolio in the morning. He doesn't own shares of the companies or ETFs mentioned above. Try any of our Foolish newsletters today, free for 30 days. The Fool's disclosure policy likes catchy three-letter acronyms like TMF and ETF.