There are over 2,000 shares listed on the Australian share market or ASX.

Of course, many of the companies are small and likely unprofitable.

However, many investors — and their advisors — become fixated on owning just a few popular names so that they overlook some of the best businesses in Australia.

In fact, many of the shares included in the top 200, or S&P/ASX 200 (Index: ^AXJO) (ASX: XJO), I personally wouldn’t buy.

Here are three blue-chip shares I wouldn’t buy in 2016.

  1. Rio Tinto Limited (ASX: RIO)

Rio Tinto is Australia’s largest iron ore miner. Its shares, perhaps surprisingly given the plummeting iron ore prices, have fallen only 10% in the past year. Rio Tinto is believed to be the lowest-cost producer at the mine level, with cash costs less than $20 per tonne. However, all it would take is further falls in volatile commodity prices to wipe out Rio’s dividend and take its shares lower.

  1. BHP Billiton Limited (ASX: BHP)

BHP Billiton was recently removed from its mantle as Australia’s biggest company. Like Rio (but to a greater extent), BHP has been rocked by falling commodity prices. By scrapping its dividend and watching its share price crumble, BHP has yet again shown why investing in even the biggest and most diversified mining shares can be risky.

  1. Australia and New Zealand Banking Group (ASX: ANZ)

ANZ shares are down 32% in a year, but that’s not why I’d avoid it in 2016. Like BHP and Rio Tinto above, ANZ – in fact all major Australian banks – has so many moving parts that it’s extremely difficult to get a firm handle on its valuation. No valuation is foolproof, I’ll admit, but given the extra uncertainty associated with having many business lines across multiple geographies and markets, investors should demand a bargain price before buying. I doubt ANZ shares will fall to that level in 2016.

Foolish takeaway

The three shares above are established companies with powerful brands, but investors must consider the risks involved with every investment. Simply because they’re the biggest doesn’t make them the best. Indeed, Australia’s share market has some 2,000 companies listed yet accounts for less than 2% of global markets.

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Motley Fool Contributor Owen Raszkiewicz does not have a financial interest in any company mentioned. Owen welcomes -- and encourages -- your feedback on Google+, LinkedIn or you can follow him on Twitter @ASXinvest.

The Motley Fool Australia has no position in any of the stocks mentioned. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy. This article contains general investment advice only (under AFSL 400691). Authorised by Bruce Jackson.