There's a similar one in the stockmarket: "The problem with investing in turnaround situations is that they often don't turn!"

It can be incredibly tempting to look at bombed-out share prices that have fallen 60, 75 or in some cases more than 95 per cent from their highs and think "if only the share prices recover to those former levels, I'll be rich". After all, remember a stock that has fallen 95 per cent from a high will increase 20-fold from that new low price if it gets back to that previous peak.

Unfortunately, the possible downside is just as serious no matter what the share price – if the company goes broke, you lose 100% of your money whether the shares are trading at $50 or 5¢.

Still, companies which have found themselves in hard times or whose shares have been abandoned by investors can be a fertile hunting ground – as long as you're careful.

Where others fear to tread

More often than not, the market has marked down the shares of a company for all the right reasons – too much debt, slowing sales, superseded technology or falling margins chiefly among them.

But from time to time, investors get it wrong – mistaking short-term problems for long-term ones, or taking too pessimistic a view on a company's future. Sometimes falling margins are temporary, or a sales contract is delayed. Other times a company is investing heavily up front – hurting profits – for a longer-term gain down the track. In yet other cases, investors get the challenges and opportunities right but are simply so pessimistic that they simply undervalue the remaining business.

Bargain hunters aren't immune from those problems, and there's an additional (and opposite) challenge. We tend to be an optimistic lot, and can see how a company might get itself out of trouble. The problem is that knowing how something might be achieved is different from the management team being able to deliver on that goal.

Three for the basket

With all of that said, we've had a look around for some potential turnaround candidates as we start 2013. These are higher-risk by their very nature, and there's a chance that one or more may not be around in a year or two if circumstances move against them.

Accordingly, they're only for investors with a high tolerance for risk and only for a small portion of their portfolios. Importantly, too, we recommend you play these situations as a "basket" of shares – that is, diversify your risk by owning them as a group.

Here's our "turnaround basket" play for 2013:

Billabong International (ASX: BBG)

We were highlighting Billabong for a spot in a turnaround basket even before a second takeover offer was lobbed for the company this week and the share price shot up. Frankly, that just gives us two opportunities. If the company is acquired at $1.10 (the indicative offer price), we'll bank a short-term gain. If it doesn't go ahead, the share price will likely fall back, but the turnaround case isn't predicated on a takeover.

There's potential in the company – both its brands and retail business. Notwithstanding the challenge it faces, today's price likely undervalues Billabong, and there is a good chance a strong management team can wring out higher profits in future.

Fairfax Media (ASX: FXJ)

Fairfax, the publisher of this website, is a leader in what is now a dying business – print newspapers. The company has a cost base and infrastructure which is more akin to its past than its future. The positive news is that management has realised that it must completely and irreversibly engage with this future, rather than try to have a foot in both camps. Having one foot on the boat and another on the wharf is rarely a good long-term strategy!

Notwithstanding its write-downs and 20th century infrastructure, Fairfax has a good underlying profit base, and some wonderful mastheads in its urban and regional newspapers, meaning the current share price will look inexpensive if the company can harness them in the digital age.

Ten Network (ASX: TEN)

The second media company in our basket is the laggard in commercial television in Australia. A fixed cost base, poor advertising market and lousy ratings are a painful trifecta. However, having recently raised capital, most of the risk of bankruptcy has receded and it has taken painful steps to reduce programming costs, including cutting large numbers of staff from its news department.

Media companies are often cyclical – advertising and ratings ebb and flow. With a newly lowered cost base, an unexciting ad market and poor ratings, Ten is at the bottom of the barrel. Economic growth helps drive advertising, and a couple of hit shows could do wonders for viewer numbers. If those things comes to pass, today's share price will likely look cheap.

Foolish takeaway

Make no mistake; one or more of these companies could turn out to be bad investments, or worse. They don't have good track records or attractive industry dynamics that would usually help to protect a business if times got tough.

That's why they're higher-risk ideas, to be bought as a basket, for investors very comfortable with risk and volatility. The odds are reasonable of overall gains from here, but nothing in investing – least of all potential turnarounds – can be taken for granted.

Attention: If high-risk turnarounds aren't your thing – or if you want to diversify your portfolio – foolish, dividend loving investors and BusinessDay readers alike can request a Motley Fool free report entitled Secure Your Future with 3 Rock-Solid Dividend Stocks.

Scott Phillips is a Motley Fool investment analyst. You can follow Scott on Twitter. The Motley Fool's purpose is to educate, amuse and enrich investors. This article contains general investment advice only (under AFSL 400691).