In the minds of many investors, buying shares in businesses at the large end of the market brings many advantages. Perceptions of stability, strength, a higher dividend yield and of course safety in size all mean that the largest stocks are owned by a far larger proportion of investors than the smaller ones.

However, some of the largest companies on the ASX have also experienced large falls in their share prices over the past year.

Here are two with strong turnaround potential, and two that are best avoided.

Two to back

Woolworths Limited (ASX: WOW) investors have been through a far bumpier ride in the last 18 months than they have in the past 18 years. A multi-decade period of uninterrupted dividend and earnings growth saw Woolies as the safe bedrock of many portfolios.

With the share price 25% below its 52-week highs, some investors are wondering whether it’s time to cut and run. However, signs are that Woolworths has dealt with the biggest issues facing it.

It now has a new leader in Brad Banducci who knows the business intimately, and has orchestrated a turnaround before, with the now market-leading Dan Murphy’s chain. Management have also made the sensible decision to cut loose the drain on capital that was the loss-making hardware division.

Woolworths is still the largest grocery retailer in the country, and not about to disappear overnight. The experience of Tesco in the United Kingdom shows that fallen market leaders can turnaround, given time and the right management team.

Woodside Petroleum Limited (ASX: WPL) was once a mainstay of many portfolios for its exposure to the massive conventional gas projects off the coast of Australia.

However, the oil price capitulation of recent years has hit the company hard, and the shares are over 25% down on their yearly highs, and almost half post-GFC levels.

But the company as a whole is one of the lowest cost producers of liquid natural gas (LNG) in the world, with multi-decade supply contracts and world class reserves.

While the low oil price might force some energy firms into bankruptcy, this would ultimately benefit low cost producers like Woodside who will remain viable for far longer than most competitors.

Two to sack

QBE Insurance Group Ltd (ASX: QBE) is still one of the 20 largest companies in Australia, but the company is over 25% below its yearly peak, and over 55% lower than its post-GFC high.

Low interest rates hurt insurance companies like QBE, as it earns significant amounts on the interest on the billions in cash it holds at any given time. In addition, more destructive weather events brought about by climate change do not bode well for mass market insurers like QBE.

Telstra Corporation Ltd (ASX: TLS) has a share price that is 20% below its yearly highs. The company has long been able to charge a premium for its services because of reliability. However, recent large-scale outages have severely dented that reputation, at a time when the company was already losing lucrative mobile subscribers to aggressive and more nimble competitors.

The company also seems stuck for growth avenues, with a recent expansion into the Philippines aborted before it was even begun and no clarity about how it will expand from its current size.

Foolish takeaway

Size does not necessarily mean safety, and investing solely in yesterday’s winners or “blue chips” of the past could lead to you missing out on much better opportunities.

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Motley Fool contributor Ry Padarath has no position in any stocks mentioned. Unless otherwise noted, the author does not have a position in any stocks mentioned by the author in the comments below. 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.