Today, I’ll be looking at three FTSE 100 giants that have more than disappointed shareholders over the last few years and asking which of them might be the first to return to full health.

Is the recovery on?

A recent report from Kantar Worldpanel suggests that while the big four supermarkets are continuing to lose market share to Aldi and Lidl, the rate of decline isn’t as great as before. Encouragingly for shareholders, Tesco (LSE:TSCO) showed the smallest drop in sales (1%) for the 12 weeks ending May 22.

While not exactly skipping down the road to recovery, Dave Lewis does appear to be stabilising the retailer (and even managing to return it to profit). His commitment to selling inessential parts, improving supplier relationships and removing the layers of complexity that seemed to dominate former CEO Philip Clarke’s tenure is encouraging.

Despite this, the lack of dividends until 2017 at the earliest may be too long a wait for some. Moreover, now that food retailing has changed for good, Tesco must compete more intensively just to stand still. Even if Kantar’s research shows that 94% of visitors to Aldi and Lidl also visit one big four supermarket at least once every four weeks, Tesco’s shares remain a hold for me until evidence appears that it’s making bigger strides in fighting back.

Ready to gallop?

With the significant wobble experienced by the market back in January now a distant memory, Lloyds (LSE:LLOY) has recovered to where it was at the start of the year. With shares exchanging hands for 71p, the bank trades on a price-to-earnings (P/E) ratio of just over 9 for 2016. That’s rather cheap. Better still, it has a rolling price-to-earnings growth (PEG) ratio of just 0.23, according to Stockopedia. This means the stock looks very undervalued based on future growth expectations.

Despite being one of the most traded shares on the London Stock Exchange, it’s understandable if long-term investors are wary of the £51bn cap and its financial peers. The past behaviour of bankers and the woeful levels of return endured by shareholders since the financial crisis can’t be easily forgotten.

Should Britain remain in the EU however, it’s likely Lloyds shares will rise significantly post-referendum. It appears well run and the expected dividend of around 6% for 2016 is impressive. As a result, I’m cautiously optimistic. Prospective investors may wish to drip-feed their cash and benefit from pound cost averaging rather than invest all their capital in one go.

Oil have some of that

A recent reduction in capex means Royal Dutch Shell’s (LSE:RDSB) dividend should be safe for now, even if the company will still need to dip into reserves to cover its obligations this year. This is good news for loyal shareholders, as are analyst predictions that earnings will rise 28% in 2016 and 84% in 2017.

Of course, the company’s future depends on what it can’t control, namely the price of black gold. While nobody can know for sure what will happen in the near term (just remember those predictions of $15 a barrel in January), it does seem like Shell might be past the worst. It won’t exactly bounce back to previous highs but a gradual ascent of its share price is feasible.

Shell’s shares currently trade at 1,666p with a forecast P/E of under 12 for 2017.

So overall, it looks Lloyds might see the biggest bounce in its share price over the next year or so, assuming that global events don't dictate otherwise.

Most companies experience tough times at some point. While some problems will be beyond the control of management (such as the recent oil price slump), investors should consider retaining the shares if a board appears to be taking action where it can. If the business model and strategies are sound, periods of volatility can present shareholders with a chance to increase their holdings as they await a recovery. As always, a detailed and dispassionate evaluation of a company is advised before any decisions are taken.

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Paul Summers owns shares in Tesco and Royal Dutch Shell. The Motley Fool UK has recommended Royal Dutch Shell B. We Fools don't all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors.