2015 was a disastrous year for FTSE 100 stalwarts BP (LSE: BP) and Tesco (LSE: TSCO). These are two of the biggest names on the index, and operate in very different sectors, yet both suffered the same grisly fate. BP is down 20% over the past 12 months, while Tesco is down 30%. And this is no short-term shakeout. Over five years BP is down 35% and Tesco is down more than 60%.

Faded glories

Investors shouldn’t approach either stock expecting a return to the glory days. At today’s price of 327p, BP is way below its all-time high of 711p, achieved back in April 2006. This is worth repeating: BP is trading at less than half its price of a decade ago. With oil in free fall, that distant peak may remain forever out of sight.

Tesco peaked at 491p in November 2007, shortly before the financial crisis. It now trades at less than one-third of its all-time high, at 152p. With the grocery sector under sustained assault from Aldi and Lidl, wage packets still slim and margin-crunching deflation rampant, few expect Tesco boss Dave Lewis to restore the glory days either.

Fighting back

That doesn’t mean you should abandon either stock. At today’s knockdown prices they don’t have to scale former peaks to be a profitable investment. There are signs of a recovery lately, as both stocks surprisingly defy the wider market rout. BP has been fuelled by a SocGen upgrade from hold to buy, with the bank praising its foresight in predicting last year that oil could drop to $45 a barrel and stay lower for longer, at a time when markets were still expecting $80 to $90.

Forewarned is forearmed, and by cutting costs early SocGen reckons BP will be able to balance cash flows and sustain its dividend until the oil price recovers. This is based on the assumption that oil will hit $60 next year, which I reckon is feasible, as the US shale shake-out belatedly begins. It would be quite some feat if BP did sustain its dividend, given that it currently yields 8.5% and cover has fallen to 0.5. But it does look a tempting play for bold contrarians.

Christmas Cracker

Tesco is actually up 5% over the past month after beating downbeat forecasts to enjoy a happy Christmas (a rarity in recent years) with UK volumes up 3.5% and transactions up 3.4%. That’s particularly impressive given the wider seasonal grocery drop. Lewis pinned the festive fun on lower prices, a strong product range and much-improved customer service, three areas where customers have been crying out for change.

Tesco has also enjoyed success in womenswear and knitwear, while posting growth in Europe and Asia, notably Thailand. Trading at 16.2 times earnings, it’s hardly dirt cheap, while its forecast yield for February 2017 is thin gruel at 1%. Also, its Christmas success must be set against signs of continuing Tesco decline in the third quarter.

Both BP and Tesco could make a surprise comeback. All BP really needs is a reversal in the oil price, which will surely come, the only question is when. Tesco has a harder task ahead of it, as the UK economy and consumer wage growth slows.

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Harvey Jones has no position in any shares mentioned. The Motley Fool UK has no position in any of the shares mentioned. We Fools don't all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors.