Shares in Tesco (LSE: TSCO) and BHP Billiton (LSE: BLT) have enjoyed a stellar run higher in recent weeks. The grocery giant has seen its stock value advance 6% during the past month, while the mining colossus has seen its shares marching 23% higher.

But are these rises indicative of a tentative turnaround in either firms’ fortunes? Or are they nothing more than a ‘dead cat bounce’?

Commodities clanger

BHP Billiton has stepped skywards thanks to the recovery of commodity prices from January’s troughs.

Iron ore, for example — by some distance BHP Billiton’s single largest market — has seen its value rocket back above the $50 per tonne marker this week thanks to fresh stimulus pledges from the People’s Bank of China.

Still, there’s no doubting that Chinese underlying demand remains washy and is unlikely to plough higher any time soon as the country’s construction sector worsens. And a steady ramping-up of global capacity also threatens to push prices to the downside again — Brazilian mining giant Vale produced a record 345.9m tonnes of the steelmaking ingredient in 2015.

With supply/demand balances also worsening across BHP Billiton’s other key markets, I believe the company’s recent share price ascent is built on shaky foundations.

Shop elsewhere

And Tesco also has plenty of work ahead of it before it can be considered to be out of the woods. Indeed, latest data from Kantar Worldpanel showed sales fell 1.6% in the 12 weeks to 31 January.

Not only is Tesco being bettered on price by Aldi and Lidl, but more affluent customers are flocking to high-end outlets like Waitrose. To add salt to the wounds, mid-tier laggard Sainsbury’s is also attracting shoppers searching for superior quality — sales at the London firm advanced 0.6% in the three months, making Sainsbury’s the only ‘Big Four’ supermarket to report a revenues rise.

And Tesco’s battered reputation took a further pasting this week after it was forced to recall a range of its own-brand butters following a listeria scare. The business is still reeling from the infamous horsemeat scandal of 2013, and this latest scandal is likely to have further ramifications for its dwindling customer base.

But this is one of many problems facing the strained supermarket. Tesco remains locked on a course of profits-crushing discounting to take on the budgeteers — all of its other previous attempts to curry favour with shoppers having fallen on deaf ears. And these competitive pressures are likely to worsen as the German firms steadily expand.

High risk, low reward?

So what does the City think about Tesco and BHP Billiton’s rebound potential?

Well, Tesco is expected to record an 81% earnings bounceback in the year to February 2017, following a predicted 50% slide in fiscal 2016. This year’s figure produces a high P/E rating of 21.5 times. I’m not so optimistic of such a sterling turnaround however, given Tesco’s intensifying battle at the checkouts.

Meanwhile, BHP Billiton is anticipated to suffer an eye-watering 85% earnings descent in the period to June 2016, resulting in an astonishingly-high P/E ratio of 66 times.

I believe that both BHP Billiton and Tesco carry too much risk for savvy investors to sagely invest considering their poor revenues outlooks. And given their bloated earnings ratios, I reckon both are in danger of a severe share price downgrade.

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Royston Wild 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.