The recovery in crude prices from January’s troughs has been nothing short of remarkable. From plunging to levels not seen since 2003 — hitting a low of $27.67 per barrel — the Brent index had leapt by more than two-thirds and is now within touching distance of the psychologically-crucial $50 marker.

Unsurprisingly, many of the Footsie’s oil and gas producers have been caught in the updraft. Shell (LSE: RDSB), for example, has seen its share price stomp 24% higher during the period. And while appetite for BP (LSE: BP) has been more volatile, the stock has still gained 4% in value from late January.

However, I believe this buying frenzy leaves both stocks looking seriously overbought.

Capex cuts illustrate patchy confidence

The muddy outlook for the fossil fuels industry was again laid bare by BP’s first-quarter results released yesterday.

Sure, the company may have seen underlying replacement cost profit improve to $532m during January-March, up from $196m in the final quarter of 2015. But BP warned that operational budgets could be cut again should an environment of low oil prices persist.

The London-listed firm — like most of its peers — has embarked on aggressive cost-cutting and asset shedding to mend their battered balance sheets. So news that BP could now slash organic capital expenditure to as low as $15bn in 2017, down from an anticipated $17bn for this year, shows that the industry remains braced for further pain.

Stockpiles growing

And BP is quite right to be concerned, in my opinion, as the recent ascent in crude prices continues to defy the broader fundamental picture.

A failure by OPEC members Saudi Arabia, Qatar and Venezuela to freeze production along with Russia earlier this month is likely to keep the market swimming in excess oil.

The political and economic fault-lines fracturing the cartel mean that an agreement to reduce capacity is as far away as ever, with Iran, for one, determined to keep ramping up production until it hits pre-sanction levels. As a consequence Tehran’s output is expected to continue rising until the middle of next year.

Global stockpiles are in desperate need of relief, latest data from the Energy Information Administration showing levels at US storage tanks hit a fresh record of 540.6m barrels last week. And insipid aggregate demand is hardly helping the situation, either.

Shockingly poor value

Against this backcloth, I believe the resurgent oil price — and with it the share prices of Shell and BP — is in danger of suffering an extreme reversal.

Indeed, BP currently changes hands on a P/E rating of 39 times for 2016, sailing way above the threshold of 10 times that is indicative of stocks with higher risk profiles. And Shell deals on an earnings multiple of 25.9 times.

This leaves plenty of room for a correction, in my opinion, a scenario that could very easily transpire, should industry newsflow continue to disappoint and Federal Reserve rate hikes bolster the US dollar.

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Royston Wild has no position in any shares mentioned. The Motley Fool UK has recommended BP and 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.