Today I’m looking at the investment case of two falling London leviathans.

Oil play keeps plunging

Shares in fossil fuels giant Tullow Oil (LSE: TLW) mirrored the behaviour of the Brent crude benchmark last week, and choppy trading conditions sent the stock 4% lower during the period.

Oil values may have steadied at $30 to $35 per barrel after recovering from January’s multi-year troughs below $28. But prices have failed to push on thanks to lasting fears over the huge imbalance washing over the crude market, leaving prices in danger of a fresh downleg.

The latest data from the Energy Information Administration (EIA) showed US stockpiles climbing by a further 2.1m barrels week-on-week, taking total supplies to a new record of 504.1m barrels.

And investor confidence over a deal between OPEC members like Saudi Arabia and Russia to put the brakes on future output has run out of steam too. With good reason, in my opinion, as production cuts rather than the proposed ‘freeze’ are needed to mitigate sluggish demand and pull inventories lower.

Despite these concerns, the City expects the bottom line at Tullow Oil to keep on improving in 2016 as production at the firm’s TEN project in Ghana kicks off. The company saw losses narrow to 111.3 US cents per share last year from 170.9 cents in 2014, and Tullow Oil is anticipated to print earnings of 14.4 cents in 2016.

However, this projection still leaves the business dealing on an elevated P/E rating of 24.8 times, sailing above the benchmark of 15 times that represents stellar value. Given the murky state of the oil market and the prospect of further revenues woes, I reckon the risks at Tullow Oil far outweigh the potential rewards.

Platinum perils

Like Tullow Oil, I reckon the chronic oversupply affecting commodity markets should keep Lonmin (LSE: LMI) on the back foot. The platinum giant surrendered 5% of its share value last week, and I reckon falls to fresh lows could be on the cards.

Lonmin has enjoyed a solid share-price bump in February despite last week’s fall as metal prices have bubbled higher. Platinum has gained 8% since the start of the month and struck three-month peaks around $960 per ounce at one point.

But fears over metal demand looking ahead remain a millstone around Lonmin’s neck thanks to China’s cooling economy, adding to intensifying concerns that the diesel market may be entering terminal decline. On top of this, monetary easing across much of the world also threatens to send the US dollar higher again in the months ahead, adding another layer of trouble to Lonmin’s top-line projections.

While it’s true the company has worked relentlessly to mend its wafer-thin balance sheet — Lonmin has slashed thousands of jobs and shuttered mines to reduce its cost base — I believe the prospect of prolonged demand weakness makes the platinum giant a risk too far.

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