One of the most interesting aspects of the stock market, in my view at least is the fact that it has the ability to make investors believe that a share has been written off by the market, only to see the tide turn when results surprise on the upside.

A turning tide?

Investors knew that trading would have been tough at FTSE 100 oil giant BP (LSE: BP) in the first quarter as the price of oil hit lows below $30 for a barrel of Brent crude, a low not seen since 2003. Along with all the other companies in a sector where prices of the extracted commodity can’t be controlled by management, the company announced that Brent oil marker price averaged $34 a barrel in the quarter, compared with $44 in Q4 and $54 in Q1 2015. This put pressure on refining margins which were at the lowest quarterly average for over five years.

However, looking into the second quarter investors were advised that prices had recovered, and have so far averaged $40 during the quarter – a welcome relief to management and investors alike.

Indeed, I felt that management sounded quietly confident in the all-important outlook statement. CEO Bob Dudley indicated that despite gloomy predictions from some corners of the investment community, market fundamentals continue to suggest the combination of robust demand and weak supply growth will move global oil markets closer into balance by year-end.

Of course, the million-dollar question on all investors lips will be what will that oil price do between now and the end of the year.

One thing is sure, management are hoping that the price will move higher, more specifically to prices at least between $50-$55 per barrel as this is the figure that management believes it can still pull oil from the ground profitably, while maintaining the dividend – one of the key attractions to this share.

Can you be sure with Shell?

Shares in BP rose by over 5% on the day that results were announced – so can Royal Dutch Shell (LSE: RDSB) do the same?

As can be seen from the chart below, the shares have been on a bit of a run over the last three months, broadly tracking the rebound in the price of oil and significantly outpacing the FTSE 100.

However, as is the case with BP, Shell doesn’t control the price oil or gas, so I would expect first quarter earnings to fall compared to both Q1 and Q4 2015 when the price of oil was higher.

That said, like BP, Shell is a vertically integrated oil major with a broad spread of assets, both upstream and downstream. This means management is capable of squeezing efficiencies from these assets as well as either selling or delaying projects that don’t offer an acceptable return in the current low price environment.

Dividend stars

Despite the rebound in the share price of both companies, the shares still offer a market-beating 7%-plus yield, which for now I believe is safe. However, should the price of oil crash again or stay lower for longer, then I suspect that the market would become more nervous about a dividend cut.

Let's face it, investors love juicy dividends, and if these dividend stalwarts aren't for you, then you should take a look at this report prepared by one of The Motley Fool's top income advisors, James Early, who has found a share that has stirred his interest.

These are the sort of investment opportunities which, when coupled with other like investments could help contribute to life-changing scenarios (a wealthier retirement for example) and right now, you can access ALL of them for just pennies a day.

To find out more, take a few moments out of your day and download A Top Income Share From The Motley Fool.

The report is free to a good home and you're not obligated in any way. So Click Here sit back, and enjoy.

Dave Sullivan 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.