I think it’s fair to say that BP (LSE: BP) took the market as a whole by surprise on Tuesday when it reported its results for the full year and fourth quarter of 2015.

The underlying replacement cost profit (this is the measure preferred by analysts as it strips out one-off charges) for the full year was $5.9bn, compared with $12.1bn reported for 2014, a fall of 51%. The underlying result for the fourth quarter was $196m, compared with $2.2bn for the fourth quarter of 2014 – down over 90%!

Rather unsurprisingly, Mr. Market marked the shares down by over 10% at one stage during trading, although the shares recovered some ground to finish the trading day at 335p, off by nearly 9%.

Following the downward trend in the oil and gas sector, in oil (Brent crude down nearly 2%) and in the FTSE 100 (off by 2.5%), was sector peer Royal Dutch Shell (LSE: RDSB). Shell saw its shares sell off to finish the day at 1435p, down by 4.3%.

Hardly surprising?

As we can see from the chart below, the share price of both companies trended lower during the course of 2015 as the decline in the oil price caused investors to believe that operations were going to be tougher for longer.

Personally, I think that BP’s results were a wake-up call to the market. In my view, it didn’t properly factor-in the effect of the falling oil price. As we’ve seen this week, the market has marked-down the shares in Shell too on the belief that we could well see similar disappointing results when they’re released tomorrow.

What’s a Fool to do?

Speaking as an investor with no position in either of the shares or the commodity under review here, I believe that investors need to take a long-term view with both of these companies.

As I’ve written before, it’s simply impossible (though some might try) to call a bottom to either the price of oil or the share prices of BP and Shell, or to any other company for that matter.

Indeed, there are so many moving parts here you’d need a degree in mathematics to come up with an algorithm to factor-in variables such as the oil price, the integration of BG Group and OPECs next move.

Sadly (or maybe fortunately for me) I don’t have the relevant degree. But I do have the patience to wait for the market to become too pessimistic about these giants of the industry, both of whom have traded in difficult conditions before.

This can also work for current holders of the shares with a view to adding to their holding. And let’s not forget, investors are being paid to wait with BP currently yielding around 8% and Shell around 9%. I think that these yields are safe currently – though, of course they would come under pressure should the oil price stay lower for longer.

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Dave Sullivan has no position in any shares mentioned. The Motley Fool UK has recommended 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.