Could a portfolio containing only BP (LSE: BP) and Vodafone Group (LSE: VOD) shares beat the market over the next few years?

It’s certainly possible. While a portfolio with just two shares in would be rightly seen as risky and lacking diversification, it could still work. Both stocks have the potential to provide a generous income plus modest capital gains over the long term.

Will lower costs boost oil profits?

Although BP’s profits have been hit hard by the falling price of oil, they’re expected to start to normalise over the next year or so.

Years of $100 oil meant that oil industry costs had become bloated and excessive. The crash forced firms to cut internal costs and negotiate lower rates for external costs, such as drilling rigs and contract staff. Over the last year, costs have fallen both faster and further than expected.

A number of oil industry analysts believe that these lower costs will mean $60 could be the new $100. If oil rises to $60, they expect companies like BP to generate profits similar to those previously earned at $100 per barrel.

If you accept this argument, then BP could certainly be worth a closer look at the moment. The firm’s stock currently looks cheap to me, as it trades on just seven times the firm’s 10-year average earnings per share. This value investing ratio — known as the PE10 — can be a good way of spotting shares that have the potential to deliver a long-term recovery.

A second attraction is BP’s forecast dividend yield of 7.2%. Although this payout isn’t expected to be covered by earnings this year, cover should improve considerably next year. It’s also worth considering that even if the forecast payout of $0.40 per share was cut by 25%, the resulting forecast yield of 5.6% would still be very attractive.

I believe BP shares are attractive for both value and income. I expect to enjoy decent returns over the next year or two.

Are telecoms stocks the new utilities?

Vodafone’s board has kept its promise to pay a dividend of not less than 11p per share, following the $130bn 2013 sale of its stake in Verizon Wireless. However, this payout wasn’t covered by earnings last year. It’s not expected to be covered this year or next year either.

One reason for Vodafone’s subdued profits is that the firm has been spending heavily on network upgrades. These are needed to meet rising demand for 4G and data services. This £19bn spending programme is now coming to an end and capital expenditure is starting to fall.

Vodafone expects its adjusted free cash flow to rise from £1bn last year to £3.2bn during the current year. That’s equivalent to 12p per share, suggesting to me that the group’s 11p dividend is likely to remain safe.

If current forecasts are correct, investing in this telecoms giant will provide you with a reliable 5.4% dividend yield. In my view, Vodafone will probably deliver on this promise. However, the lack of dividend cover means that a cut is still possible.

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Roland Head owns shares of BP and Vodafone Group. The Motley Fool UK has recommended BP. We Fools don't all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors.