Two of Warren Buffett's biggest stock holdings -- oil giants Chevron (CVX 1.54%) and Occidental Petroleum (OXY 0.89%) -- got some unexpectedly good news this week. Saudi Arabia revealed it would cut its output by 500,000 barrels per day (BPD) beginning next month, with Russia and others following with their own reductions. That news shocked the oil sector and sent oil prices soaring above $80 a barrel. It could drive crude prices even higher in the coming months as demand rebounds. 

Here's a look at the news and how Buffett stands to benefit.

Drilling down into the news

Saudi Arabia is leading a surprise cut in global oil supplies. The country said it will make a voluntary 500,000 BPD reduction in its output starting next month that will last until the end of this year. In addition, several other OPEC members will cut their output. Meanwhile, Russia agreed to extend its 500,000 BPD cut from last month through the end of the year. That amounts to a more than 1 million BPD reduction in global oil supplies. 

What makes that cut so surprising is that demand is on pace to rebound sharply in the coming months. The International Energy Agency (IEA) expects global oil consumption to accelerate throughout the year. It forecasted demand to grow by 710,000 BPD during the first quarter and 2.6 million BPD by the fourth quarter. While the IEA predicted that global oil supplies from non-OPEC countries would increase this year, it anticipates that demand will begin to outstrip supplies in the second half. That gap will widen now that Saudi Arabia and Russia are slashing their supplies. 

Those conditions could push crude prices higher in the coming months. A return of $100 oil before the end of the year isn't out of the question.

A well-timed oil bet

Warren Buffett is in an excellent position to capitalize on higher oil prices, especially following his recent moves to bolster his position in Occidental Petroleum. Buffett's company, Berkshire Hathaway (BRK.A 1.18%) (BRK.B 1.30%), has purchased shares of Occidental several times over the past month, taking advantage of a lower price point. Berkshire now owns about 23.5% of Occidental's outstanding shares. They're worth around $13.8 billion, roughly 4% of Warren Buffett's stock portfolio, making it the sixth-largest holding. 

Meanwhile, Berkshire has an even larger position in Chevron. Buffett's company owns 8.8% of the oil giant's outstanding shares, worth about $28.4 billion. That's Berkshire's third-largest position at 8.3% of its portfolio. 

The value of both oil stocks will likely rise alongside oil prices. That's because higher oil prices would enable Chevron and Occidental to produce more cash. That will give them more money they can return to shareholders.

Chevron could use its oil-fueled cash flows to buy back shares at the top end of its $10 billion to $20 billion repurchase range. At the high end, the oil giant could retire up to 6% of its outstanding shares each year. The company could also continue building cash on its balance sheet, putting it in an even stronger position for the future.

Occidental Petroleum will also likely use its oil-fueled cash flows for shareholder returns. The company already increased its dividend by 38% this year and replenished its $3 billion share repurchase program. That will bring shareholder returns close to the $4 per share level that would allow the company to start redeeming some of Berkshire's $10 billion preferred stock investment in the company. That move would free up cash flow -- Occidental pays Berkshire 8% per year or $800 million in preferred dividends -- that it could reallocate toward rewarding all shareholders through dividends and repurchases.

Higher oil prices will benefit Buffett's oil stocks

Saudi Arabia's unexpected decision to slash production should boost oil prices in the coming months, especially given the demand catalysts. That should benefit oil producers, including Chevron and Occidental. It could enable them to produce more free cash flow that they'd likely return to shareholders. Those catalysts could boost their stock prices, which will benefit Buffett and other investors.