What happened

Oil stocks sizzled on Tuesday after a soft start to the week, with shares of some notable names from the industry clocking big gains during the day. At their highest points in Tuesday trading, Occidental Petroleum (OXY 0.07%) stock surged 8.7%, while Devon Energy (DVN 0.33%) and Diamondback Energy (FANG -2.30%) gained 6% each.

Crude oil prices jumped more than 3% Tuesday, which explains the rally in these oil stocks. Investors in Occidental Petroleum, though, found an even bigger reason to load up on the oil stock while they still can, making it one of the best-performing oil stocks for the day.

So what

The relationship between oil prices and upstream oil and gas companies is pretty straightforward: Rising crude oil prices fetch these companies more money for the oil they sell, and more money means bigger cash flows. Occidental, for example, can generate annualized incremental cash flows worth nearly $225 million for every $1 change in the per-barrel price of crude oil.

More importantly, since most oil companies are also committed to paying a stable and growing dividend, higher cash flows also often translate into bigger shareholder returns. That's one of the primary reasons oil dividend stocks rallied on Tuesday.

For perspective, Occidental increased its annual dividend payout by a whopping 1,200% earlier this year after paring debt aggressively. Yet, while Occidental still pays a small fixed dividend, Devon Energy and Diamondback Energy have emerged as monster dividend stocks thanks to their fixed-plus-variable dividend policies. Put simply, their dividend payouts rise alongside crude oil prices.

Devon, for instance, pays a fixed dividend per share as well as a variable dividend equivalent to 50% of the excess cash flows remaining after accounting for capital expenditures and the fixed dividend component. Under the policy, Devon has used this year's oil boom to pay monster dividends: It has boosted its total dividend per share by more than 200% over just four quarters.

Diamondback Energy's dividend growth has been equally monstrous. It has bumped up its quarterly dividend from only $0.60 per share in the fourth quarter of 2021 to a whopping $3.05 per share in the second quarter.

The lure of such dividend growth, when backed by strong financials, is so strong that even legendary investors like Warren Buffett who have historically steered clear of cyclical stocks are giving in. Buffett, in fact, had a key role to play in Occidental stock's Tuesday jump.

Now what

Buffett has been aggressively buying shares in Occidental Petroleum in recent months and owns nearly a 20% stake in the oil company as last reported. What no one knew, though, was that Buffett is eyeing a 50% stake in the oil giant. On Aug. 19, the Federal Energy Regulatory Commission cleared an application from Buffett's Berkshire Hathaway to buy up to a 50% stake in Occidental.

The development, unsurprisingly, has triggered frenzied buying activity in Occidental as the market expects the oil stock to head even higher as Buffett buys more shares. Speculation is rife that Buffett could even acquire Occidental. 

With oil prices rebounding as well on Tuesday, the Buffett angle proved to be the perfect impetus for Occidental's rising stock price.