The stock market has been volatile lately, but all concerns seemed to evaporate on Wednesday. Favorable comments from Fed chair Jay Powell continued to make investors more comfortable with the current state of affairs, and that helped markets recover from some choppy sessions earlier in the week. As of 2 p.m. EST, the Dow Jones Industrial Average (DJINDICES:^DJI) had soared 411 points to 31,949, which will be an all-time high if it closes there. The S&P 500 (SNPINDEX:^GSPC) was up 40 points to 3,922, and the Nasdaq Composite (NASDAQINDEX:^IXIC) had more modest gains of 81 points to 13,546.

When people are nervous about the market, they often look for stocks that pay high dividends. When it just so happens that those stocks are in an area that is enjoying a big rebound, that just bodes all the better for their prospects. Today, energy stocks are once again in the spotlight, and powerhouse dividend payers ExxonMobil (NYSE:XOM) and Chevron (NYSE:CVX) are among the industry's giants leading the entire stock market higher.

Calculator, cash, glasses, and notebook with Dividends written in it, and a pen.

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Getting a boost from the oil patch

Throughout the oil and gas industry, shareholders got good news from their holdings. ExxonMobil was up more than 3%, while Chevron tacked on nearly 4%. Elsewhere, oil giants BP (NYSE:BP) and ConocoPhillips (NYSE:COP) also managed to rise more than 4%.

The immediate cause of the good news came from the oil market. Crude prices jumped another 3% on the day, sending the price of West Texas intermediate above the $63 per barrel mark. That's the highest level since before the COVID-19 pandemic, and for many players in the oil and gas exploration and production arena, getting back above $60 has been an essential step toward regaining profitability and generating enough cash flow to finance operations and exploratory activity.

More broadly, market participants have increasingly talked about reflationary trends. With many looking for the economy to bounce back once coronavirus vaccines are distributed, beaten-down industries stand to benefit the most. Specifically for energy, the anticipated surge in demand for goods and services that the pandemic kept pent up could result in greater demand for energy as well -- both from consumers looking to travel and from manufacturers ramping back up their production.

The power of dividends

To be clear, these particular energy stocks aren't the best performers on the day. You'll find plenty of other companies with exposure to oil and gas that are doing even better. For instance, the much smaller E&P players Northern Oil and Gas (NYSEMKT:NOG) and Vermilion Energy (NYSE:VET) are both up more than 10% on the day.

However, many smaller players don't pay dividends. That's largely because these smaller companies face greater financial risk than their bigger peers. Small E&P stocks have to take whatever cash flow they can generate and use it to invest in development efforts and maintain what in many cases are huge loads of debt. For them, even small changes in oil prices can mean the difference between survival and bankruptcy.

For investors looking for the income that dividends provide and the stability that a company's ability to pay a consistent dividend implies, bigger oil plays look attractive. Exxon pays a 6% dividend yield right now, with Chevron and BP weighing in at 5% and ConocoPhillips yielding almost 3.5%. Moreover, many of those companies have been boosting dividends regularly for decades. Both ExxonMobil and Chevron are Dividend Aristocrats with histories of more than a quarter-century of rising payouts for shareholders.

Get what you need

It's true that energy stocks have suffered in the past several years, even as other sectors of the economy have raced higher. However, oil and gas players are having their day in the sun right now. If that's interesting to you, then taking advantage while also getting a nice payday from quarterly dividends is a powerful one-two combination for your portfolio.

This article represents the opinion of the writer, who may disagree with the “official” recommendation position of a Motley Fool premium advisory service. We’re motley! Questioning an investing thesis -- even one of our own -- helps us all think critically about investing and make decisions that help us become smarter, happier, and richer.