There's a lot of debate about whether we're in a new bull market after the S&P 500 rebounded more than 20% from its recent bottom. While this current rally might fizzle out if we experience a recession later this year, bear markets always give way to a new bull market -- eventually. When that upswing finally occurs, cyclical stocks that fell during the bear market could rally sharply.

The recent bear market hasn't been kind to Devon Energy (DVN 0.19%) and NextEra Energy Partners (NEP -0.89%). They both currently sit more than 30% below their 52-week highs. This sell-off has pushed their dividend yields up to much higher levels. Here's why these high-yield dividend stocks could skyrocket in a bull market.

The fuel to return more cash to shareholders

As an oil producer, Devon Energy's cash flow rises and falls with crude prices. Oil prices have fallen during the current bear market on concerns that the economy will slow down and sap demand for oil. However, crude prices tend to rally during bull markets because the economy is growing, fueling more demand for oil.

Oil prices also impact Devon Energy's dividend because of its fixed-plus-variable framework. The company pays out about half of its free cash flow in dividends.

With oil prices declining in recent quarters, its combined dividend payment has fallen from a peak of $1.55 per share last fall to $0.72 per share last quarter. Despite that decline, Devon still offers a high annualized dividend yield of 5.9% since its share price has also fallen sharply (it's down more than 35% from its 52-week high). 

A new bull market in oil prices would enable Devon Energy to produce a lot more cash to pay dividends. A rising dividend would likely boost its share price.

Meanwhile, Devon uses a portion of the cash flow it retains to repurchase shares. The company recently boosted its buyback program by 50% to $3 billion, enough to retire 9% of its outstanding shares. That buyback could provide its stock with an additional boost during a bull market.

Expect a rebound when optimism returns

The recent bear market has weighed on NextEra Energy Partners. The renewable energy producer's shares have declined by about 30% from their 52-week high.

That's partly due to concerns about its ability to secure new growth funding as investors pull back on supplying capital amid worries that the economy is slowing down. This decline has pushed the company's dividend yield up to 5.8%.

NextEra Energy Partners recently unveiled a plan to significantly reduce its near-term financing needs. It expects to sell its remaining natural gas pipeline assets over the next few years.

This will give it the money to redeem some outstanding financing and fund new renewable energy investments as its shifts its focus to becoming a pure-play renewable energy producer. Meanwhile, its parent, NextEra Energy (NEE -1.36%), agreed to suspend its management fees through 2026 to provide additional financial support during this transition period. 

These financing initiatives should enable NextEra Energy Partners to deliver on its plan to grow its dividend at a 12% to 15% annual rate through 2026. They'll give it the financial flexibility to continue acquiring cash-flowing renewable energy assets from NextEra Energy and third parties to power the dividend. 

While the current bear market is weighing on NextEra Energy Partners' valuation, a future bull market should lift the weight on its share price. That's because a return to optimism would make investors more willing to provide NextEra Energy Partners with capital to continue expanding. That could give it the power to continue growing at a rapid rate in the future.

Get paid well while awaiting the rebound

The recent bear market has weighed on the valuations of Devon Energy and NextEra Energy Partners, pushing up their dividend yields. Because of that, investors can earn a lucrative income stream while waiting for the eventual stock market recovery. That potentially sets them up to earn strong total returns in the next bull market.