The Dogs of the Dow is a popular investing strategy, where you simply invest in the Dow Jones Industrial Average (^DJI 0.40%) components least favored by the Street in a given year.

The idea is simple. You start with a heavily vetted list of elite American companies, narrow it down to the names under heavy market fire, and invest in the concept that these titans of industry surely will recover from whatever brought them to this shortlist in the first place. Sit down with a list of Dow stocks at the start of the year, identify the ten components with the highest dividend yields, and invest equal dollar amounts across these ten stocks.

Due to the math involved in calculating dividend yields, a lofty value often indicates weak stock price performance -- coupled with a willingness to share cash profits with shareholders through dividend payouts.

Then you wait a year and rebalance the portfolio to the updated list of so-called Dogs. Lather, rinse, repeat, and laugh all the way to the bank.

It's more than a theory, too. The Dogs of the Dow beat the market in 2022, stopping at a loss of 1.6% versus an 8.3% drop for the Dow as a whole. The more inclusive S&P 500 (^GSPC 1.02%) index suffered an even deeper 19.4% loss in the same period.

But it's not a perfect system. In the first 10 months of 2023, the Dow lost 0.3% and the S&P 500 gained 9.2%. But a portfolio featuring equal investments in last year's 10 Dogs of the Dow lost 5% of it value in the same span. Not a backbreaking underperformance, but worse than the standard alternatives.

On a related note, some of last year's worst performers among the Dow elite have delivered strong gains in 2023. Intel (INTC -9.20%), Salesforce.com cs CRM), and Walt Disney (DIS -0.04%) all took haircuts of more than 40% last year. Disney is down another 2% in 2023 but Intel has gained 44% and Salesforce is up by 56% so far.

With swings like these in the rearview mirror, why not take a peek at this year's deepest Dow losses? I'm not saying that Chevron (CVX 0.37%), 3M (MMM 0.46%), and Walgreens Boots Alliance (WBA 0.57%) are surefire winners starting from their currently low prices, but they certainly deserve a closer look. Are these struggling veterans getting back on their feet anytime soon?

Chevron: Down 14.5% in 2023

Oil and natural gas giant Chevron is struggling with a sea change in the energy sector. Old-school carbon fuels are going out of style, pushed aside by greener alternatives such as solar power, hydrogen from carbon-capture systems, and wind turbines. The market shift was arguably started by Tesla (TSLA -1.11%) years ago, as the company made all-electric vehicles cool and paired that sentiment with a focus on solar energy. Now, the whole auto industry is moving away from gas-powered cars and trucks. That's not good news for a gas veteran like Chevron.

Now, Chevron is a well-heeled business with $5.8 billion of cash equivalents and a stunning $264 billion in total assets. The value of those oil fields adds up in a hurry. This would be a good time to shift the oil-focused business over to a greener strategy. Chevron does run some solar and hydrogen operations, but they didn't even merit a mention of their financial results in last week's third-quarter report. Instead, Chevron is issuing $53 billion of new stock in order to acquire smaller oil producer Hess (HES 0.67%).

So it looks like the oil giant is doubling down on the wrong ideas nowadays. Some of my Foolish colleagues see the stock as a solid dividend investment at the moment, arguing that the energy industry won't turn on a dime. I'm not so sure. Chevron's substantial price drop in 2023 looks well-deserved and I wouldn't recommend buying it today.

3M: Down 23.8% in 2023

Industrial materials specialist 3M has been grappling with legal issues on top of the inflation-based economic pressures in recent years.

The company recently signed a $6 billion settlement for the suitability of 3M's earplug materials in military combat situations. At the same time, preliminary agreements to fix chemical pollution in 3M's wastewater could be a precursor to an even larger legal payout.

With falling revenues and free cash flows over the last two years, 3M seems poorly equipped to handle a plethora of expensive legal adventures. And while the earplug settlement doesn't include any admission of guilt, investors must wonder whether there are more skeletons in the Minnesotan closet. These issues shine an unflattering light on 3M's management.

The company is bulking up its balance sheet by spinning off its healthcare business -- but that's actually one of the company's most successful divisions. Kicking a star player to the sidelines in a time of weaker financial results and big-ticker legal challenges doesn't seem like a good move.

So that's another potentially well-deserved price drop. Will our third underperformer break the downtrend?

Walgreens Boots Alliance: Down 40.8% in 2023

Alright, what's going on with the multinational convenience store and pharmacy chain? Well, the C-suite is packed with new names, including the all-important CEO and CFO seats. Getting the replacements up to speed on this massive and complicated operation may take some time, exposing Walgreens to unexpected challenges in an unstable economy.

The business isn't exactly running on rails today. Top-line sales got back to modest year-over-year growth in recent quarters, but free cash flows are still down in the last three years. The company is deeply unprofitable, and the ongoing cost-cutting program may not be enough to push the bottom line across the breakeven threshold.

So the stock trades at a hair-raising 0.1 times sales and 6 times forward earnings projections today. Valuation ratios like these are usually reserved for companies on the brink of financial catastrophe. Is that a glaring market-maker mistake? I don't know for sure, but the painful stock chart looks like an overreaction. Freshly installed CEO Tim Wentworth has a long history running Walgreens' pharmacy services and should hit the ground running.

You shouldn't bet the doghouse on this potential Dog of the Dow; still, a small investment in Walgreens Boots Alliance could pay off over time if I'm right about Wentworth's prospects.