September was a tough month for the Dow Jones Industrial Average (^DJI 0.40%), but that wasn't the case for every Dow constituent. A small handful of the index's components managed to gain a bit of ground last month.

This raises a question: Are last month's rare rallies a sign of lasting growth, or are they just volatility-driven moves that will soon be unwound? If you look at the context of these bullish moves, you can make a reasonable decision regarding the Dow's best-performing stocks in September.

What went right

Last month's biggest Dow winners were UnitedHealth Group (UNH 0.30%), Amgen (AMGN 0.22%), and Chevron (CVX 0.37%), gaining 5.8%, 4.9%, and 4.7%, respectively, versus the Dow's loss of 3.5%.

UNH Chart

UNH data by YCharts.

With UnitedHealth shares, there was no company-specific reason. The insurer was named as a service provider for a select number of Texas' Medicaid enrollees, but that's not exactly game-changing for the company.

Rather, if you look at the timing of most of the stock's September gain, it correlates strongly with the broad market's most bearish days. Fearing that more marketwide selling was on the way, investors specifically sought out safe-haven names like UnitedHealth Group.

Amgen shares also benefited from this flight to more economically resilient names when most other stocks were crashing mid-month. But that wasn't its big bullish driver. Early in the month, the Federal Trade Commission announced it would allow the biopharma to proceed with its acquisition of Horizon Therapeutics with only modest stipulations.

In the meantime, Amgen made presentations at a couple of different investor conferences, stoking interest in the stock and its obesity treatments AMG-786 and AMG-133 in particular.

As for Chevron, the underpinnings of its strength are pretty obvious. Oil prices continue to rise, setting the stage for even fatter profits. Crude oil futures advanced from less than $70 per barrel in late June to a multi-month high of just under $90. And given its relatively tight supply at this time, CEO Mike Wirth believes oil could top $100 (albeit only temporarily) in the near future.

To buy or not to buy?

So, are any or all of these Dow stocks worth buying in the wake of last month's market-beating rallies? As always, it depends on so much more than one month's headlines and performance.

Take UnitedHealth Group as an example. It's the epitome of consistency, and analysts believe it's undervalued. The current consensus price target of nearly $571 per share is nearly 12% above the stock's present price near $511. Moreover, there's good reason to see UnitedHealth as a safe-haven stock.

Nevertheless, most investors might be better served looking at other options. That's because as a slow-growth dividend-paying name, UnitedHealth shares are priced pretty richly at more than its trailing and projected earnings. The current dividend yield of 1.4% is subpar, too.

Besides, what happens if and when the overall market starts to perform again? This company has already shown its inverse relationship with most other stocks. If they're rising, that puts pressure on UnitedHealth.

Amgen is also a tough name to get excited about after its September run-up. Indeed, the stock's 24% jump from June's low pushes it past analysts' current consensus price target of $261.94, and they had every opportunity to raise that target in the meantime.

More of them also rate the stock a mere hold rather than a buy, suggesting any net benefit of its acquisition of Horizon Therapeutics is already priced in.

On the flip side, Amgen's dividend yield of 3.2% is compelling, and its forward-looking price-to-earnings ratio of 14 is about as cheap as you'll find with any biopharma stock right now. If your portfolio needs some exposure to this industry and you also need some income, there's a narrowly focused case to be made for a long-term position in Amgen.

Lastly, Chevron is a buy -- plain and simple -- for most investors. That's not to suggest crude prices will remain uncomfortably high forever. Analysts with Citigroup believe they'll be back near $70 per barrel next year, and not even Chevron's CEO believes his near-term price expectation of $100 per barrel will persist.

Nevertheless, oil's cyclical price surges could last for a decade. The world is nowhere near being ready to wean itself from oil. Consumption hit yet another new record last year despite the planet's continued work toward transitioning to cleaner alternative energy. And the International Energy Agency doesn't even expect to see this consumption growth start slowing until 2028.

This subsequent (and mostly bullish) price volatility ultimately does oil companies like Chevron more good than harm, as exhausting as its volatility may be.

This is how you should be thinking all the time

These particular buy/avoid rationales won't always be in play. Eventually, the overall market will be on a steady enough footing that investors won't be worrying about safe-haven stocks like UnitedHealth. Amgen's drug portfolio will eventually be underestimated. Oil prices will eventually be under more long-term (and perhaps permanent) pressure.

Right now, though, these dynamics look to be in place long enough for all investors to take heed of them. And no stock should ever be bought based on one month's performance or one single criterion. There's always more to the story with a stock and its underlying company, and most of that story matters to some degree.

The part of the story that matters the least? Probably the previous month's performance.