Alcoa (AA) celebrated the beginning of earnings season last night with a strong quarterly report, and while the Dow Jones Industrials (^DJI -1.72%) no longer gets a direct boost from its former member's rising share price, the blue-chip still rose 82 points as of 12:30 p.m. EDT. Yet even though the stock market benefits from the good mood that Alcoa's report gave investors, those who track the Dow could learn a lot from the index's mistakes that have become clear in hindsight, not only with Alcoa but with former Dow components Bank of America (BAC -2.26%) and Hewlett-Packard (HPQ -0.11%).

Alcoa is just one example of stocks that have done extremely well after getting kicked out of the Dow Jones Industrials. Since it left the Dow last fall, Alcoa has climbed 56%, crushing the index's return by more than 50 percentage points. Today's 3.7% rise for the aluminum stock shows just how much progress it has made, with the company reporting adjusted income that nearly doubled what investors had expected. Alcoa hasn't been able to entirely escape a poor environment for aluminum, but by cutting back on raw production capacity while focusing more on promising tailor-made products for key customers in the aerospace and automotive segments, Alcoa has set the stage for a strong turnaround.

As you can see below, Alcoa's performance isn't unique:

AA Chart

Stock return data by YCharts.

Hewlett-Packard has also managed to rise more than 50% since last fall, crushing the Dow Jones Industrials' return, and although Bank of America's returns were relatively minor, they reflected follow-through share-price increases from already-impressive gains prior to the bank leaving the index. For Hewlett-Packard, long-term turnaround efforts are still under way, as CEO Meg Whitman presses forward with a strategic plan that she hopes will move the tech giant into more prosperous lines of business. Similarly, Bank of America has made huge progress since the financial crisis, getting the go-ahead last month to boost its dividend by fivefold.

Patience is a profitable virtue
What all three of these stocks show is that although the committee that chooses components for the Dow Jones Industrials doesn't necessarily have the patience to deal with turnaround candidates, smart value investors can make big profits from steering clear of the sell button. By identifying these stocks right after they were evicted from the Dow, investors could have cashed in on what turned out to be a lucrative opportunity.

For long-term investors, it's important to note that none of these three stocks has come close to recovering past losses -- something that the Dow Jones Industrials has done for more than a year in setting new record highs repeatedly during 2013. But the lesson that even those with a long time horizon can learn is that just because a stock has suffered huge losses doesn't mean that it's automatically smart to sell your shares. Sometimes, stocks with promising prospects can bounce back and help you get more from your position than you would by cutting the cord too early.

The Dow Jones Industrials members are all prestigious companies with track records of success. But smart investors realize that stocks that have investors doubting their future have more potential for gains when things go right. That's the lesson you can learn from Alcoa today and from Bank of America, Hewlett-Packard, and countless other stocks with impressive turnaround stories.