Yesterday was a great day for anyone who has been bullish on most anything tied to the steel industry. Three companies in particular that performed well were AK Steel Holding Corporation (AKS), Alpha Natural Resources (NYSE: ANR), and Arch Coal (NYSE: ACI), each of which were up more than 8% with Alpha Natural Resources leading the pack with a 9.42% gain.

The rally came after positive news coming out of China that the Chinese economy appears to be picking up steam, led primarily by its service sector, combined with a report issued by Goldman Sachs stating that the steel industry is beginning to look more attractive; the market read between the lines and perceived this as a strong signal to buy. For the companies involved in the steel business, this should serve as positive news, especially if analysts' expectations about the industry outlook prove to be true.

However, what does this mean for existing shareholders or prospective shareholders of the businesses positively affected by this news? Does it present investors with a buying opportunity, or should they take their gains now and walk? In an effort to arrive at a conclusion, I've taken each company listed above and provided an analysis of its fundamental quality and what the news above means for it.

AK Steel
Although AK Steel is an American company, it is one of the largest beneficiaries of China's economy improving. You see, as the producer of around 50% of the world's steel, China's much-feared slowdown would serve to depress steel prices (and pretty much anything else related to it) further. The underlying reason here is that, with the world already experiencing excess steel supply relative to demand, signs of a slowdown would indicate that it would take longer to work through the supply before steel manufacturers can increase their prices and stop operating at a loss. 

This is especially helpful for AK Steel, seeing as how the company has struggled for the past few years. For instance, in four of the past five years, the company has operated at a loss, a phenomenon that has resulted in larger net losses every year. While the company posted a modest profit of $4 million in 2008, this quickly swung to a loss by 2009 and has continued, even forcing the company to book a nearly $1.03 billion loss in 2012. Unfortunately, this trend has persisted into the company's 2013 fiscal year, even in spite of marginally successful attempts to mitigate expenses.

Alpha Natural Resources
As is the case of AK Steel, Alpha Natural Resources is another major player in steel that is affected by what happens in China. However, instead of being affected as a producer of steel, it's affected as a supplier of metallurgical coal used in the production of steel.

In spite of increased revenue, which has risen by 182.5% from $2.47 billion in 2008 to $6.97 billion in 2012, the company has seen increasing pressure on its bottom line, as demonstrated by its two most recent years resulting in net losses. In sum, these net losses amount to $3.17 billion on paper, while its income from operating activities has declined by a more modest 25.3% since 2010.

In addition to being a beneficiary of China's reports of growth and the announcement made by Goldman Sachs on steel, the company has also been pushed up by investors following a better-than-expected earnings release. In it, the company announced that it had lost $0.55 per share for its most recent quarter compared to the $0.76 that the market expected. 

Arch Coal
Another strong performer yesterday was Arch Coal, which saw its shares rise by nearly 8.4%. In some ways, the company is very much like Alpha Natural Resources in that it also produces metallurgical coal and in the fact that it too, last week, reported earnings that were better than what the market expected. For the quarter, the company saw its revenue decline by 18.9% from $975.2 million in the same quarter last year to $791.3 million in the quarter this year.

This was significantly short of the $878.3 million the market expected, but the company made up for it by posting negative earnings per share (after removing one-time expenses) of $0.01. Although this sounds disappointing, it is far higher than the net loss of $0.31 per share that analysts had been counting on. 

Unlike Alpha Natural Resources though, the company has held up relatively well in this challenging environment. Even though the company's revenue rose by 39.4% over the past five years (which is a fraction of Alpha Natural Resource's growth), it has only reported a net loss in one of the past five years; 2012, when the company reported a net loss of $684 million.

Foolish takeaway
If you were an early investor in companies related to the steel industry, then congratulations for your gains, especially those accumulated in the past few days. Additionally, if China is indeed continuing to expand at an exceptional rate, it is only a matter of time before these steel-related businesses turn around and report more attractive margins than they have in the past few years.

However, it should be noted that each of these companies discussed above has relatively unstable fundamentals due to poor earnings. This should serve as a warning that any long-term investment in any one of these companies will likely result in either a significant disappointment for shareholders or in outsized gains, based entirely on the confluence between management decisions and the direction the economy heads.