It's taken months of patience, but finally, China's markets have dug out of the red in 2013.

Hong Kong's Hang Seng's (HSIINDICES: ^HSI) gains this past week of 2.7% were enough to push the index just into the green over the course of the year, capping off a long journey, as investors stumbled through months of the index's losses earlier in 2013. In fact, from its lows in late June, the Hang Seng has since become the best-performing market in Asia -- although that's only been enough to bring investors back to breakeven on the year.

But can China's economy match the level of its markets in recent months after its slowdown?

Is improvement on the way?
China's shown strong signs of a rebound from its slump in recent months. Industrial production rose to its highest point in more than a year in August, and factory production rose by more than 10%. Considering how manufacturing in the country's been hurt by the slowing economy and recent cash crunch in the nation, the rise of industry in August is a good sign for the sector going forward -- if it can sustain such growth.

Sustaining it will be the problem. Barclay's cut its outlook for China's economic growth in 2014 to 7.1%, from an earlier 7.4% this week. That's not only a drastic decline from the double-digit growth percentages the country managed in the last decade, and the 8% annual growth once touted by economists as necessary for the country's future, it's also below the 7.5% growth China's GDP posted in this year's second quarter.

Industrial production's gains pushed Barclay's to raise its outlook for China's growth to 7.6% this year, but that short-term outlook does little for investors unless China can keep its growth up for the long term. True, China's most recent Five-Year Plan in 2011 only targeted 7% average annual growth between 2011 and 2015. However, the country will also have to deal with revamping its infrastructure in future years -- an area still badly in need of improvement, particularly in transportation, where titanic traffic jams have popped up in recent years -- including a monster gridlock of more than 100 km back in 2010.

Infrastructure improvements will help China's business environment, and develop the economy to emerge as more competitive in future years, if Beijing takes the right steps now. A more competitive climate is a better one for investors -- and China's recent ranking as the 29th most-competitive economy in the World Economic Forum's recent global ranking won't inspire investors when compared against higher-ranked competitors such as Germany and the U.S.

Investors will be feeling a lot better when Beijing's corruption probes that began this summer wind down. From the pharmaceutical sector, Chinese regulators have spread out across industries, and even have looked into domestic Chinese firms' activities. Massive oil giant PetroChina (PTR) has come under the eye of investigators recently, and the company's already experienced the loss of several top managers. PetroChina's status as state-owned means that any significant finding by Beijing could mean more upheaval on the way for the firm, and for investors.

PetroChina's stock has certainly suffered for it, with shares losing more than 21% year to date. A massive infrastructure overhaul would be a good way for PetroChina to reinvigorate its presence domestically, but the company's not just struggled against regulators at home: It's also battling governments in Africa, one of China's biggest targets for raw materials, which have tired of Chinese firms' rapid expansion into the continent. Africa might be a lucrative target, but it's also an unstable one -- and for income investors who enjoy PetroChina's 4.2% dividend yield, instability is a big threat to this stock's performance.

Don't expect PetroChina to collapse. After all, its parent company, CNPC, is one of the largest firms in the world. However, if investigations continue, and Africa increases its stiff-arming of major Chinese energy and resource firms, PetroChina and other major resource stocks in China will be slow to bounce back.

Major Chinese refiner Sinopec (SNP) isn't helping the situation for China's oil giants, as the company is expected to step up its diesel exports in the fourth quarter of 2013, despite waning demand in several Southeast Asian nations that has hit market prices for diesel recently. Oversupply has crippled some of China's biggest materials stocks in recent quarters, and a similar move by state-owned Sinopec here could slam the company's profit margin and hinder the stock, which has already lost more than 11% year to date.

China investors, keep both eyes on these developments for the sake of your portfolio.