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The big recent bull run on Wall Street may have whet the appetite of investors looking for big returns. They should note that each issue of our Investment Survey includes a Summary & Index that lists a number of screens, and one of these screens is for stocks with the highest 3- to 5-year price appreciation potential.

Popular investment theory teaches that greater reward comes with greater risk. Indeed, we preface our big price growth potential screen in the Summary & Index with a caution for these risky investments, which may not be timely for the next six months to a year, according to our Timeliness ranking system. In fact, this group of stocks has a disproportionately high number of low-ranking stocks.

Nevertheless, a portfolio of some of these stocks, to diversify away company-specific risk, would likely outperform the broader market, we believe. According to academic studies, thirty stocks would make a good number for this purpose. An understanding of company-specific risks and how these companies make money can also help the selection process. Here are some of the stories behind stocks we think have big capital appreciation potential.

Spirit AeroSystems and AAR

The commercial aerospace business has been doing well of late. Despite that, Spirit AeroSystems (SPR) and AAR Corp. (AIR) stock have low P/E ratios relative to the broader market.

Spirit has been experiencing some execution problems of late. Nevertheless, this company supplies the two biggest civil airplane producers, Boeing (BA - Free Boeing Stock Report) and Airbus, with fuselage parts, among others. If its execution improves, the company should be able to ride the wave of increased demand for commercial planes.

At AAR Corp., another provider of aircraft components, earnings haven’t been growing in the past few years, but this stock can really take off if business strengthens, as we would expect. Recent trends, and increased orientation to commercial aircraft (rather than selling to government sources), augur well for the company’s prospects.

Apple

Apple (AAPL) stock has lost its shine in recent months after an impressive run, as the company lost share of the smartphone market to Samsung and other Android operating system products. The slide has been big enough for Apple, a bellwether of the NASDAQ, to end up on our list of stocks with wide capital appreciation potential. Despite its fall from grace, the company has been a cash cow consistently for many years.  Meanwhile, the company, known for a history of producing innovative and compelling products, may well still have some tricks up its sleeve. Reports are circulating of an Apple smart watch, and a new venture into the television arena. The company’s dividend could well be icing on the cake.

Skullcandy

Skullcandy (SKUL) is a maker of popular headphones that went public in 2011, and has been growing sales since. Skullcandy is facing some short-term difficulties, including the loss of a big customer, but we still think this stock has the potential to outperform over time. The company looks to increase its prices, while also expanding into adjacent categories through either acquisitions or organically.

Petroleo Brasileiro

Petroleo Brasileiro (PBR), or PetroBras for short, is one of the largest companies in the world. Headquartered in Brazil, it has a market capitalization that recently reached almost $100 billion. This company’s earnings and stock price peaked at around the eve of the financial crisis. An increase in energy prices and improved economic activity would benefit this heavyweight nicely. Its current valuation is compelling, even for the recently depressed energy industry.

What these stocks all have in common is a low P/E ratio, a history of profitability, some bad short-term news, and a bright outlook for earnings that should drive their capital appreciation potential. They would be suited best for venturesome investors in a diversified portfolio. Conservative investors should be warned; As some of these stocks carry above-market-average Betas, the potential for capital loss in the wake of a market correction is considerable. For more information and the complete list of stocks with high 3- to 5-year price appreciation potential and also their Timeliness rankings, please see our Survey.

At the time of this article’s writing, the author did not have positions in any of the companies mentioned.