If you have $10,000 to invest and are willing to take on some risk, now may be an opportune time to invest in some beaten-down stocks. In the short term, it can be scary to buy stocks that are falling and are at multi-year lows. But if the businesses are sound and you're willing to hang on for years, doing so could help you turn an attractive profit.

Two stocks that haven't been this cheap in years are Biogen (BIIB -0.70%) and Alibaba Group Holdings (BABA -0.94%). Their businesses aren't broken, but they are facing some headwinds. Investing $5,000 into each of these stocks could be an attractive option for contrarian investors.

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1. Biogen

Healthcare company Biogen looked like it might be headed for the moon last year after the Food and Drug Administration (FDA) granted accelerated approval for its Alzheimer's medication, Aduhelm. As a result, the stock soared to a high of more than $460 before giving back those gains. Today, it trades around $220; the last time the healthcare stock traded lower than this was 2013. 

The problem is the company's sales have been decreasing. For the period ending Sept. 30, 2021, the revenue of $2.8 billion declined 18% year over year. Growing competition has led to sales for the multiple sclerosis drug Tecfidera, which has been Biogen's flagship product, dropping by 48%. And the company expects the decline to continue in future periods now that Viatris has launched a generic version of the drug. 

Aduhelm is key to replacing lost revenue for Biogen and a lot will hinge on whether the drug can be a winner. Right now, that isn't the case. Multiple experts quit their roles in the FDA last year over what was a controversial approval of the drug, with many simply not believing that it proved it was effective in treating Alzheimer's. Medicare may only end up covering a small fraction of patients who use the drug, such as those who are involved in qualifying clinical trials. However, a final decision won't come until April.

But, with Aduhelm representing the first new Alzheimer's drug the FDA has approved in almost two decades, it still could be a solution many patients seek out. And with Biogen announcing late last year that it would slash the price of Aduhelm in half to a yearly cost of $28,200, that could make the drug much more accessible to patients. If the drug proves to be a blockbuster, the company could expect to generate revenue for years to come.

Biogen's stock currently trades at a forward price-to-earnings (P/E) multiple of 12, which is lower than where it has been trading in the past year. Although sales are falling, this is still a company that has generated a profit margin of 14% over the trailing 12 months and that could be a viable investment. If there's some progress in showing that there is more enthusiasm around Aduhelm from doctors and patients, especially now that it is cheaper, that could help lead to more bullishness around Biogen. 

I wouldn't go all-in on Biogen. Yet for a risk-taker with a diverse portfolio, who can afford to invest $10,000 right now, putting half that amount into this stock may not be a bad move over the long haul.

2. Alibaba

Another risky stock that has plenty of upside is the Chinese tech stock Alibaba. Last year, I thought the stock might be a cheap buy at less than $200. Then it fell to below $150. And now, it's trading at less than $120 a share. Outside of the decline this year, we have to go back to 2017 for the last time shares of Alibaba were trading much lower. At that time, the stock was still under $100. 

The big risk here is the uncertainty of U.S. and China relations and whether there will be crackdowns in China that impact Alibaba's business. In 2021, Chinese regulators fined the company $2.8 billion after an anti-monopoly investigation. But U.S. tech companies are also facing similar risks. Meta Platforms may be broken up due to antitrust violations, and yet, it trades at a forward P/E of more than 20 while Alibaba is at just under 14. There will always be some risk involved in investing in tech companies and Alibaba is no exception. Some investors, however, may be more concerned about the Chinese government coming down harder on its businesses than the U.S. might on Silicon Valley. 

But, without a crystal ball, it's impossible to know how those things will play out. That's where investing style comes into play. If an investor wants to play it safe and wait to see, they can certainly do so, but by then, if the situation looks more promising for Alibaba, the stock is likely to be trading much higher than it is now.

And there's still a lot to like about the stock. For the 12-month period ending Sept. 30, 2021, Alibaba reported that its annual active customers in its ecosystem (which includes multiple e-commerce sites) at 1.2 billion, which is 62 million higher than in the previous reporting period. Sales of $31.1 billion also rose by 29% year over year. Although the company projects that its growth rate in 2022 will fall to no more than 23%, that's still a decent rate for a company that's as big as Alibaba.

Alibaba's stock is low to the point where the potential reward may outweigh the risks. For contrarian investors, this could make for another promising long-term investment in their portfolios.