With the market hovering near all-time highs, it might seem tough to find stocks with significant upside potential from current levels. But for investors willing to take a risk on more beaten-down or volatile plays, these three picks might double within the next few years -- Twilio (TWLO 1.01%), CyberArk (CYBR 0.09%), and AMD (AMD -0.31%).

Image source: Getty Images.

Twilio

Twilio's cloud platform links popular apps like Facebook Messenger, WhatsApp, Uber, and Airbnb to users' phone numbers. Its service lets users add contacts, send text messages, or call each other via their phone numbers within an app. That feature is tough for a developer to create and scale up on its own, so it's generally more convenient, economical, and reliable to subscribe to Twilio's platform.

Growing demand for Twilio's services boosted its revenue by 62% annually to $71.5 million last quarter, and its active customer accounts grew 45%. Twilio expects its revenue to rise 61%-62% for the full year, compared to 88% growth in 2015. Twilio still isn't profitable, but its non-GAAP net losses narrowed last quarter.

Twilio's core business looks promising, but it's been on a roller-coaster ride since its IPO in late June. It initially surged from its IPO price of $15 to nearly $70 by late September, inflating its price-to-sales ratio into the high 20s. Twilio then announced a secondary offering in early October, triggering a massive sell-off that knocked the stock back to the low $30s. But now that Twilio's P/S ratio has cooled off to 12, and short interest has surged to 50% as of Oct. 25, I believe that the stock is poised for a rebound.

CyberArk

Cybersecurity company CyberArk is the market leader in the PAM (privileged account management) market. Its platform protects companies from internal threats, like disgruntled employees, by locking down compromised computers before they impact the rest of the network.

Image source: Getty Images.

CyberArk doesn't face much competition in this market because most cybersecurity companies focus on external threats with next-gen firewalls and threat detection systems. Yet a report from Intel (INTC -0.80%) Security last September found that 43% of data breaches were actually caused internally.

As a result, rising demand for CyberArk's services boosted its revenue 37% annually to $55 million last quarter. CyberArk expects its revenue to rise 33%-34% for the full year, compared to 56% growth in 2015. Unlike many other cybersecurity firms, CyberArk is profitable on a GAAP basis. Its GAAP net income rose 4% to $7.1 million last quarter, while its non-GAAP net income improved 28% to $11.8 million.

Despite those strong numbers, CyberArk stock has stayed almost flat over the past 12 months due to concerns about its slowing sales growth, weak enterprise spending, and its high valuations (8.5 times sales and 62 times earnings). However, the rising number of data breaches worldwide could continue boosting CyberArk's top and bottom line growth for years to come. With an enterprise value of just $1.2 billion, CyberArk could also be a lucrative takeover target for larger cybersecurity, networking, or IT companies.

AMD

It might seem greedy to believe that chipmaker AMD, which already rallied 200% over the past 12 months, could still double from its current price. However, the stock remains fairly cheap with a P/S ratio of 1.4, which is much lower than Intel's ratio of 2.7 and Nvidia's (NVDA 1.27%) ratio of 6.7.

AMD stock has been rising on the growth of its EESC (Enterprise, Embedded, and Semi-Custom) business, which is mainly supported by its sales of custom SoCs for the PS4 and Xbox One. New versions of these consoles -- like the PS4 Pro, PS4 Slim, Xbox One S, and Xbox Scorpio -- will require even more AMD chips. AMD has also been pushing hard against Nvidia in the "VR ready" GPU market with low-cost GPUs like the RX 480. Looking ahead, AMD's next-gen Vega GPUs and Zen CPUs could help it narrow its performance gaps with Nvidia's high-end GPUs and Intel's high-end CPUs.

Back in July, AMD posted 9% annual sales growth for its second quarter, marking its first year-over-year sales growth in two years. It followed that up with 23% sales growth in the third quarter, and is on track to grow its annual sales by 6% for 2016 -- compared to a 28% decline in 2015. AMD remains unprofitable on a GAAP basis, but it squeezed out a non-GAAP profit of $27 million last quarter. If that bottom line improvement continues, AMD's price might head back to the double-digits within the next few years.

But don't get greedy...

Twilio, CyberArk, and AMD all have upside potential, but they are also fairly risky plays which shouldn't be considered core investments. I personally own both Twilio and CyberArk, but only as minor positions designated as "higher risk, higher reward" plays. These stocks could certainly double over the long term, but I also wouldn't be surprised if they were cut in half during a market downturn.