In the investing world, a two-bagger refers to a stock that gains 100% -- that is, it doubles your initial capital. Doing so in a mere five years is no easy feat. It requires a compound annual growth rate (CAGR) of about 14.9% -- which, incidentally, is pretty much what the S&P 500 has posted in the past half-decade.

However, this has been an unusual period; the broader market's average annual return is usually below that level. So returns of this type are by no means a guarantee. But if I had to bet on two stocks doubling my money in the next five years, Shopify (SHOP 1.11%) and Axsome Therapeutics (AXSM 0.27%) would be on that list. Read on to find out why.

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1. Shopify

Shopify has more than doubled investors' money in the past five years, and that is no guarantee it will do so again. Still, a few things are worth pointing out. First, the company's shares soared early in the pandemic when the e-commerce industry got a boost due to the outbreak. Shopify gave up much of these gains between late 2021 and 2022 but has recovered over the past year.

Second, Shopify made significant changes to its business in 2023. One of the most important was to divest its logistics segment to focus on its core e-commerce operations. The move will almost certainly boost margins and help the business become consistently profitable. The persistent red ink on the bottom line and Shopify's seeming desire to pursue growth at all costs had long been one of the bears' arguments against the company, making this move all the more critical.

What do the next five years have in store for Shopify? The company should continue to profit from the fast-growing e-commerce industry, where it has become a leader. Shopify offers merchants everything they need to build and customize online storefronts, as well as sell their products on various social media sites. It also provides a single integrated brick-and-mortar and e-commerce payment platform.

Shopify benefits from switching costs. Merchants will be hesitant to switch to a competing provider after spending time, energy, and money to build an online storefront from scratch with Shopify. The company is also investing in various initiatives, including artificial intelligence-centered changes to its platform to make it more efficient for merchants.

Shopify is also likely to become consistently profitable in the next five years. For the first nine months of 2023, Shopify's net loss per share shrunk to $0.41, versus $2.24 in the comparable period of the previous fiscal year. Meanwhile,the company's revenue grew by about 27% year over year to $4.9 billion.

With the top line still increasing at a good clip, as well as improvement in the bottom line and margins, Shopify could once again more than double investors' money in the next five years.

2. Axsome Therapeutics

Over the past five years, Axsome Therapeutics has seen steady clinical progress on multiple fronts. The company transformed itself from a clinical-stage biotech into one with two products on the market. However, there is plenty of growth fuel left for Axsome.

The drugmaker is looking at several important catalysts this year that could send its stock price soaring -- and, more importantly, help it build a solid base for the future. It is expecting two regulatory submissions to the U.S. Food and Drug Administration, three phase 3 clinical trial data readouts, and the start of three brand-new phase 3 studies in 2024. Let's address one in each category.

First, Axsome Therapeutics plans to seek approval for AXS-14 in treating fibromyalgia, a chronic disease that causes pain throughout the body and difficulty sleeping.

Second, the biotech expects to release data from a late-stage study for one of its approved products, Auvelity, in treating Alzheimer's disease (AD) agitation. This is the second phase 3 trial for this medicine in this indication, with Auvelity having aced the first.

Third, Axsome will kick off a phase 3 study for Sunosi in targeting major depressive disorder.

Axsome Therapeutics is not profitable yet, although it hasn't been a commercial-stage company for that long. However, the biotech has crushed the market in the past five years because of significant progress with some key programs. Axsome is likely to continue down that path, and within three years, its lineup should be completely transformed. That's how Axsome Therapeutics can attain multi-bagger status again in the next five years.