The stock market has been on an absolute tear this year. The S&P 500 is up by 27%, which is almost triple its average annual gain dating back to when the index was established in 1957.

The technology sector has been leading the market higher, and companies involved in the artificial intelligence (AI) revolution are performing particularly well. For example, shares of Duolingo (DUOL -2.50%) and Lemonade (LMND -10.78%) are up 50% and 150%, respectively, in 2024. Here's why they could carry their momentum into 2025.

Two students sitting at a table studying languages, with flags in the background.

Image source: Getty Images.

The case for Duolingo

Duolingo is the world's largest digital language education platform. It takes a mobile-first approach to put highly interactive, gamified lessons at the fingertips of practically anyone with a smartphone. During the third quarter, the platform had 113.1 million monthly active users, which was a 36% increase from a year ago.

However, Duolingo grew its paying user count at an even faster rate of 47% to 8.6 million. Those who pay those monthly subscription fees can accelerate their learning with extra features, and that's where AI comes into the picture. Earlier this year, Duolingo rolled out a new subscription tier called Max, which is more expensive than its other plans because it includes two powerful AI features -- Roleplay and Explain My Answer.

Roleplay provides a chatbot interface to help users practice their conversational skills in a foreign language of their choice, and Explain My Answer offers personalized feedback based on the user's mistakes in their lessons. In September, Duolingo expanded the AI feature set with Video Call, which allows users to initiate a video chat with a digital avatar whenever they want to practice speaking their foreign language.

Duolingo's long-term goal is to deliver a learning experience that rivals a human tutor, and AI will be central to that effort. The Max plan is only available to around half of the platform's global users right now, but the rollout will continue throughout next year. According to management, it's already contributing to the company's strong financial results.

During the third quarter, Duolingo generated $192.6 million in total revenue. That was a 40% increase from the year-ago period, and comfortably above $189.7 million, which was the high end of management's forecast range. The strong result prompted the company to raise its 2024 revenue guidance for the third time. It now expects to generate up to $744 million.

Duolingo stock isn't cheap. Its price-to-sales (P/S) ratio is 23.5, which is a big premium to its average of 15.1 since the company went public in 2021. However, it's growing its revenue so fast that the stock won't look expensive for long.

Wall Street's consensus forecast for 2025 (according to Yahoo) is that Duolingo will generate $962 million in revenue, giving it a forward P/S ratio of 15.5 -- almost in line with its trailing average.

DUOL PS Ratio Chart

DUOL PS Ratio data by YCharts.

If Duolingo maintains its current P/S ratio and Wall Street's 2025 revenue forecast is accurate, its stock could climb by 52% next year. However, it might do even better over the long term if the company continues to grow at this pace, so it looks like an especially good buy for investors who could hold it for the next five years or more.

The case for Lemonade

Lemonade is an insurance technology company that operates in five markets: renters insurance, homeowners insurance, life insurance, pet insurance, and car insurance. It serves 2.3 million people, and it has successfully attracted customers from younger cohorts who have traditionally been underinsured.

Its approach to technology might be one reason its products resonate with customers. The company has developed its AI tools since it was founded in 2015, long before hype over the technology gripped Wall Street. When a potential customer visits Lemonade's website, they can speak to an AI chatbot named Maya, which can give them a quote for a policy in under 90 seconds. When it's time for a Lemonade policyholder to make a claim, AI Jim can take care of processing that claim and getting their money out to them in less than three minutes, usually without human intervention.

That means no more frustrating phone calls with insurance companies, and no lengthy waiting times to get paid when making a claim.

But Lemonade's use of AI runs much deeper than customer service. It uses the technology to price premiums, and also to manage its operations. The company's Lifetime Value (LTV) models predict the likelihood of a policyholder making a claim, switching insurers, and buying multiple products, which helps it calculate the most appropriate premium. Premiums that are accurately priced lead to long-term savings for customers and less risk for Lemonade.

Lemonade ended the third quarter with a record in-force premium (the value of premiums from all active policies) of $889 million. That was a 24% increase from the year-ago period, marking accelerated growth from its second-quarter increase of 22%. Here's the kicker: The company shrank its employee headcount by 7% and still managed to deliver that strong result, because it's relying more heavily on AI to calculate premiums and automate business processes.

Lemonade's gross loss ratio (the percentage of premiums paid out as claims) also fell to 73% in the third quarter . That was its lowest level in four years, which is a great sign the company's models are working. The falling gross loss ratio, combined with accelerating in-force premium growth and the reduction in employee costs, drove Lemonade's net cash flow to a record $48 million during the quarter -- a whopping 1,500% jump from the year-ago period.

Lemonade stock is trading at a P/S ratio of just 6.1 as of this writing, which is significantly below its average of 19.3 going back to when the company went public in 2020.

LMND PS Ratio Chart

LMND PS Ratio data by YCharts.

In that context, Lemonade stock actually looks cheap despite its 150% gain in 2024 so far. In my opinion, this is the best Lemonade's business has ever looked in its short history as a publicly traded company. Plus, it's one of the few companies successfully monetizing AI right now, so I expect the momentum in its stock to roll on in the new year.