Whether you're new to investing or you've been doing it for decades, the past year has been a difficult one. The growth stock-laden Nasdaq Composite index is down around 21% over the past 12 months, and nobody's sure when it can start to bounce back.

Despite a market that isn't cooperating with investors of any description, there are plenty of billionaires out there who continue to plow money into their favorite growth stocks. Here are two particularly interesting businesses that billionaires bought hand over fist in the fourth quarter. Read on to see why folks with enough net wealth to move mountains find them so compelling.

1. The Trade Desk

Shares of The Trade Desk (TTD 1.71%) are still down 49.6% from the peak they reached way back in 2021. Billionaire hedge fund manager Israel Englander isn't deterred by the stock's poor performance. The fund he runs, Millennium Management, added nearly 700,000 shares of the stock to its portfolio during the last three months of 2022.

The Trade Desk operates an independent demand-side platform that advertisers use to plan, launch, and optimize their digital ad campaigns. Unlike the digital ad industry's biggest players, Meta Platforms and Alphabet, The Trade Desk doesn't own the content it's asking ad buyers to bid on.

With a heightened level of transparency for ad buyers, The Trade Desk is eating into Alphabet's and Meta's share of the digital ad industry. In 2022, The Trade Desk reported revenue that rose 32% compared to the previous year. Meta Platforms reported a 1% revenue contraction, and Alphabet reported Google advertising revenue that fell 3.6% over the same time frame.

2. Doximity

Doximity (DOCS 18.07%) soared following its market debut in 2021, but the stock has fallen around 67% from its high-watermark. The company's billionaire CEO, Jeffrey Tangney, hasn't let the stock's performance dent his confidence. In the fourth quarter of 2022, he raised his stake by 2.6 million shares. Now he owns 48% of the company.

At the end of the day, inside investors are people who have bills to pay and luxuries to acquire, just like the rest of us. They have millions of good reasons to sell their shares, but there's only one reason to buy. Tangney keeps adding to his Doximity position because he expects it to rise.

It's not hard to see why Tangney is so confident about Doximity's ability to outperform. The company operates a social media platform that's exclusive to U.S. healthcare professionals.

Following Tangney and buying some shares of Doximity looks like a smart move. With a membership roster that includes around 80% of the nation's physicians, pharmaceutical ad buyers are flocking to Doximity during a difficult time for its generalist peers. During the nine-month period that ended Dec. 31, total revenue rose 23% year over year.

Are these good stocks to buy now?

These stocks have fallen a long way from their peaks, but they're hardly cheap. At recent prices, you can buy Doximity for around 48 times forward-looking earnings estimates. Expectations for The Trade Desk are slightly higher. It's been trading for around 49 times estimates.

Most conservative investors would consider these growth stocks too risky after taking one look at their earnings multiples. Less risk-averse investors, though, are probably right to assume these companies can justify their lofty valuations and outperform over the long run.

Doximity's cementing its position as the social network of choice for healthcare professionals with increasingly popular productivity tools. For example, a record 375,000 physicians accessed its telehealth tools during the last three months of 2022. 

The Trade Desk also has an advantage that could keep competitors at bay for the foreseeable future. Its proprietary approach to providing relevant advertising while preserving anonymity is likely to become the industry standard.

The $1.6 billion in total revenue that The Trade Desk reported last year is just a tiny sliver of its addressable market. With a clear advantage over its industry's largest players, following Englander into this stock looks like a smart move.