What’s flying higher than bitcoin? The software company buying up bitcoin.

Bitcoin prices have surged 40% since Election Day. MicroStrategy has climbed even faster.

The software company turned itself into a bitcoin buying machine in 2020 and now holds some $32 billion worth of tokens. For many individual investors, the stock is a more popular bitcoin play than the cryptocurrency itself and they are willing to pay up for it.

With a $95 billion market value, MicroStrategy is trading at about three times the value of its underlying bitcoin. The shares have soared more than sixfold this year and 85% since Nov. 5, with traders betting that the digital-assets industry will flourish under President-elect Donald Trump. Bitcoin prices are hovering just below $100,000.

“MicroStrategy found a way to outperform bitcoin,” Michael Saylor, the company’s founder and executive chairman, said in an interview. “The way that we outperform bitcoin, in essence, is we just lever up bitcoin.”

And Saylor says he is just getting started. He unveiled an audacious plan just days before the election to hire investment banks to raise $42 billion in capital over three years through stock and bond offerings to buy more tokens. His company had $4.3 billion in convertible debt outstanding as of Oct. 29.

MicroStrategy’s mix of bitcoin maximalism and Wall Street-style financial engineering has paid off for its investors, but skeptics question whether it is sustainable.

Saylor’s heavy use of leverage, or borrowed money, to buy bitcoin backfired during the 2022 crypto-market meltdown when the collapse of Sam Bankman-Fried’s FTX dragged bitcoin prices below $16,000. Quarter after quarter, MicroStrategy incurred mounting losses tied to bitcoin and Saylor stepped down as CEO, a position he had held since 1989.

“This stock has become detached from reality,” said Andrew Left, a prominent short seller and founder of Citron Research.

Left describes himself as bullish on bitcoin itself and praised MicroStrategy in 2020 when it first began amassing bitcoin. But in a Thursday post on X, Left said he had taken out a bet against MicroStrategy, which caused its stock to tumble.

Some analysts warn MicroStrategy’s stunning run-up is part of a broader investor euphoria for speculative assets and will inevitably collapse. David Trainer, founder of research firm New Constructs, said MicroStrategy is a bad business by conventional metrics—for instance, it has posted a net loss for the past three quarters.

“It’s symptomatic of a market that has become obsessed with believing in get-rich-quick schemes,” Trainer said. “If you like bitcoin, go buy bitcoin. But don’t invest in a company that’s losing money and also buying bitcoin, because then you’ve sort of doubled your risk.”

Some traders say a key part of the stock’s appeal is its volatility, which can help amplify their gains over a short period.

Garrett Shirey, a barber in Florence, Ala., bought one share of MicroStrategy at $436.53 in his retirement account Tuesday afternoon and sold it at $472.40 Wednesday morning, notching a quick profit.

Restricted from purchasing bitcoin in his Roth IRA account, the 39-year-old crypto enthusiast has had to settle for bitcoin proxies like MicroStrategy stock and bitcoin exchange-traded funds. He holds some shares of the Bitwise Bitcoin ETF.

“I don’t think bitcoin went up 8% in the last 24 hours, but MicroStrategy did,” said Shirey, who has been investing in cryptocurrencies since the pandemic.

Saylor said he came up with the bitcoin strategy in 2020 when Covid-19 forced lockdowns and the Federal Reserve cut interest rates to zero. MicroStrategy was competing with tech giants such as Microsoft and falling behind. The company was under pressure to return cash to shareholders through stock buybacks and dividends.

“It was either a fast death or a slow death, or take a risk, do something out of the box,” he said.

Saylor has often boasted about MicroStrategy’s volatility. “When you embrace volatility, then you’re outperforming the S&P,” he said during last month’s earnings call.

MicroStrategy’s volatility has helped it find ready buyers for its repeated issuances of convertible bonds—debt that can eventually be converted into shares, if the stock price rises to a specified level. Such bonds are often purchased by hedge funds that protect themselves against a collapse in the stock’s price by going short, or placing a bet that the stock will fall. Such funds generally don’t focus on whether the company is a good long-term investment, and instead seek to profit from the volatility of its stock.

MicroStrategy is an attractive trade for convertible-bond arbitragers, said Vadim Iosilevich, a veteran hedge-fund trader in New York.

“We can definitely agree that the volatility will be there,” he said.

Some investors are turning to ETFs that seek to amplify the return of MicroStrategy shares using borrowed money or derivative contracts. One such fund, the Defiance Daily Target 2x Long MSTR ETF aims to double the daily return of the stock and has attracted $1.8 billion in assets since it launched in August. Other funds allow traders to make inverse bets.

Chase Furey, a 25-year-old trader in Newport Beach, Calif., said he started buying bitcoin-related stocks including Coinbase Global, MicroStrategy and BlackRock’s bitcoin ETF in October. Hoping to turbocharge the gains, he moved all of his investments, worth about $112,000, into the Defiance ETF instead and has grown his portfolio to about $400,000.

The Harvard graduate, who studied economics in college, convinced his parents to let him manage $700,000 of their retirement assets. He said he came up with a “less dangerous and smarter” plan for them, investing 27% of their portfolio in the Defiance ETF and the rest in MicroStrategy shares. The money has more than doubled to $1.8 million, he said.

“I think bitcoin could hit $400,000 and I think MicroStrategy could possibly 10x from where it is now by the end of next year, so that’s kind of my game plan with that,” he said.

Even some bitcoin bulls have expressed unease about the risks investors face by betting on MicroStrategy. Mike Novogratz, the billionaire CEO of crypto-trading firm Galaxy Digital, warned in an interview on CNBC Thursday that bitcoin could fall 20% after peaking at $100,000—in part because of leveraged bets on MicroStrategy available through some exchange-traded funds.

“The crypto community is levered to the gills right now, so there will be a correction,” Novogratz said.

Write to Vicky Ge Huang at vicky.huang@wsj.com and Alexander Osipovich at alexo@wsj.com