Davos may not have welcomed Brazil's newly-elected president with open arms, but the world's business elite are cautiously optimistic about his plans for reform.

Brazilian President Jair Bolsonaro delivered the keynote address at the World Economic Forum (WEF) in Davos, Switzerland this week, touting a "new Brazil " that's open for business.

The far-right leader vowed to transform Latin America's largest economy into one of the most investment-friendly places in the world.

"I think he did make his case for why Brazil could be the country to invest in," Robin Niblett, director of the Chatham House think tank in London, told CNBC on Tuesday.

"He was incredibly disciplined I thought, on message… (but) the mood in the room was totally different. I mean, he came on stage to almost no applause at all — and at the end of his speech, a little grudging applause."

A rise of populism has been a pressing concern for those at the Forum, with nationalist and far-right parties making significant electoral gains worldwide in recent months.

Brazil's president arrived in snow-clad Davos less than three weeks after his inauguration. His sweeping electoral victory late last year marked a dramatic swing away from the left in Brazil.

Critics of the so-called "Trump of the Tropics" have expressed deep concerns about his brazen praise of the country's former dictatorship and by his comments concerning women, race and human rights.

Chatham House's Niblett pointed out that Bolsonaro's keynote address at WEF was in stark contrast to this time last year, when French President Emmanuel Macron came off the Congress Center stage "like a rock star surrounded by the crowds."

Macron was widely considered the European leader to watch 12 months ago, with the world's business leaders audibly excited to hear his ambitious plans to reform the country.

However, the French premier is currently struggling to appease a momentous backlash against his administration.

The so-called "yellow vest " uprising, named after the high-visibility jackets protesters wear during demonstrations, has prompted Macron to stay away from the annual meeting this week.

And he is not alone.

Several world leaders have chosen not to attend the January get-together, choosing to fight domestic crises rather than be seen socializing with the rich and famous.

The absence of some of the biggest names in Davos has thrust Bolsonaro firmly into the spotlight.

"We think Jair Bolsonaro has a big chance to reform the country," Francesco Starace, chief executive at Enel, told CNBC on Tuesday.

"His agenda is a reform agenda. If it is populist or not populist, we don't care — it is a reform agenda that we think is good for the country and the country needs it," he added.

Bolsonaro has attended a number of working lunches with global institutional investors in Davos, hoping to showcase the "unique point in time" his country is going through. He was spotted on the same dinner table as Apple CEO Tim Cook and Microsoft CEO Satya Nadella on Wednesday.

The photo of the unlikely group was widely shared on social media, after Axios reporter Felix Salmon posted it to Twitter, likely due to the seemingly conflicting views Bolsonaro holds to those of Cook and Nadella.

When CNBC's Nancy Hungerford asked whether Bolsonaro was capable of delivering on his promises, Itau's Latam Chairman Ricardo Marino replied: "That's the big question."

"The top priority is, for sure, the approval of the social security reform," Marino said.

The country's benchmark stock index reached a fresh all-time high on Thursday, amid improving investor sentiment about the new government's pension reform plans.

On Friday, the Bovespa — one of 2018's top performing indexes worldwide — stood at 97,677 points.