Fireworks and confetti filled the air over Copacabana beach on a Friday morning last month and 30,000 people, many wearing the national colours of green and yellow, leapt and danced for joy as Rio de Janeiro won its bid to hold the 2016 Olympic Games.

It was, as many pointed out, an historic moment. Coming soon after news that the country had emerged from a short recession, apparently shrugging off the effects of the global crisis, it seemed to confirm that after years of underperformance and self-doubt, Brazil's time had come at last.

Two weeks later, another first for the history books: a police helicopter was shot down over one of Rio's favelas – the shanty towns that sprawl over hillsides throughout the city – and 10 suspected drug traffickers were killed at the start of a week of violence between police and criminal gangs that left at least 42 people dead. As so often in Brazil, exuberant optimism had been tempered with a dose of harsh reality.

Yet the balance has shifted. Underperformance and self-doubt will persist. However, the country's enormous potential, its tremendous natural and human resources, are at last bringing within its grasp the bright future that not long ago seemed destined to remain forever out of reach.

"Nothing is guaranteed," says Antonio Quintella, country manager at Credit Suisse in São Paulo. "But it is reasonable to assume that we won't repeat the mistakes of the past ... It is very difficult not to be bullish."

Success has been a long time coming and the notion that their country is changing has crept over Brazilians only slowly.

The foundations of change were laid 15 years ago by former President Fernando Henrique Cardoso, who conquered run away inflation and brought in orthodox economic policies that have delivered lasting stability.

Those policies have been maintained since 2003 by President Luiz Inácio Lula da Silva and supplemented with cheap but effective income transfer programmes that, along with low inflation, have brought millions of poor people into the consumer market for the first time.

Mr Lula da Silva won the presidency at his fourth attempt. The fact that a lifelong leftwinger turned out to be no threat to stability laid to rest the spectre of adventurism that had overshadowed politics for so long.

Not that Brazil's political future is set in stone. Without changing the constitution – which, to his credit, he has vowed not to do – Mr Lula da Silva cannot run for a third consecutive term next October. Dilma Rousseff, his chief minister and probable chosen successor, is a tough technocrat. Her likely adversary, José Serra, governor of São Paulo state, is from a similar mould. Neither has Mr Lula da Silva's personal charm or popular appeal.

Yet neither is likely to veer far away from Brazil's course over the past decade and a half.

For one thing, says Mailson da Nóbrega, a consultant and former finance minister, Brazil's solid institutions and the population's intolerance of inflation rule out any radical change of policies.

The central bank, for example, has de facto rather than de jure independence. But politicians know that, for example, ordering it to lower interest rates against its judgment would risk provoking a walk-out of its board and plunging the country into crisis. Clearing the air of such uncertainties has allowed Brazil's advantages to emerge into focus. Stability has brought lower interest rates and the creation of a mortgage market, fuelling a boom in construction.

Expansion of agriculture, led by a new generation of tech-savvy farmers applying modern management techniques, has turned the country into one of the world's biggest exporters of food commodities.

Capital markets have come to life after lying almost dormant for decades. A surge of issuance since 2004, briefly interrupted by the global crisis, has provided the capital companies need to expand at home and abroad. The banking sector, where regulations are cautious and conservative and where little credit is sourced overseas, has emerged unharmed from the crisis. The volume of credit, though small by international standards, has begun to increase. Driving growth has been the emerging middle class, which as of this year makes up more than half the population for the first time. Such is their new sense of optimism that the services sector, where many of the poor spend a large share of their income, avoided recession even at the height of the global crisis.

Brazil's resilience has opened up a wealth of investment opportunities. Many investors are tapping them through equities and public debt. In the eight months to the end of August, net inflows to equities on the BM&FBovespa, the São Paulo futures and stock exchange, were $13.2bn (with gross inflows of $89.1bn); net inflows to fixed income instruments were $2.5bn (with gross inflows of $27.3bn). But investment in the real economy has also remained strong – even during the crisis. Foreign direct investment in the same period was $15.9bn. Brazil, however, needs much more, not only to prepare for the 2014 World Cup – awarded a year ago – and 2016 Olympics. Roads, railways, ports, energy and other vital infrastructure are all in need of modernisation and expansion.

To keep attracting that money, it seems, Brazil needs do little more than avoid rocking the boat – and pray the global crisis does not enter a second stage. But investors will be watching carefully for any change of direction. Two episodes in recent months have given some of them cause for concern.

One is the government's plans for the "pre-salt" oil fields, potentially enormous reserves discovered over the past two years. The planned creation of a new state company to oversee contracts under a new regime of production-sharing agreements appears to put ideology above pragmatism and jeopardise the efficiency and dynamism that has been created in Brazil's oil industry over the past decade and a half.

Similarly, the government's attempts – apparently successful – to put pressure on Vale, the mining giant, to go beyond its core business and invest in steelmaking, has raised additional concerns about an increase in state involvement in the private sector.

"You see it everywhere," says Mr da Nóbrega. "The state has taken on a new role in the economy." At worst, the combination of a deepening global crisis and a policy shift could raise barriers on what seems to be an assured path to faster growth.

For now, though, such concerns seem unlikely to knock the country off course.