“Certainly diversification and better inclusion would not hurt Hong Kong,” she says.

On the issue that keeps Financial Secretary John Tsang Chun-wah awake at night – the possibility that our fiscal reserves may, at some point in the far future, dwindle to nothing – Lagarde says the IMF is frustrated by the trend among the governments of developing and “peripheral” economies to stuff full their coffers, rather than using those assets to boost consumption and investment in a way that would help the global recovery.

However, she says, the issue is clouded in Hong Kong’s case by its unusual role as a relatively small but open economy with a large financial sector.

Hong Kong “is such a peculiar economy in many respects [because] it is at the forefront” of many global economic trends and “experiments” in financial management.

THE BENEFITS OF GIVING women greater access to the workforce in general, and then to executive ranks, is a subject particularly close to the heart of Lagarde, who has spent many years as the sole woman at tables of powerful men.

Now 58, the former French finance minister was the first woman to lead a global law firm (in 1999), the first woman to be finance minister of a major industrial nation (2007) and the first woman to run the IMF, where she now oversees US$1 trillion of loan capacity as the lender of last resort to troubled countries. Elegant and with a penchant for Chanel designs and eye-catching jewellery, she is also the only person to have been on the cover of Forbes magazine at the same time as being featured in Vogue.

“It is very distressing that there is in many corners still hostility towards women entering certain fields,” she says.

While she has strived to promote geographical diversity within the IMF, for instance appointing Zhu Min, a former deputy governor of the People’s Bank of China, as the IMF’s first Chinese deputy managing director, Lagarde has also openly favoured women for promotion.

“I have made a point whenever there were equally talented candidates for a position and there was a man and a woman, I have picked a woman.”

In her own case, being a woman at the top of law, politics and finance has meant a life of being “well surrounded but quite lonely”, she says.

Lagarde joined the Chicago-based law firm Baker & McKenzie at the age of 25 after a French firm had told her that it might give her a job but it would never make her a partner because of her gender. As she rose through the ranks in the Paris office of Baker & McKenzie she began to make personal sacrifices that, because she was a woman, raised eyebrows.

Such decisions would barely have been noticed had she been male.

At 39, she was promoted to the firm’s global executive committee, meaning she had to spend half her time in Chicago. Her sons, Pierre- Henri, then nine, and Thomas, seven, stayed in Paris with their banker father, Wilfried Lagarde, from whom she had recently divorced.

Four years later, she became the firm’s president and moved to Chicago, meaning throughout her sons’ teenage years she was in Paris for just one week a month.

In 2011, she told an interviewer, “I had to accept I could not be successful at everything – you draw up priorities and you accept a lot of guilt.”

Speaking to Post Magazine, she notes that men in similar situations come under much less pressure.

“I don’t think [the subject would have arisen] if I were a male, that is true. And I wish some of them would feel a bit more guilty about [making family sacrifices] as well, but I am not sure they do.

“But that sense of guilt fades away over time. As you age it reduces because children grow up, grandchildren arrive and you sort of reconcile yourself with what you have done,” she says.

“My companion [Marseilles businessman Xavier Giocanti] has two children whom I very, very much love, and one of them has a little boy and is expecting a baby girl, so I regard myself also as a grandmother and I love time with the family.”

Having built her career without a well-connected partner such as Bill Clinton or a wealthy patron like Denis Thatcher, Lagarde has increasingly spoken out on women’s issues, backing executive quotas for women and chiding countries such as Japan for not doing enough to involve women in their workforces.

When Dominique Strauss-Kahn was forced to step down as IMF chief in 2011 due to an alleged sexual assault on a New York hotel maid, the widely trusted Lagarde was seen as the ideal candidate to help Europe retain its 70-year hold on the IMF’s top job.

Susan Schwab, a former United States trade representative, has known Lagarde since she was France’s trade minister, from 2005 to 2007, and says Lagarde has had to be careful in the way she advocates women’s issues: “She has been conscious not to do it in a way that pigeonholes her or undermines the perception of her as a well-rounded professional, and she has done that brilliantly.”

Peter Westmacott, another old friend from the international circuit, who is now the British Ambassador to the US, says Lagarde is as passionate about women’s issues in private as she is in public: “I have seen her raise those matters in big speeches but I have also seen her do it in tiny groups by encouraging women not to be reticent in fulfilling their ambitions,” he says. “With Christine, the gap between her private and public personalities is much smaller than for most people, because she is so comfortable with herself.”

At 17, Lagarde spent a year as an exchange student at the same exclusive girls’ school in the suburbs of Washington that Jacqueline Kennedy Onassis had attended, struggling to understand teenage American slang but eventually getting to the point where, even today, she prefers to work in English, a penchant that is mildly scandalous in France.

Back in Paris she studied law and was twice rejected by the Ecole Nationale d’Administration (ENA), the elite training school for politicians and bureaucrats, before choosing Baker & McKenzie, the largest international law firm, over more sexist French law firms. Her elevation in 1999 to run the whole firm came when it desperately needed to shake up its culture and image after having been successfully sued by a secretary for sexual harassment, by a female partner for sex discrimination and by a male employee for discriminating against him for having Aids, a case that inspired the 1993 movie Philadelphia.

When the conservative then French president Jacques Chirac appointed her as a junior minister for trade in 2005, the glamorous interloper’s arrival ruffled the feathers of Paris’ career politicians and bureaucrats, who resented her foreign ways and US-influenced, pro-market leanings enough to dub her “l’Americaine”.

“She was a French teenager in America,” says Sonia Criseo, who was a personal assistant to Lagarde for 18 years, “then a European at Baker & McKenzie. She was in government without being a graduate of ENA or a civil servant, let alone a big political beast. She’s generally been a woman among men, of course, and even now she is running the IMF as a lawyer among economists.

“I think being an outsider has actually been a strength for Christine because she’s been able to take a totally outside view of whatever domain she is in.

“The trick for Christine has just been amazingly hard work. She has a discipline and capacity for work I have never seen before and will never again. Yes, she keeps herself extremely fit but it’s more than that – some people are born with a capacity that the rest of us will never have.

“She has huge concentration so she can be racing from one place or time zone to another but still absorb information and take decisions, so she ends up doing as much in one day as others do in a week. As a working mother she would try to go home for dinner and then come back to the office or work late into the night at home.”

While her time in the US had left her more market-oriented than most of her compatriots and deeply sceptical about French work practices, such as the 35-hour week, Lagarde says she has never been motivated by any ideological commitment to the conservative cause. In fact, her parents were left-leaning and Lagarde voted for Socialist president Francois Mitterrand in 1981, admitting to a diffidence about party politics that has left her without a factional power base in Paris.

“I was in politics and I am fascinated by politics but I am not a political animal,” says Lagarde, who has never been elected to public office. “I have strong principles and beliefs, about the strength of the individual and the sort of old-fashioned 18th-century economic liberalism.

“I am a very strong believer in free access for all, provided that they put the effort in, so I have many principles but does that put me on the right, on the left, in the centre or in a political party? I don’t think so.”

During a ministerial visit to Marseilles in 2006, Lagarde ran into Giocanti, an old university colleague, and they have been an item ever since. A jovial, extroverted figure, Giocanti has joked that he is Lagarde’s “gross domestic pleasure”, but he remains based in France and her relentless travel from her Washington office means they are together about one week a month.

In 2007, Lagarde was moved to the agriculture ministry for a few weeks, then the new president, Nicolas Sarkozy, gave her the crucial post of finance minister. Her biographer, Cyrille Lachevre, a former finance editor of Le Figaro newspaper, says she made little progress in trying to reform things such as the 35-hour week “and by the beginning of 2008 we were all thinking that she would not last much longer as a minister”.

It was the collapse of Lehman Brothers in September of that year and the global financial crisis that, in Lachevre’s words, “saved her ministerial career” and thrust Lagarde into the spotlight as one of the key architects of the efforts to save the euro.

“Sarkozy discovered that [then US president] George W. Bush and his team really liked her, and in euro-zone negotiations she was incredible,” says Lachevre.

Germany’s chancellor, Angela Merkel, and finance minister, Wolfgang Schauble, “came to trust her more than they trusted Sarkozy because she operated like a lawyer: when she said something it would stand. They found her frank and reliable and that made her a very important asset for Sarkozy,” he says.

“The interesting thing is you never really know if she personally agrees with what she has been asked to pursue,” says Lachevre.

I put that critique to Lagarde, asking if she is, for instance, embarrassed by the contradiction between her advocacy now at the IMF for free trade and her record as a French minister defending the bloated farm subsidies of Europe’s Common Agricultural Policy (CAP).

“The CAP was something I was asked to defend and there is no question that I did that,” she says. “And I am personally convinced that it was a good cause in many respects – not all respects but in many respects.”

One of her key assets in endless rounds of late-night talks is her durability and stamina. A former synchronised swimming champion, she does 20 minutes of yoga each morning, swims when she can, rarely drinks alcohol and does not touch meat or coffee.

Lagarde says that nowadays she needs six hours of sleep instead of the five hours that have sustained her in the past but friends say she is still generally the last person standing in negotiations with the overweight, middle-aged men she often finds herself up against.

Lachevre says that beneath her warmth and charm is the competitive streak of both an athlete and a hungry US lawyer, recalling that during one late-night round of talks in Brussels over German attempts to stop France reducing restaurant taxes, Lagarde ensured that no food was served to negotiators “and the Germans eventually gave up out of hunger”.

Lagarde gives a conspiratorial smile when asked about that incident.

“All of that is true except it wasn’t 2am, it was more like three in the afternoon by the time we agreed. But yes, there was no lunch,” she says.

“We were going nowhere so I told the chairman of the meeting, ‘If you want to wrap it up, you have to kick out of the room all the advisers so the ministers have to make a decision themselves … and don’t serve any food.’” Another rumour has it that Lagarde has at times worn down her male rivals by dressing in warm clothes while organising extra air-conditioning.

She concedes only that “I always have with me two things: a scarf or a shawl, something to keep my shoulders warm or my neck warm, and a Spanish or Japanese fan, depending on the colours of my clothes.”

Clothes are important to her – on the day we meet she is wearing a jacket made to her own Chanel-inspired design from material she gave to a Parisian couturier.

In Europe, rumours are beginning to swirl that Lagarde will soon replace the lacklustre Jose Manuel Barroso as head of the European Commission, the executive arm of the European Union. I tell Lagarde that well-placed people in six countries have told me they think she might end up in the European job when it becomes vacant in October, even though she would then still have almost two years left to run in her IMF term.

“I want to complete my five-year term,” she says, offering a denial that does not rule out a change of course. “When people start speculating and brewing rumours you cannot stop them so I have said, and I will repeat until the cows come home, as you say, ‘I am not campaigning, I am not a candidate [and] I am not planning to leave.’” When I point out that expressing her current intention is different to declaring that she definitely will stay, she says it is impossible to be definitive about the future.

“What about if I get run over by a bus? What about if something happens to me, God forbid? Destiny is not in my hands.”

Any push to draft Lagarde into the European Commission would face two political hurdles. One is that she would have to be nominated by France’s Socialist President, Francois Hollande – and he may not want to promote a conservative rival. Just as important is the European fear that, if Lagarde changed jobs, the continent would lose the IMF post, something that former IMF chief economist Simon Johnson argues is long overdue.

“It is not supposed to be the European Monetary Fund and she has been very favourable to the Europeans during the whole euro crisis.”

Lagarde denies she has been soft on Europe, insisting that Greece and other struggling countries have been pushed to make even larger fiscal turnarounds than those demanded of Asian countries in the 1990s.

“I have always tried to not be French, not be European when I do my job,” she says. “And I think I have achieved that, yes, very much so.”