The world is going wild for lady bankers. For the first time, a woman, Christine Lagarde, is in charge of the International Monetary Fund (IMF), her tender hand stewarding the institution away from the testosterone-sodden tenancy of Dominique Strauss-Kahn.

Meanwhile, the press is profiling high-ranking female executives, such as the Facebook chief, Sheryl Sandberg, and a new campaign group, the 30 Per Cent Club, is working to increase the representation of women in FTSE 100 company boardrooms from around 13 per cent to just under a third.

It is implied that doing so will turn banking into a caring industry, in which profits soar like bluebirds in corridors that ring with the clatter of Manolos on marble. There are three distinct problems with this hypothesis.

The first is that it's arrant twaddle, based on cod science and lazy stereotypes. The 30 Per Cent Club's claim that companies with more women bosses tend to perform better wasn't pulled out of thin air but it hasn't been proven that this is because women's pink and squishy brains make them more careful investors, as the pseudoscience of "neuroeconomics" suggests -- it could simply be that more progressive companies tend to hire more women.

Sexism is rife in the City of London. The Fawcett Society's Sexism in the City campaign in 2008 drew attention to a culture of unequal pay, disregard for the practicalities of childcare, laddish posturing and business deals done in strip clubs.

Yet it is ludicrous to suggest, as many have done, that if we were to temper the big, bad boy's world of business with a few more fragrant females, then these institutions would suddenly become a force for good.

Lagarde can certainly work a pencil skirt -- the Observer's gushing profile heralded her as "the world's sexiest woman" -- but that won't stop the IMF imposing austerity measures across the eurozone that will leave many unemployed and destitute.

The second problem with this obsession with female representation in business is its cynicism. Speaking on 5 July at a seminar organised by the 30 Per Cent Club, the Home Secretary, Theresa May, suggested that "more diverse boards are better boards" because they "outperform their male-dominated rivals".

As Minister for Women and Equalities, May should know that we pursue equality in the workplace because it's good for women, not because it's good for business.

Trying to justify feminism on the basis of profit is dangerous because, at its root, feminism is pretty bad for business. Maternity provisions, equal pay, higher taxes to finance a welfare state that supports hard-working mothers -- all of these things cost money and affect returns.

May recognised this in December 2010, when she scrapped the Labour government's plans to compel employers to publish equal-pay audits -- a move that was applauded by the City of London.

The third problem with this "trickle-down" feminism is that giving women more power at the top of the socio-economic pile does not necessarily increase the power of women at the bottom of the heap.

Ensuring that a slightly larger minority of females get to wield power in finance does next to nothing for the cause of women's liberation, because the real issue is not that women have too little power in business but that business has too much power. Three years of global economic meltdown have dispelled the liberal delusion that making life easier for the men and women in the boardrooms of London and Wall Street makes life easier for everyone else.

Trickle-down feminism is as nonsensical a liberation strategy as trickle-down wealth redistribution. The problem with a glass ceiling is that nothing trickles down. While we all worry about the glass ceiling, there are millions of women standing in the basement -- and the basement is flooding.

There is nothing wrong with personal ambition. After all, if equality means anything, it means the right for a woman to be as much of a ruthless, power-hungry bastard as any man and to be judged accordingly.

Let's not pretend, however, that a few more skirt suits in the palaces of finance will deliver the change that women need.

This post was written with the help of Zoe Stavri.