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The increase was driven by huge prices in the Contemporary and Modern art sectors, as well as expansion in Asia. What's more, say the auctioneers, 30% of buyers were new and they accounted for 22% of all sales by value.

What is not clear from the figures, however, is how profits have grown by comparison. Such is the competition for trophy lots in the fields of Contemporary and Modern art that consignors have been able to demand a slice of the buyer's premium in some cases, as well as refusing to pay any vendor's commission at all. Add to this the increasing re-emergence of guarantees, and margins for these sectors are clearly being squeezed to a degree.

It is this tendency to sacrifice profits and investor value for market share that has reportedly angered corporate investor Daniel Loeb, who has tried to unseat Sotheby's chief executive Bill Ruprecht in recent months.

Sotheby's publish their full results later in February but have promoted highlights from the past year to coincide with Christie's announcement. The bulk of these come from the Contemporary, Impressionist and Modern sectors for both houses, with Post War and Contemporary art alone accounting for 29% of all Christie's sales at £1.3bn ($2bn).

Although Sotheby's have yet to publish their annual totals, they listed the works that gave them seven of the top ten prices in the Impressionist and Modern sector, including Grande tête mince (Grande tête de Diego), the 1954 bronze sculpture by Alberto Giacometti, which scored the highest auction price for an Impressionist and Modern work in 2013 when it took $44.5m in New York on November 5.

Asian Expansion

Both auctioneers are making the most of their expansion in Asia, both in terms of holding live sales in mainland China and in securing the top prices for Contemporary Chinese art.

However, it is the burgeoning importance of private sales that is perhaps most interesting. Sotheby's have only released figures for the first nine months of 2013 so far, but even these stand at £602m ($951m), 37% up on the same period for the previous year, while year-end figures put Christie's private sales at £760.5m ($1.19bn), a rise of 20% in sterling terms on 2012.

Steven P. Murphy, chief executive at Christie's, said: "Our strategy to invest in new markets such as China, new channels such as private sales and online sales… has enabled Christie's to grow."

At Sotheby's Mr Ruprecht was equally upbeat: "The exceptional growth this year of buyers new to Sotheby's contributed to our 21% rise in sales of Impressionist & Modern Art, 50% increase in sales of Asian Art, and stellar results across the business."