Two per cent of Fairfax shares were bought in one transaction yesterday, sparking speculation that Gina Rinehart is increasing her hold in the media company.

Forty-two million Fairfax shares were purchased at a price of 60 cents per share.

There has been intense speculation that the world's richest woman would increase her stake in the company as she ups the pressure for seats on the Fairfax board.

Ms Rinehart has recently confirmed she owns more than 13 per cent of the company, which makes her the largest single investor.

If yesterday's purchase belongs to Ms Rinehart, it pushes her stake to 15 per cent.

Assuming that Ms Rinehart is the purchaser, fund manager Roger Montgomery says it will be hard for Fairfax to deny her a seat on the board.

"She is the largest shareholder in the company, and 15 per cent is more than enough to warrant a board seat.

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"Remember, the board's working for the shareholders. They're supposed to be representing all shareholders, not any particular interest.

"But it is right for a 15 per cent shareholder to be protecting their own interests by asking for a board seat."