Alliance Trust has dismissed the challenge to its board by rebel shareholder Elliott Advisors as "completely unacceptable", as the war of words over the £2.9billion trust intensifies.

Its chairman Karin Forseke has also defended the board against criticism that it has failed to stand up to powerful chief executive Katherine Garrett-Cox, saying it subjects her to "robust" scrutiny.

Alliance shares closed the week up 6per cent at an all-time high despite its board's uncompromising refusal to entertain Elliott's proposal to add three "independent" non-executives to its seven-strong board.

Battle was joined yesterday morning as Alliance issued its rebuttal to Elliott's requisition notice last Monday. The company said it unanimously recommended that shareholders vote against Elliott's resolutions at the annual meeting in Dundee on April 29, because the proposed directors would not be truly independent and might "seek to exert undue influence" . Alliance had a clear strategy with "positive results already coming through", and the board maintained "strong oversight of the executive team".

Elliott had noted that Ms Garrett-Cox had been in post longer than any of the board, and complained that she had first appointed then replaced the trust's investment manager without consulting on other options - Aberdeen made a private bid to manage the trust in 2012.

Ms Forseke commented: "We have a strong chief executive, we also have a very strong board." She said changing chief executives regularly was "not something to strive for", and internal fund manager appointments were "common practice" in the industry.

Elliott had accused the company of a "lack of meaningful engagement" but Ms Forseke said it had "engaged with them 13 times" and criticised the shareholder for failing to forewarn her of their proposal a recent meeting.

Alliance claimed that Elliott had "repeatedly" proposed that Alliance should liquidate 40 per cent of the trust in a tender for shares, proving that it was seeking an immediate exit. But this was hotly denied by the 12per cent shareholder. A spokesman for Elliott said it had been "proposed in 2011 as one of a number of options and that was the last time it was mentioned", and went on: "What is short-term about adding three non-executives to a board of seven people? If we were short-term we would not have been a patient shareholder for five years and we would be pushing for a particular outcome."

Elliott had said in its rejoinder to Alliance yesterday morning that its open correspondence showed no such proposal had been made.

However the spat became increasingly ill-tempered as Alliance issued a second statement later yesterday, detailing a recent letter apparently showing Elliott had advocated " the several hundreds of millions of pounds worth of value creation available to all shareholders ".

But Elliott issued a second statement complaining that the letter "was referring to a conversation in 2011, in the context of another shareholder (proposal)".

Alliance said a tender offer "potentially threatens the very existence of the company, and rides roughshod over our long-term shareholders, our customers and our over 250 employees", while Elliott put no value on the growing dividend in "stark contrast" to other shareholders.

It said the resolutions were a "pre-cursor for further disruptive actions from Elliott which are likely to focus solely on engineering an exit from their shareholding and would not be in the interests of all of our shareholders".

Alliance said that "outperformance of the equity portfolio against its benchmark" was among the things it "expects to deliver" for shareholders. It said total shareholder returns were "top quartile since the new equities leadership team was put in place almost six months ago and are above median over one and five year periods".