The aim of the buyback is to reduce the discount to net asset value at which the shares presently trade, which is currently 6.9 per cent.
By buying back shares, the share price of all the shares should rise and so the discount to net asset value would fall.
In the annual results statement of the trust, released this morning (11 June) and covering the year to April 30, 2019, the board said the plan for a buyback was in the “best interests of shareholders”.
During the year, the trust returned 0.2 per cent, compared with a return of 2.6 per cent for the FTSE All Share.
Baillie Gifford took over the management of the trust from Schroders in June 2018 after its previous managers left to work elsewhere.
Almost all of the investments in the trust when Baillie Gifford took over were sold and replaced, with the new managers switching from the value style of investing to the growth style. The board said this trading activity cost about 1 per cent of net asset value.
The trust's chairman, Carolan Dobson, warned investors this change in style would mean dividend payments would gradually fall.
She said: "As our new portfolio managers are growth investors, with any underlying income received being a by-product of that approach, revenue earnings for this and future years are expected to be notably lower than previously."
Ms Dobson added: "The board and managers have considered the implications of Brexit and the current political uncertainties. As of the date of this statement, there are so many uncertainties that there seems little that could be done to hedge the portfolio against such a wide range of potential negative outcomes other than our portfolio managers remaining focused on backing exceptional UK companies that have the potential to exploit their competitive advantage.
"Whilst the benefits of this approach will not always be reflected in short term returns, the board and managers firmly believe it will reward the patient investor over the long-term."