Alliance Trust, the investment trust that has been under siege from activist investor Laxey Partners, burnt through £19.4m buying back shares to boost its share price in the first quarter of the financial year.The trust's acquisition of 5.4m of its own shares in the three months to 30 April contributed to a narrowing of the share price discount to net asset value (NAV) from 17.1% at the end of 2010 to 15.3% at the end of April.Total shareholder return over the three month period was 5.4%and the NAV total return (with debt at fair value and inclusive of income) was 2.9%.NAV per share, including income, stood at 381.5p at the end of April. The company is in the process of changing its year-end to 31 January to move in sync with other trusts.The step-change in the trust's active use of buybacks in recent months - a change in tack some observers suggest has been prompted by Laxey's criticism of the trust's management - will continue, taking into account the company's discount relative to the peer group, Alliance Trust said.During the February to April period the trust continued to change the emphasis in its portfolio away from Japan and emerging markets, while increasing its exposure to other developed Asian markets.The largest sector exposures remain in Financials, Industrials and Oil & Gas, the company said. A bias to higher growth markets and stocks which should perform throughout the economic cycle has been maintained, though some of the dependency on cyclical sectors has been reduced.--jh