Prior to his appointment to the Future Fund, Murray was the Chief Executive Officer of the Commonwealth Bank between 1992 and 2005.

In Murray's 13 years as Chief Executive, the Commonwealth Bank transformed from a partly privatised bank with a market capitalisation of $6 billion in 1992 to a $49 billion integrated financial services company,[2] generating in the process total shareholder returns (including gross dividend reinvestment) at a compound annual growth rate of over 24 per cent, one of the highest total returns of any major bank in Australia.

In 2007 Murray was appointed an Officer of the Order of Australia for service to the finance sector nationally and internationally through strategic leadership and policy development, to education, particularly fostering relations between educational institutions and business and industry, and to the community as a supporter of and fundraiser for cultural and church organisations.

[9] Murray led a push against the Australian Stock Exchange in 2019 for companies to have a social licence included in their Corporate Governance Guidelines, labelling the proposal "politically correct nonsense".

[11][12][13] As of 2019, Murray is chair of The Butterfly Foundation[14] a registered charity helping people with eating disorders.