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"We can't say that we tolerate bad things, but we have got to live in the real world, and living in the real world means that life is often very complicated and you can't escape the complexity," he said.
Welby conceded that it was almost impossible for the church to make an investment that was not somehow tainted because of the complexity of investment funds and the multiple activities of some companies. He asked, for example, what should be done about an investment into a sock maker who might make products for soldiers going into combat.
"If you exclude any contact with anything that directly or indirectly gets in any way bad, you can't do anything at all," he told the BBC.
Welby suggested all of the church's finances might be examined and said he couldn't promise all the rules had been followed.
"I don't know the answer to that, because I don't know how the detail processes work in the Church Commissioner's investment management arm," he said. "What's clear is that ... this is an embarrassment."