I personally prefer “entrusted investment”.

In my limited experience, “outsource” seems to suggest the outsourced business is not a core business or at least not as important as the other businesses of the outsourcing company. For example, a large stockbroker may have a translation department established to handle translation of documents on stockbroking. Needless to say, translation is a trivial business compared to the stockbroking business of the broker. It may someday elect to “outsource” translation to a company which is primarily engaged in providing language services.

In China, when a bank (commercial bank) appoints an asset manager to conduct investing on its behalf, it is usually not because the bank thinks investing is not an important business. Rather, it is probably because the bank is incapable of achieving satisfactory returns to assets if it conducts direct investment.

需要倒过来，才是符合英文习惯的表达。investment outsourcing



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Note added at 22 days (2017-05-19 17:09:15 GMT) Post-grading
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很多时候，汉译英的表达，我们不能单纯的从字面上理解。即使创造出来一个措辞，首先要求证西方人是如何理解的。这个词，本质是委外，不是投资二字，从英文角度而言。与汉语的归纳式总结不同。应该颠倒过来，强调outsourcing, 才是点题的翻译。

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Note added at 22 days (2017-05-19 17:09:43 GMT) Post-grading
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本质上，这是一个语感的问题。微妙。