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Assume that you have invested half of your wealth in a risk-free asset

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Assume that you have invested half of your wealth in a risk-free asset
A and half in a risky portfolio B. Is it theoretically possible to lower your portfolio risk if you move your risk-free asset holdings (A) into another risky portfolio C? In other words, can you ever reduce your risk more by buying a risky security than by buying a risk-free asset?

 
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