Why is portfolio standard deviation not a weighted average of the standard deviations of the underlying securities?

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Why is portfolio standard deviation not a weighted average of the standard deviations of the underlying securities?
Portfolio
A portfolio is a grouping of financial assets such as stocks, bonds, commodities, currencies and cash equivalents, as well as their fund counterparts, including mutual, exchange-traded and closed funds. A portfolio can also consist of non-publicly...
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Introduction to Corporate Finance

ISBN: 978-1119171287

4th edition

Authors: Laurence Booth, Sean Cleary, Ian Rakita

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