Why is the standard deviation of a portfolio typically less than the weighted average of the standard

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Why is the standard deviation of a portfolio typically less than the weighted average of the standard deviations of the assets in the portfolio, while a portfolios beta equals the weighted average of the betas of the stocks in the portfolio?
Stocks
Stocks or shares are generally equity instruments that provide the largest source of raising funds in any public or private listed company's. The instruments are issued on a stock exchange from where a large number of general public who are willing...
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: 978-0324657937

2nd edition

Authors: Scott B. Smart, William L Megginson

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