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The market risk of a portfolio is equal to the weighted average market risk of its...

The market risk of a portfolio is equal to the weighted average market risk of its components, and the total risk of a portfolio is equal to the weighted average total risk of its components. Ture or False. the correct answers are False but why? I need some explanation.

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Expert Solution

The risk of a portfolio is measured by its standard deviation. However, the risk is not the weighted average risk as the individual stocks do not have perfect correlation with each other .

The standard deviation of a portfolio is given by

Where Wi is the weight of the security i,

is the standard deviation of returns of security i.

and is the correlation coefficient between returns of security i and security j

If correlation coefficient = +1 for all the pairs of securities in the portfolio, then only the standard deviation is the highest and is the weighted average standard deviation of its components

Else, the standard deviation of the portfolio is lesser (which is usually the case) than the weighted average standard deviation of the components.

So, the statement is FALSE for the reasons above

jeff jeffy answered 1 year ago
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