Which one of the following statements is correct concerning the standard deviati
ID: 2802699 • Letter: W
Question
Which one of the following statements is correct concerning the standard deviation of a portfolio consisting of randomly selected securities.
The greater the diversification of the portfolio, the greater the standard deviation of the portfolio.
The standard deviation of a portfolio is equal to a value weighted average of the standard deviations of the individual securities held in the portfolio.
The standard deviation of a portfolio is equal to a geometric average of the standard deviations of the individual securities held in the portfolio.
The standard deviation of a portfolio is greater than an arithmetic average of the standard deviations of the individual securities held in the portfolio.
The standard deviation of a portfolio is less than a value weighted average of the standard deviations of the individual securities held in the portfolio.
A.The greater the diversification of the portfolio, the greater the standard deviation of the portfolio.
B.The standard deviation of a portfolio is equal to a value weighted average of the standard deviations of the individual securities held in the portfolio.
C.The standard deviation of a portfolio is equal to a geometric average of the standard deviations of the individual securities held in the portfolio.
D.The standard deviation of a portfolio is greater than an arithmetic average of the standard deviations of the individual securities held in the portfolio.
E.The standard deviation of a portfolio is less than a value weighted average of the standard deviations of the individual securities held in the portfolio.
Explanation / Answer
A. Standard deviation means total risk, which can be reduced through diversification, hence statement is wrong
B. Standard devition will be reduced if correlation is "<1", it can not be reduced ( equals to Weighted average SD of securities in taht portfolio" where " correlation is "+1". Thus it is not always weighted average of SD of securities in that portfolio.
C. Portfolio SD = Square root [ ( W1*SD1)2 + ( W2*SD2 )2 + 2 (W1*SD1)*(W2*SD2)*r ]
Thus it is not GP os SDs in that portfolio.
D. Portfolio SD is max equals to weighed average SD of securities in that portfolio that to where "r=1", it never exceeds weighted average SD of securties in that portfolio.
E.
Portfolio SD = Square root [ ( W1*SD1)2 + ( W2*SD2 )2 + 2 (W1*SD1)*(W2*SD2)*r ]
it ( Portfolio SD will be less than weighted average SD where -1</= r < 1
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