Which one of the following statements is correct concerning the standard deviation of a portfolio?

A) The greater the diversification of a portfolio, the greater the standard deviation of that portfolio.
B) The standard deviation of a portfolio can often be lowered by changing the weights of the securities in the portfolio.
C) Standard deviation is used to determine the amount of risk premium that should apply to a portfolio.
D) Standard deviation measures only the systematic risk of a portfolio.
E) The standard deviation of a portfolio is equal to a weighted average of the standard deviations of the individual securities held within the portfolio.

The standard deviation of a portfolio can often be lowered by changing the weights of the securities in the portfolio. This is because the standard deviation of a portfolio is influenced not only by the standard deviation of each individual security within the portfolio, but also by the correlation among the securities. By adjusting the weights of the securities, an investor may be able to reduce the correlation among them and lower the overall standard deviation of the portfolio. The other answer choices are incorrect. A is incorrect because the greater the diversification of a portfolio, the lower the standard deviation of that portfolio. C is incorrect because standard deviation is not used to determine the amount of risk premium that should apply to a portfolio. D is incorrect because standard deviation measures both systematic and unsystematic (idiosyncratic) risk of a portfolio. E is incorrect because the standard deviation of a portfolio is not simply a weighted average of the standard deviations of the individual securities held within the portfolio, as correlations among securities also affect the overall standard deviation.