SIE Exam Question 857: Answer and Explanation

Question: 857

The standard deviation of an investment portfolio must be __________ the weighted average of the standard deviation of returns of the individual securities.

• A. equal to
• B. greater than
• C. less than
• D. less than or equal to

Correct Answer: D

Explanation:

The standard deviation of an investment portfolio must be less than or equal to the weighted average of the standard deviation of returns of the individual securities. If the securities in a portfolio are perfectly correlated, then the standard deviation of the portfolio will be equal to the weighted average of the standard deviations of the individual securities within the portfolio. If the securities in a portfolio are not perfectly correlated, then the standard deviation of the portfolio will be less than the weighted average of the standard deviations of the individual securities making up the portfolio. By adding additional securities, the standard deviation of the portfolio can never increase.