Practice Question
When two risky securities with correlation less than one, are held in a portfolio, which of the following is true?
A) The portfolio standard deviation will be greater than the weighted average of the individual security standard deviations.
B) The portfolio standard deviation will be less than the weighted average of the individual security standard deviations.
C) The portfolio standard deviation will be equal to the weighted average of the individual security standard deviations.
D) The portfolio standard deviation will always be equal to the securities' covariance.
E) None of the above are true.
Key Concepts:
- Portfolio Standard Deviation: Measures the total risk of the portfolio.
- Correlation: If correlation between assets is less than 1, diversification reduces risk.
Formula:
\[ \sigma_p = \sqrt{w_1^2 \sigma_1^2 + w_2^2 \sigma_2^2 + 2 w_1 w_2 \sigma_1 \sigma_2 \rho_{12}} \]
Why B is Correct: When \( \rho_{12} < 1 \), the diversification benefit means that the portfolio’s standard deviation is lower than the weighted average of individual standard deviations.
Conclusion: Answer B captures the effect of diversification when correlation is less than 1.