Answer-first summary for fast verification
Answer: 13.4%. This option correctly calculates the portfolio standard deviation by taking the square root of the portfolio variance.
The correct answer is **C**. The portfolio standard deviation is calculated using the formula: \[ \sigma_p = \sqrt{w_1^2 \sigma_1^2 + w_2^2 \sigma_2^2 + 2 w_1 w_2 \rho_{1,2} \sigma_1 \sigma_2} \] Substituting the given values: \[ \sigma_p = \sqrt{(0.4)^2 (0.15)^2 + (0.6)^2 (0.18)^2 + 2 (0.4)(0.6)(0.20)(0.15)(0.18)} \] \[ \sigma_p = \sqrt{0.017856} \approx 0.1336 \text{ or } 13.4\% \] Options A and B are incorrect due to errors in the calculation method.
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A portfolio consisting of two securities has the following characteristics:
A
1.8%. This option incorrectly calculates the portfolio variance instead of the standard deviation.
B
9.1%. This option incorrectly uses standard deviations instead of variances in the formula for the portfolio standard deviation.
C
13.4%. This option correctly calculates the portfolio standard deviation by taking the square root of the portfolio variance.