Financial Risk Manager Part 1

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Carla Mayes, a portfolio manager created the following portfolio:

Security	Expected Return (%)	Expected Standard Deviation (%)
A	5	8
B	10	14

If the correlation of returns between the two securities is -0.20, then what is the standard deviation of a portfolio invested 75% in Security A and 25% in Security B?

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NNikitesh

Last updated: February 2, 2026 at 10:22

0.51%

0.81%

5.12%

6.31%

Explanation:

The standard deviation of a two-asset portfolio is calculated using the formula:

$\sigma_P^2 = w_A^2 \sigma_A^2 + w_B^2 \sigma_B^2 + 2w_A w_B \rho_{AB} \sigma_A \sigma_B$

Where:

$w_A = 0.75$ , $w_B = 0.25$
$\sigma_A = 0.08$ (8% converted to decimal)
$\sigma_B = 0.14$ (14% converted to decimal)
$\rho_{AB} = -0.20$

Plugging in the values:

$\sigma_P^2 = (0.75)^2(0.08)^2 + (0.25)^2(0.14)^2 + 2(0.75)(0.25)(-0.20)(0.08)(0.14)$

$= (0.5625)(0.0064) + (0.0625)(0.0196) + 2(0.75)(0.25)(-0.20)(0.0112)$

$= 0.0036 + 0.001225 - 0.00084$

$= 0.003985$

$\sigma_P = \sqrt{0.003985} = 0.06312 = 6.312\%$

This matches option D (6.31%). The negative correlation helps reduce portfolio risk through diversification, but the portfolio standard deviation is still higher than Security A's individual standard deviation due to the higher risk of Security B.

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