Financial Risk Manager Part 1

Explanation

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

$\sigma_p = \sqrt{w_A^2\sigma_A^2 + w_B^2\sigma_B^2 + 2w_Aw_B\rho_{AB}\sigma_A\sigma_B}$

Where:

• $w_A = 0.20$ (20% weight)
• $w_B = 0.80$ (80% weight)
• $\sigma_A = 0.04$ (4% standard deviation)
• $\sigma_B = 0.10$ (10% standard deviation)
• $\rho_{AB} = 0.60$ (correlation)

Substituting the values:

$\sigma_p = \sqrt{(0.2)^2(0.04)^2 + (0.8)^2(0.10)^2 + 2(0.2)(0.8)(0.6)(0.04)(0.10)}$

$\sigma_p = \sqrt{(0.04)(0.0016) + (0.64)(0.01) + 2(0.16)(0.6)(0.004)}$

$\sigma_p = \sqrt{0.000064 + 0.0064 + 0.000768}$

$\sigma_p = \sqrt{0.007232} = 0.0850 = 8.50\%$

The calculation shows that the portfolio standard deviation is 8.50%, which represents the weighted combination of the individual securities' volatilities adjusted for their correlation._