Financial Risk Manager Part 1

The portfolio standard deviation is calculated using the formula:

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

Where:

• $w_A = 0.20$, $\sigma_A = 4\%$
• $w_B = 0.80$, $\sigma_B = 10\%$
• $\rho_{AB} = 0.60$

Plugging in the values:

$\sigma_p = \sqrt{(0.20)^2(4\%)^2 + (0.80)^2(10\%)^2 + 2(0.20)(0.80)(0.60)(4\%)(10\%)}$

$\sigma_p = \sqrt{(0.04)(0.0016) + (0.64)(0.01) + 2(0.20)(0.80)(0.60)(0.04)(0.10)}$

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

$\sigma_p = \sqrt{0.007232}$

$\sigma_p = 0.0850 = 8.50\%$

This matches the calculation shown in the provided solution.