Financial Risk Manager Part 1

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Hakim Ahmed has recently joined Lampard Investment Inc. He was given the data related to the assets of a portfolio provided in the following table. If the weight of Asset X is 35% and the weight of Asset Z is 65%, then what is the variance of the portfolio?

Variance Asset X | 0.1225
Variance Asset Z | 0.4225
Covariance | 0.19

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TTanishq

0.28

0.1156

0.2245

0.2587

Explanation:

Explanation

The portfolio variance is calculated using the formula:

$\sigma_p^2 = w_X^2 \sigma_X^2 + w_Z^2 \sigma_Z^2 + 2w_Xw_Z\text{Cov}(X,Z)$

Where:

$w_X = 0.35$ (weight of Asset X)
$w_Z = 0.65$ (weight of Asset Z)
$\sigma_X^2 = 0.1225$ (variance of Asset X)
$\sigma_Z^2 = 0.4225$ (variance of Asset Z)
$\text{Cov}(X,Z) = 0.19$ (covariance between X and Z)

Step-by-step calculation:

$w_X^2 \sigma_X^2 = (0.35)^2 \times 0.1225 = 0.1225 \times 0.1225 = 0.01500625`$ 2. $w_Z^2 \sigma_Z^2 = (0.65)^2 \times 0.4225 = 0.4225 \times 0.4225 = 0.17850625 $3`. `$ 2w_Xw_Z\text{Cov}(X,Z) = 2 \times 0.35 \times 0.65 \times 0.19 = 0.08645 $4`. **Total portfolio variance:**$ \sigma_p^2 = 0.01500625 + 0.17850625 + 0.08645 = 0.2799625 \approx 0.2800$

Therefore, the portfolio variance is 0.28, which corresponds to option A.

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