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 | 0.3721
Covariance | 0.19
Other
Community
NNikitesh
A
0.3712
B
0.1156
C
0.2245
D
0.2587
Explanation:
Calculation:
Given:
- Weight of Asset X (w_x) = 35% = 0.35
- Weight of Asset Z (w_z) = 65% = 0.65
- Variance of Asset X (σ_x²) = 0.1225
- Variance of Asset Z (σ_z²) = 0.3721
- Covariance between X and Z (Cov_xz) = 0.19
Portfolio Variance Formula: σ_p² = w_x² * σ_x² + w_z² * σ_z² + 2 * w_x * w_z * Cov_xz
Step-by-step calculation:
- w_x² * σ_x² = (0.35)² * 0.1225 = 0.1225 * 0.1225 = 0.01500625
- w_z² * σ_z² = (0.65)² * 0.3721 = 0.4225 * 0.3721 = 0.15716225
- 2 * w_x * w_z * Cov_xz = 2 * 0.35 * 0.65 * 0.19 = 2 * 0.2275 * 0.19 = 2 * 0.043225 = 0.08645
Total Portfolio Variance: σ_p² = 0.01500625 + 0.15716225 + 0.08645 = 0.2586185 ≈ 0.2587
Therefore, the portfolio variance is approximately 0.2587, which corresponds to option D.
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