Financial Risk Manager Part 1

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Explanation:

Calculate the initial covariance: $Cov_{n-1} = \rho \times \sigma_X \times \sigma_Y = 0.4 \times 0.02 \times 0.03 = 0.00024`$ 2. Calculate the updated covariance using EWMA: $Cov_n = \lambda Cov_{n-1} + (1-\lambda) R_{X} R_{Y} = (0.94 \times 0.00024) + (0.06 \times 0.03 \times 0.04) = 0.0002256 + 0.000072 = 0.0002976 $3`. Calculate the updated variances:$ \sigma^2_{X, n} = (0.94 \times 0.02^2) + (0.06 \times 0.03^2) = 0.000376 + 0.000054 = 0.00043\sigma^2_{Y, n} = (0.94 \times 0.03^2) + (0.06 \times 0.04^2) = 0.000846 + 0.000096 = 0.000942$4. Calculate the updated correlation: $\rho_n = \frac{Cov_n}{\sigma_{X, n} \sigma_{Y, n}} = \frac{0.0002976}{\sqrt{0.00043} \times \sqrt{0.000942}} = \frac{0.0002976}{0.020736 \times 0.030692} \approx 0.4676$

Explanation:

Calculate the initial covariance: $Cov_{n-1} = \rho \times \sigma_X \times \sigma_Y = 0.4 \times 0.02 \times 0.03 = 0.00024`$ 2. Calculate the updated covariance using EWMA: $Cov_n = \lambda Cov_{n-1} + (1-\lambda) R_{X} R_{Y} = (0.94 \times 0.00024) + (0.06 \times 0.03 \times 0.04) = 0.0002256 + 0.000072 = 0.0002976 $3`. Calculate the updated variances:$ \sigma^2_{X, n} = (0.94 \times 0.02^2) + (0.06 \times 0.03^2) = 0.000376 + 0.000054 = 0.00043\sigma^2_{Y, n} = (0.94 \times 0.03^2) + (0.06 \times 0.04^2) = 0.000846 + 0.000096 = 0.000942$4. Calculate the updated correlation: $\rho_n = \frac{Cov_n}{\sigma_{X, n} \sigma_{Y, n}} = \frac{0.0002976}{\sqrt{0.00043} \times \sqrt{0.000942}} = \frac{0.0002976}{0.020736 \times 0.030692} \approx 0.4676$

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Last updated: June 22, 2026 at 14:11

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0.4676

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