The EWMA model for updating the covariance between return X and return Y is

$$\text{Cov}_n = \lambda \text{Cov}_{n-1} + (1 - \lambda) X_{n-1} Y_{n-1}$$

Where λ is the weight of the most recent covariance on day n - 1, Covₙ is the updated covariance.

First, let's find the initial covariance $\text{Cov}_{n-1}$: $\text{Cov}_{n-1} = \text{Correlation} \times \text{Volatility}_X \times \text{Volatility}_Y = 0.4 \times 0.02 \times 0.03 = 0.00024$

Next, we calculate the updated covariance $\text{Cov}_n$: $\text{Cov}_n = (0.94 \times 0.00024) + (0.06 \times 0.03 \times 0.04) = 0.0002256 + 0.000072 = 0.0002976$

Then, we must calculate the updated variance for both assets using EWMA: $\text{Var}(X)_n = \lambda \text{Var}(X)_{n-1} + (1 - \lambda) X_{n-1}^2 = 0.94 \times (0.02)^2 + 0.06 \times (0.03)^2 = 0.000376 + 0.000054 = 0.00043$ $\text{Var}(Y)_n = \lambda \text{Var}(Y)_{n-1} + (1 - \lambda) Y_{n-1}^2 = 0.94 \times (0.03)^2 + 0.06 \times (0.04)^2 = 0.000846 + 0.000096 = 0.000942$

Finally, the updated correlation coefficient is: $\text{Corr}_n = \frac{\text{Cov}_n}{\sqrt{\text{Var}(X)_n \times \text{Var}(Y)_n}} = \frac{0.0002976}{\sqrt{0.00043 \times 0.000942}} = \frac{0.0002976}{0.00063644} \approx 0.4676$