Using the EWMA model, we first need to find the updated covariance and updated individual variances. (Note: The mention of assets X and Y is a typo for A and B).

Initial Covariance ($Cov_{n-1}$): $Cov_{n-1} = \text{Correlation} \times Vol_A \times Vol_B = 0.5 \times 0.01 \times 0.02 = 0.0001$

Updated Covariance ($Cov_n$): $Cov_n = \lambda \times Cov_{n-1} + (1 - \lambda) \times Return_A \times Return_B$ $Cov_n = 0.9 \times 0.0001 + 0.1 \times (0.02 \times 0.03)$ $Cov_n = 0.00009 + 0.1 \times 0.0006 = 0.00009 + 0.00006 = 0.00015$

Updated Variance for A ($Var_{A, n}$): $Var_{A, n} = \lambda \times Var_{A, n-1} + (1 - \lambda) \times (Return_A)^2$ $Var_{A, n} = 0.9 \times (0.01)^2 + 0.1 \times (0.02)^2 = 0.00009 + 0.00004 = 0.00013$ $Vol_{A, n} = \sqrt{0.00013} \approx 0.01140$

Updated Variance for B ($Var_{B, n}$): $Var_{B, n} = \lambda \times Var_{B, n-1} + (1 - \lambda) \times (Return_B)^2$ $Var_{B, n} = 0.9 \times (0.02)^2 + 0.1 \times (0.03)^2 = 0.00036 + 0.00009 = 0.00045$ $Vol_{B, n} = \sqrt{0.00045} \approx 0.02121$

Updated Correlation ($Corr_n$): $Corr_n = \frac{Cov_n}{Vol_{A, n} \times Vol_{B, n}} = \frac{0.00015}{0.01140 \times 0.02121} = \frac{0.00015}{0.0002418} \approx 0.62$