Your task is to estimate VaR for an equity portfolio using the "Model-Building" approach. Suppose you have invested in two of the Fama-French factors, namely Mkt-RF and HML. Assume conditionally the returns of Mkt-RF and HML follow a bivariate normal distribution. Assume the portfolio return is the sum of the factor returns.

a. Estimate the daily volatilities and the correlation using the EWMA model with = 0.94. Plot the daily volatilities for Mkt-RF and HML on the same graph. Plot the daily correlations on a separate graph. Estimate the one-day 99% VaR for the portfolio.

Note: You are not required to use maximum likelihood to estimate , we simply assume = 0.94. You may assume the initial variance for the first rate of return is equal to the sample variance, and the initial covariance is equal to the sample covariance. (4 Marks)

b. Back-test the VaR model in Part (a) using the Kupiec two-tailed test at the 5 percent significance level, and at the 1 percent significance level. Write down your conclusion. (3 Marks)