Your task is to estimate expected shortfall (ES) for an equity portfolio using the "historical simulation" approach. Suppose you have invested in two of the Fama-French factors, namely Mkt-RF and HML. You are provided with the daily returns for the last five years. a. Use the "exponential weighting" method (Section 13.3.1) to estimate the one-day 97.5% ES for the portfolio. Note: in our context each scenario is represented by the "rate of return" instead of "value". Therefore, the ES should also be estimated as a rate of return. b. Use the "volatility-scaling" method (Section 13.3.2) to estimate the one-day 97.5% ES for the portfolio. The daily volatilities for Mkt-RF and HML should be estimated by GARCH (1,1). You may assume the initial variance (v) for the first daily return and the long-run variance (V) are both equal to the sample variance. The parameters, a and B, should be estimated by maximum likelihood method for each market variable. Note: As in Part (a), each scenario should be represented by rate of return. In the case of volatility-scaling, the simulated rate of return under the ith scenario is given by n+1 i o is the estimated volatility for the ith scenario, On+1 is the volatility forecast for next trading day, r, is the rate of return without volatility adjustment.