Your task is to estimate expected shortfall (ES) for an equity portfolio using the historical simulation...

  

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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 (v₁) for the first daily return and the long-run variance (V₁) 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 σ n+1 σi 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. 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 (v₁) for the first daily return and the long-run variance (V₁) 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 σ n+1 σi 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.

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Estimating Expected Shortfall ES for an Equity Portfolio While I cannot execute the calculations involved due to the lack of specific data on daily returns and volatilities I can guide you through the ... View the full answer