Q9

The following table provides the worst 20 monthly rates of return in the last 100 months for a portfolio of stocks: Jan 2021 -6.67% Dec 2018 -13.00% Feb 2020 -1.67% Jul 2015 - 15.00% Mar 2020 - 11.67% Nov 2016 -7.33% Apr 2018 -0.83% Mar 2016 -3.33% Aug 2015 -18.33% Aug 2019 -5.00% Dec 2017 -7.50% May 2013 -8.33% Oct 2016 -4.50% Sep 2017 - 10.83% Jan 2017 -1.83% Oct 2019 -10.17% May 2020 -9.17% Jul 2017 -7.83% Aug 2015 -18.33% Aug 2019 -5.00% Dec 2017 -7.50N May 2013 -8.3396 Oct 2016 -4.50% Sep 2017 - 10.83%, Jan 2017 -1.83% Oct 2019 -10.17% May 2020 -9.17% Jul 2017 -7.83% Jun 2014 - 10.00% Nov 2014 -3.83% Using the historical simulation method with a confidence level of 90%: a) What is the Value at Risk (VaR) of this portfolio? [3 marks) b) What is the expected shortfall (ES) of this portfolio? [3 marks] d) What is the conceptual difference between the VaR and ES? Which metric is more appropriate for portfolios with a larger exposure to extreme returns? Explain. [9 marks]