Compute the daily position of the trader

Question

Problem 1: Using the prices on the S&P500 Index as in Module 1 from January 1, 2000, to December 31, 2013:

a) Starting on July 1, 2008, compute the VaR_(t,t+10)^(0.01) using a model in which the innovation term is distributed as a standard normal and the variance is given by the RiskMetrics model, that is:

R_(t+1)=σ_(t+1) z_(t+1) where z_(t+1)~N(0,1) and σ_(t+1)² = λσt²+(1-λ) Rt²

Hint: Estimate the RiskMetrics model on the full sample.

b) Compute the daily position of the trader.

c) Compute the daily profit of the trader (simply multiply each daily position by the log-return over the next day)

d) Compute the cumulative profit and losses of the trader starting from July 1, 2008, to December 31, 2009.

e) Compare the result with what you obtained in Question 1 of Hands-On assignment in Module 1.

Problem 2: Expected Shortfall (ES)

Using the same data used in the Hands-On assignment in Module 2 (i.e., the stock index data that you selected from the Manchester Oxford Institute dataset):

a) Compute, starting on January 1, 2014, the next day 5% VaR and ES, on each day of the sample, using a model in which the innovation term is given by a standard normal distribution and the variance is given by the GARCH model.

b) Compute, starting on January 1, 2014, the next day 5% VaR and ES, on each day of the sample, using a model in which the innovation term is given by a standard normal distribution and the variance is given by the HAR model.

c) Plot the daily losses, along with the VaR and ES measures computed in the previous two questions.

Attachment:- Assignment - Value at Risk.rar