Questions 1-5 are concerned with Value at Risk and Expected Shortfall. Assume that the tail

probability of interest is 1%. The daily Amazon (AMZN) and Coca Cola (KO) prices from

January 2, 2003 to April 30, 2015 can be downloaded from Yahoo via the quantmod package.

Use the adjusted closing prices to compute the daily log returns. Assume that you hold both

stocks valued at $1 million each.

1- Consider the Amazon stock only. (20 points)

A. Calculate the VaR of your position for the next trading day using the RiskMetrics method

on April 30, 2015. Write down the model based on which you calculate VaR. What is the

associated expected shortfall? Also, what is the VaR for the next 10 trading days?

B. Build a GARCH(1,1) model for the log return series with Gaussian innovations. What is the

VaR based on the fitted model for the next trading day? What is the corresponding

expected shortfall?

C. Build a GARCH(1,1) model with Student-t innovations for the log return series. What is

the VaR for the next trading day based on the fitted model? What is the corresponding

expected shortfall?