Question 2 You are interested in investing in the financial industry, and would like to learn the behavior of stocks in this industry. The company you look at in particular is Bank of America (symbol BAC).

1.(A)Download the daily stock prices using the getSymbols function in the quantmod R package for the period from January 3rd 2000 to March 20th 2018. Make a plot of the daily closing prices during this period.

2.(B)Estimate the daily 1% VaR using the parametric GARCH(1,1) model. When estimat- ing the model, use a window of 500 days. Make a plot of the estimated VaRs.

3.(C)Redo the same exercise in (B) using the Filtered Historical Simulation method. Com- pare with the results in (B) and explain the differences.

4.(D)Are returns of the Bank of America stock unconditionally normally distributed during this period?

5.(E)Are returns of the Bank of America stock conditionally normally distributed if you standardize the returns with volatility estimated from a GARCH(1,1) model?

6.(F)You would like to diversify your portfolio by investing one third of your portfolio in Bank of America, one third in Apple (symbol AAPL), and one third in BP (symbol BP). Calculate daily returns on your portfolio and redo parts (B) and (C) on your new portfolio. Do you find signs that diversification reduces risk?