Question

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

(A) Download the daily stock prices using the getSymbols function in the quantmod R package for the period from January 3rd 2000 to March 21th 2022. Make a plot of the daily closing prices during this period.
(B) Estimate the daily 1% VaR using the parametric GARCH(1,1) model. When estimating the model, use a window of 500 days. Make a plot of the estimated VaRs.
(C) Redo the same exercise in (B) using the Filtered Historical Simulation method. Compare with the results in (B) and explain the differences.
(D) Are returns of the Bank of America stock unconditionally normally distributed during this period?
(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? (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?

Answer 1

The question deals with analyzing the stock prices for Bank of America, estimating daily 1% VaR, testing for the distribution of stock returns, and evaluating the benefits of portfolio diversification in the financial sector.

Step-by-step explanation:

The student has asked a question related to investing in the financial sector, specifically focusing on daily stock price analysis, Value at Risk (VaR) estimation, and portfolio diversification including stocks of Bank of America. To address the questions, one would typically utilize the quintom R package for retrieving stock prices, estimate VaR using GARCH(1,1) models, compare it with Filtered Historical Simulation method, and perform statistical tests to assess the distribution of returns. Portfolio diversification would be evaluated by computing the daily returns for the new portfolio comprising of Bank of America, Apple, and BP stocks and then estimating and comparing the VaR for the diversified portfolio.

It should be noted that financial data analysis requires careful evaluation of historical prices, volatility, and risk assessment techniques to make informed investment decisions. A thorough understanding of the financial market's behavior is essential for such analyses.