Download historical daily price data for the S\&P 500 from 2015-01-01 to 2020-07-01. Assume that "today" is 2020-01-01, and you have a portfolio that perfectly tracks the S\&P 500. You believe that the returns are normally distributed and want to know the one-day VaR of your position. - Calculate daily returns based on the close prices for the entire time period. (For simplicity, we ignore dividends and/or capital gain distributions.) - Use the daily returns from 2015-01-01 up to "today" 2020-01-01 to estimate the volatility of the process. - Estimate the daily 5\% VaR (short time horizon) in percent of some fixed notional W based on "past" returns. - Looking at the period from "today" 2020-01-01 to the "future" 2020-07-01: How often would you expect to see more extreme returns than the 5% VaR, and how often do you actually see more extreme returns? - Plot the return time series and explain what you see