1. You need to download the closing prices for heating oil futures from Yahoo Finance (the symbol is HO=F)
2. You need to download data for jet fuel prices using FRED (the symbol is DJFUELUSGULF)
3. Merge the two time series altogether and compute the return for each. This should correspond to a daily time series ranging between Sept 2000 and Dec 2020. As a confirmation, plot the cumulative return of both time series in a single plot. What do you observe?
4. As a summary, report the annual volatility for each. How does it compare with that of the SPY over the same period?
5. Regress the return on the jet fuel using the return on the futures contract. Report the regression results, especially the beta and the coefficient of determination, i.e. R squared.
6. Consider the return on the hedged portfolio that shorts N contracts while longs a single jet fuel index. In this case, the portfolio return is equal to the return on the jet fuel minus N times the return on the futures contract, i.e., . Given this, compute the volatility of this portfolio with different fractions of N ranging between 0 and 2. Plot the annual portfolio volatility as a function of N and highlight the minimum point both on the y-axis and the x-axis. How do you relate these points to the regression results? Which one is which? Elaborate.

In R or Excel Please