1. Comparing US and International Stock ETFs Please download daily data (2019-2023) from Yahoo Finance using...

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1. Comparing US and International Stock ETFs Please download daily data (2019-2023) from Yahoo Finance using the below codes and calculate the daily simple returns. We use VTI for the US bond and VXUS for the Ex-US international stock ETF portfolios. You need to practice your R codes for answering the below questions. = "2018-12-31", to="2023-12-31") library (quantmod) # install.packages ("quantmod") if needed get Symbols ('VTI', from get Symbols ('VXUS', from = "2018-12-31", to="2023-12-31") %23 calculate the simple returns VTI = VTI$VTI. Adjusted; VXUS L = length (VTI) = VXUS$VXUS. Adjusted rtn.VTI = as.numeric (VTI [-1])/as.numeric(VTI [-L]) - 1 rtn.VXUS = as.numeric (VXUS [-1])/as.numeric (VXUS [-L]) - 1 (a) What are the maximum and minimum returns for VTI and VXUS, respectively? (b) Could you plot the histograms for VTI and VXUS, respectively? Do they look like normal distributions? [HINT: use hist() and set breaks=100] (c) What are the percentages of observations within two standard deviations from the aver- age for VTI and VXUS, respectively? Do we have a 95% coverage for the regression fit? [HINT: we use 2 to approximate 1.96 for the 95% confidence interval.] (d) Could you plot the cumulative returns for these two ETFs in the same figure with dif- ferent colors. [HINT: check codes on the notes] (e) Please run a simple regression for VXUS on VTI, report the coefficients, plot the scatter plot with the fitted regression line. Please provide a short summary for explaining the regression results. [HINT: check codes on the notes] (f) Finally, please run a simple regression for VTI on VXUS, and report the coefficients. What is the difference between this model and the previous one? 1. Comparing US and International Stock ETFs Please download daily data (2019-2023) from Yahoo Finance using the below codes and calculate the daily simple returns. We use VTI for the US bond and VXUS for the Ex-US international stock ETF portfolios. You need to practice your R codes for answering the below questions. = "2018-12-31", to="2023-12-31") library (quantmod) # install.packages ("quantmod") if needed get Symbols ('VTI', from get Symbols ('VXUS', from = "2018-12-31", to="2023-12-31") %23 calculate the simple returns VTI = VTI$VTI. Adjusted; VXUS L = length (VTI) = VXUS$VXUS. Adjusted rtn.VTI = as.numeric (VTI [-1])/as.numeric(VTI [-L]) - 1 rtn.VXUS = as.numeric (VXUS [-1])/as.numeric (VXUS [-L]) - 1 (a) What are the maximum and minimum returns for VTI and VXUS, respectively? (b) Could you plot the histograms for VTI and VXUS, respectively? Do they look like normal distributions? [HINT: use hist() and set breaks=100] (c) What are the percentages of observations within two standard deviations from the aver- age for VTI and VXUS, respectively? Do we have a 95% coverage for the regression fit? [HINT: we use 2 to approximate 1.96 for the 95% confidence interval.] (d) Could you plot the cumulative returns for these two ETFs in the same figure with dif- ferent colors. [HINT: check codes on the notes] (e) Please run a simple regression for VXUS on VTI, report the coefficients, plot the scatter plot with the fitted regression line. Please provide a short summary for explaining the regression results. [HINT: check codes on the notes] (f) Finally, please run a simple regression for VTI on VXUS, and report the coefficients. What is the difference between this model and the previous one?