Pull the daily stock returns of GM and TSLA from $2013$ to today using the following chuck on code.

library$($tidyquant$)$

library$($dplyr$)$

library$($tidyr$)$ # for spread function to reshape data.frame from long table to wide table

library$($lubridate$)$

dattq$\_$get$($c$(\text{'}$GM$\text{'},$'TSLA'$),$ get $=$ "stock.prices", complete$\_$cases $=$ TRUE$)$

# data of different tickers are stacked together

dat $\%>\%$ head$()$

datdat $\%>\%$

select$($symbol$,$date,adjusted$)\%>\%$

spread$($symbol$,$adjusted$)$

dat $\%>\%$ head$()$

# data operation: get monthly returns

datdat $\%>\%$

mutate$($

GM$=$GM$/$lag$($GM$)-1,$ # returns are raw monthly percentage returns not excess return

TSLA$=$TSLA$/$lag$($TSLA$)-1$

$)\%>\%$

filter$(!$is$.$na$($GM$),!$is$.$na$($TSLA$))$ # make sure there is no missing values

View$($dat$)$

Use the two return series to find the global minimum variance portfolio through allocating your fund between

the two assets. Answer the following questions.

$1.$ What is the weight allocation for the first asset and the second asset?

$2$

$2.$ What is the average portfolio return historically? $($Hint: check with mean function$).$

$3.$ What is the standard deviation of the portfolio return? $($Hint: check with sd function$).$

$4.$ What are the standard deviation of the first asset and the standard deviation of the second asset?

$5.$ Is the portfolio standard deviation lower than both of the individual assets? What is the benefit of

holding multiple assets in a portfolio?

$6.$ If the two assets span the entire investment opportunity set, i$.$e$.,$ the market only has the two assets

and the weighted sum of the two assets with all possible weight allocations, is this global minimum

variance portfolio on the efficient market frontier?