The following questions rely on the numbers for the share prices given below.

The share prices of American Airlines Group Inc. $($AAL$),$ Delta Air Lines Inc. $($DAL$),$ and Southwest Airlines Co$.($SAL$)$ for March $28,2022$ are listed here under $$Prev$.$ Price$$ and for April $28,2022$ under $$Price$.$ The shares outstanding on March $28,2022$ for each company are listed under $$Shares$.$ Prices observations listed are at the close and any adjustments also are assumed to occur at the close of the relevant day.

An Airlines index is established starting on March $28,2021.$ The information from the above companies is used to create an $$AIR$3$ index.

Answer the following questions for each of three possible indexes: AIR$3$VW$,$ AIR$3$PW$,$ and AIR$3$EW $($value$-$weighted, price$-$weighted, and equal$-$weighted$).$ Choose a divisor to set the initial index value equal to $100$ in each of the three index cases.

$($a$)$ Calculate the index values for each of the three cases $($value$-$weighted, price$-$weighted, and equal$-$weighted$)$ at the close on March $28.$ Obtain the divisor on March $28,2021$ for each of the three cases.

$($b$)$ What are the monthly returns based on each of the possible indexes?

You establish an ETF with $$20,000$ initial investment at the close on March $28$ that promises to track exactly the AIR$3$ index

$($c$)$ What is the composition of your ETF$$s portfolio in terms of the number of shares held of each asset for each of the three possible AIR$3$ index choices?

$($d$)$ What is the final US dollar market value of the ETF $($at the close on April $28)$ for each of the three index types?