Number Ticker

$1$ XLB

$2$ XLE

$3$ XLF

$4$ XLI

$5$ XLK

$6$ XLP

$7$ XTL

$8$ XLV

$9$ XLY

$10$ VPU

$11$ VNQ

Obtain the indexes at the monthly frequency, starting on December $31,2009$ and ending on December $312019$

$4.$ Compute the arithmetic mean monthly return for the $11$ sector ETFs. What is the meaning of the arithmetic mean?

$5.$ Compute the geometric mean monthly return for the nine sector ETFs. What is the meaning of the geometric mean, and how does it differ from the means in the descriptive statistics table?

$6.$ Focus on the values of the total return index over the $12$ months of $2016.$ What is the average monthly return for that year? What is the annualized return? What is the APR $($Annual Percentage Rate$)?$ What is the EAR $($effective annual rate$).$ Suppose you were only given the value of the total return index on the XLF ETF in December $2015.$ Suppose that this index value is your initial wealth. Using one of the above rates, would you be able to estimate the value of your wealth at the end of December $2016?$ Which rate would you use $($APR$,$ EAR, monthly rate, etc$)?$