Using the below, answer each of the following questions. Note each element my be weighted differently.

You may upload an Excel file or Google Sheets to help show your work.

The following are monthly percentage price changes for four market indexes:

Month

DJIA

S&P $500$

Russell $2000$

Nikkei

$1$

$0\mathrm{.}03$

$0\mathrm{.}02$

$0\mathrm{.}04$

$0\mathrm{.}04$

$2$

$0\mathrm{.}07$

$0\mathrm{.}06$

$0\mathrm{.}10$

$-0\mathrm{.}02$

$3$

$-0\mathrm{.}02$

$-0\mathrm{.}01$

$-0\mathrm{.}04$

$0\mathrm{.}07$

$4$

$0\mathrm{.}01$

$0\mathrm{.}03$

$0\mathrm{.}03$

$0\mathrm{.}02$

$5$

$0\mathrm{.}05$

$0\mathrm{.}04$

$0\mathrm{.}11$

$0\mathrm{.}02$

$6$

$-0\mathrm{.}06$

$-0\mathrm{.}04$

$-0\mathrm{.}08$

$0\mathrm{.}06$

Compute the following:

A$.$ Average monthly rate of return for each index. $(5$ points$)$

B$.$ Standard deviation for each index. $(5$ points$)$

C$.$ Covariance between the rates of return for the following indexes:

DJIA$-$S&P $500(1$ point$)$

S&P $500-$Russell $2000(1$ point$)$

S&P $500-$Nikkei $(1$ point$)$

Russell $2000-$Nikkei $(1$ point$)$

D$.$ The correlation coefficients for the same four combinations. $(5$ points$)$

E$.$ Using the answers from parts $($A$),($B$),$ and $($D$),$ calculate the expected return and standard deviation of a portfolio consisting of equal parts of $(1)$ the S&P $500$ and the Russell $2000$ and $(2)$ the S&P $500$ and the Nikkei. $(5$ points$)$

Discuss the two portfolios $($meaning: compare, contrast, treat as if you were trying to explain the two portfolios to someone$)(6$ points$)$