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

Month DJIA S&P $500$ Russell $2000$ Nikkei

$10\mathrm{.}040\mathrm{.}010\mathrm{.}030\mathrm{.}03$

$20\mathrm{.}050\mathrm{.}040\mathrm{.}09-0\mathrm{.}01$

$3-0\mathrm{.}02-0\mathrm{.}02-0\mathrm{.}030\mathrm{.}07$

$40\mathrm{.}010\mathrm{.}030\mathrm{.}030\mathrm{.}02$

$50\mathrm{.}040\mathrm{.}040\mathrm{.}110\mathrm{.}02$

$6-0\mathrm{.}07-0\mathrm{.}06-0\mathrm{.}100\mathrm{.}06$

Compute the following.

Average monthly rate of return for each index. Round your answers to five decimal places.

DJIA:

S&P $500$:

Russell $2000$:

Nikkei:

Standard deviation for each index. Do not round intermediate calculations. Round your answers to four decimal places.

DJIA:

S&P $500$:

Russell $2000$:

Nikkei:

Covariance between the rates of return for the following indexes. Use a minus sign to enter negative values, if any. Do not round intermediate calculations. Round your answers to six decimal places.

Covariance $($DJIA$$S&P $500)$:

Covariance $($S&P $500$Russell $2000)$:

Covariance $($S&P $500$Nikkei$)$:

Covariance $($Russell $2000$Nikkei$)$:

The correlation coefficients for the same four combinations. Use a minus sign to enter negative values, if any. Do not round intermediate calculations. Round your answers to four decimal places.

Correlation $($DJIA$$S&P $500)$:

Correlation $($S&P $500$Russell $2000)$:

Correlation $($S&P $500$Nikkei$)$:

Correlation $($Russell $2000$Nikkei$)$:

Using the unrounded 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 and the Russell $2000$ and $(2)$ the S&P and the Nikkei. Do not round intermediate calculations. Round your answers to five decimal places.

Expected return $($S&P $500$ and Russell $2000)$:

Standard deviation $($S&P $500$ and Russell $2000)$:

Expected return $($S&P $500$ and Nikkei$)$:

Standard deviation $($S&P $500$ and Nikkei$)$:

Since S&P $500$ and Russell $2000$ have a strong

$-$Select$-$

correlation, meaningful reduction in risk

$-$Select$-$

if they are combined.

Since S&P $500$ and Nikkei have a strong

$-$Select$-$

correlation, meaningful reduction in risk