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Problem $6-07$

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

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

$10\mathrm{.}020\mathrm{.}030\mathrm{.}030\mathrm{.}03$

$20\mathrm{.}070\mathrm{.}060\mathrm{.}10-0\mathrm{.}01$

$3-0\mathrm{.}01-0\mathrm{.}02-0\mathrm{.}050\mathrm{.}06$

$40\mathrm{.}010\mathrm{.}040\mathrm{.}040\mathrm{.}02$

$50\mathrm{.}040\mathrm{.}050\mathrm{.}110\mathrm{.}02$

$6-0\mathrm{.}05-0\mathrm{.}02-0\mathrm{.}080\mathrm{.}04$

Compute the following.

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

DJIA:

$0\mathrm{.}01333$

S&P $500$:

$0\mathrm{.}02333$

Russell $2000$:

$0\mathrm{.}02500$

Nikkei:

$0\mathrm{.}02667$

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

$-$Select$-$

if they are combined.