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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
1	0.03		0.01		0.04		0.04
2	0.09		0.08		0.13		-0.02
3	-0.02		-0.01		-0.05		0.06
4	0.01		0.02		0.02		0.01
5	0.04		0.04		0.15		0.01
6	-0.06		-0.03		-0.08		0.07

Compute the following.

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

   DJIA:

   S&P 500:

   Russell 2000:

   Nikkei:

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

   DJIA:

   S&P 500:

   Russell 2000:

   Nikkei:

3. 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):

4. 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):

5. 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-negativepositiveItem 21 correlation, meaningful reduction in risk -Select-is not observedis observedItem 22 if they are combined.

   Since S&P 500 and Nikkei have a strong -Select-negativepositiveItem 23 correlation, meaningful reduction in risk -Select-is not observedis observedItem 24 if they are combined.