Question

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

Month	DJIA		S&P 500		Russell 2000		Nikkei
1	0.02		0.03		0.04		0.04
2	0.08		0.07		0.10		-0.01
3	-0.03		-0.01		-0.04		0.07
4	0.01		0.02		0.02		0.01
5	0.06		0.05		0.11		0.01
6	-0.07		-0.06		-0.09		0.08

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-(negative positive) Item 21 correlation, meaningful reduction in risk -Select-is not observe dis observed Item 22 if they are combined.

   Since S&P 500 and Nikkei have a strong -Select-(negative positive )Item 23 correlation, meaningful reduction in risk -Select-is not observe dis observedItem 24 if they are combined.

Answer 1

		Month	DJIA	S&P 500	Russell 2000	Nikkei
		1	0.02	0.03	0.04	0.04
		2	0.08	0.07	0.1	-0.01
		3	-0.03	-0.01	-0.04	0.07
		4	0.01	0.02	0.02	0.01
		5	0.06	0.05	0.11	0.01
		6	-0.07	-0.06	-0.09	0.08
		SUM	0.07	0.1	0.14	0.2
		AVERAGE =SUM/6	0.0116667	0.016666667	0.023333333	0.033333
		Average Monthly Return DJIA	0.0116667	1.17%
		Average Monthly Return S&P 500	0.0166667	1.67%
		Average Monthly Return Russel	0.0233333	2.33%
		Average Monthly Return Nikkie	0.0333333	3.33%
	b	Standard Deviation of DJIA:	R	D1=R-0.011667	E=D1^2
		Month	Return	Deviation from Average	Deviation Squared
		1	0.02	0.008333	6.94389E-05
		2	0.08	0.068333	0.004669399
		3	-0.03	-0.041667	0.001736139
		4	0.01	-0.001667	2.77889E-06
		5	0.06	0.048333	0.002336079
		6	-0.07	-0.081667	0.006669499
				SUM	0.015483333
		Variance =Sum/(6-1)	0.0030967
		Standard Deviation=Square Root Variance	0.0556477	5.56%
		Standard Deviation of S&P 500:	R	D2=R-0.016667	E=D2^2
		Month	Return	Deviation from Average	Deviation Squared
		1	0.03	0.013333	0.000177769
		2	0.07	0.053333	0.002844409
		3	-0.01	-0.026667	0.000711129
		4	0.02	0.003333	1.11089E-05
		5	0.05	0.033333	0.001111089
		6	-0.06	-0.076667	0.005877829
				SUM	0.010733333
		Variance =Sum/(6-1)	0.0021467
		Standard Deviation=Square Root Variance	0.0463321	4.63%
		Standard Deviation of RUSSEL 2000:	R	D3=R-0.023333	E=D3^2
		Month	Return	Deviation from Average	Deviation Squared
		1	0.04	0.016667	0.000277789
		2	0.1	0.076667	0.005877829
		3	-0.04	-0.063333	0.004011069
		4	0.02	-0.003333	1.11089E-05
		5	0.11	0.086667	0.007511169
		6	-0.09	-0.113333	0.012844369
				SUM	0.030533333
		Variance =Sum/(6-1)	0.0061067
		Standard Deviation=Square Root Variance	0.0781452	7.81%
		Standard Deviation of Nikkie:	R	D4=R-0.033333	E=D4^2
		Month	Return	Deviation from Average	Deviation Squared
		1	0.04	0.006667	4.44489E-05
		2	-0.01	-0.043333	0.001877749
		3	0.07	0.036667	0.001344469
		4	0.01	-0.023333	0.000544429
		5	0.01	-0.023333	0.000544429
		6	0.08	0.046667	0.002177809
				SUM	0.006533333
		Variance =Sum/(6-1)	0.0013067
		Standard Deviation=Square Root Variance	0.0361478	3.61%