Question

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

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

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 or positive correlation, meaningful reduction in risk -Select-is not observed is observed if they are combined.

   Since S&P 500 and Nikkei have a strong -Select-negative or positive correlation, meaningful reduction in risk -Select-is not observed or is observed if they are combined.

Answer 1

a Aug return for DJIA (2) = 0.04+ 0.07+(-0.02 +0.02 +0.05 -0.07 = 0.01500 Ava return 0.014 0.06-0.02+0.02 +0.05+1-oow) 6 - 0.01333 Aug return for Russell (rp) = 0.04+0.1+(-0.03) +0:02+0.11 -0.09 - 00500 Aug return for Nikkei low=0.04-0.03 +0.08+0.01 +0.0110-05 = 0.026 67 b. Std deviation = {(x; - u) ² 3 Where x = individual monthly returns - mean returns n= no. of months.

Using the above formula. Std der for DJIA ( ) = 0.0517 Stader for S&P (5)= 0.0388 Std. der for Russell (R)=0.0766 Sta. der for Nikkei (ON) = 0.0333 11 (C) Corariance = E (2;-2 ) Cy-y) 12 - index where nga monthly neown of 1st index I U= mean of monthly neturn for 4. = monthly preturn of and index y = mean monthly return of and index n= no. of months. Using the above tormula: coreDJIA, S&P) = 0.001900 cor (S&P, Russell) = 0.00 2900 cor (S&P, Nikkei) = -0.001287 Cor (Russell, Nikhei) = -0.002200 5

(d) correlation & Cor(x,y) Tr. Ty where a represents one index sa representa standard deviation of a Similarly y represents the seconde index Dy represents standard deviablon of y. using above: corr (DJIA, S&P 500) = 0.001900 - 0.9473 (0.05178 0.0388) corr (EPSOO, Russell) = 0.002900 -0.9751 10.0328x 0.0766) corr (S&P500, Nikkei) = -0.00 1287 (0:0388%0.0383) -0.8655 corr (Russell, Nikkei) & -0.002200 (0.0766x0.0383) - - 0.7498