Problem # 1

Following are actual price and dividend data for three companies for each of seven months.

TIME in months	Firm A		Firm B		Firm C
	Price	Dividend	Price	Dividend	Price	Dividend
1	57.75		333		106.75
2	59.88		368		108.25
3	59.38	0.73	368.50	1.35	124	0.40
4	55.50		382.25		122.25
5	56.25		386		135.50
6	59	0.73	397.75	1.35	141.75	0.42
7	60.25		392		165.75

Compute the rate of return for each company for each month.

Compute the average rate of return for each company.

Compute the standard deviation of the rate of return for each company.

Compute the correlation coefficient between all possible pairs of securities.

Compute the average return and standard deviation for the following portfolios:

50% in A ; 50% in B

50% in A ; 50% in C

50% in B ; 50% in C

1/3 in A ; 1/3 in B ; 1/3 in C

1/2 in A ; 1/4 in B ; 1/4 in C

Problem # 2

Assume that the average variance of return for an individual security is 50 and that the average covariance is 10. What is the expected variance of an equally weighted portfolio of 5, 10, 20, 50, 100, 500 & 1000 securities?

Problem # 3

Consider the following 4 assets:

Market Condition	Probability	Returns
		Asset 1	Asset 2	Asset 3
Good	1/4	16	4	20
Average	1/2	12	6	14
Poor	1/4	8	8	8

Asset 4
Rainfall	Probability	Return
Heavy	1/3	16
Average	1/3	12
Light	1/3	8

Assume that there is no relationship between the amount of rainfall and the condition of the stock market

Solve for the expected return and the standard deviation of return for each asset.

Solve for the correlation coefficient and the covariance between each pair of assets.

Solve for the expected return and standard deviation of each of the following portfolios:

	Weight of Each Asset
Portfolio	Asset 1	Asset 2	Asset 3	Asset 4
A	1/2	1/2	0	0
B	1/2	0	1/2	0
C	1/2	0	0	1/2
D	0	1/2	1/2	0
E	0	0	1/2	1/2
F	1/3	1/3	1/3	0
G	0	1/3	1/3	1/3
H	1/3	0	1/3	1/3
I	1/4	1/4	1/4	1/4

Plot the original assets and each of the portfolios in expected return standard deviation space.

Please show all work.