Question

Mean	8.00%	11.00%
Variance	1.71%	2.67%
Standard deviation	13.08%	16.34%
Covariance		0.20%
Correlation	0.09360
Proportion of stocok A in portfolio	Portfolio Variance	Portfolio standard deviation	Portfolio mean
0%	2.67%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%

1) Given the data, figure out the correlation between two stocks.

2) Fill out the table for the mean, variance, and standard deviation for the portfolio

3) Draw a plot for the relationship between risk and return, as shown below.

Answer 1

a) correlation is calculated as follows:

b) Portfolio Expected return is calculated by solving the following equation:      

r is the mean of the stock

Portfolio standard deviation is calculated by solving the following equation:

Variance is the square of standard deviation

Now for different weights the data table can be created by substituting the values in the above equations, for example if weight of A is 10% and that of B is 90% then the above equations will give the following values:

Variance = 14.89 x 14.89 =   2.22%

Now we can create the data table

Weight of A	Variance	Standard deviation	Mean
0.00%	2.67%	16.34%	11.00%
10.00%	2.22%	14.89%	10.70%
20.00%	1.84%	13.57%	10.40%
30.00%	1.55%	12.43%	10.10%
40.00%	1.33%	11.54%	9.80%
50.00%	1.20%	10.93%	9.50%
60.00%	1.14%	10.67%	9.20%
70.00%	1.16%	10.78%	8.90%
80.00%	1.27%	11.25%	8.60%
90.00%	1.45%	12.04%	8.30%
100.00%	1.71%	13.08%	8.00%

c) Below is the plot of portfolio mean and standard deviation