Lets return to the data given what is the minimum variance

Question

Questions -

Q1. Consider two stocks, with the random rates of return being r₁ and r₂. The expected rates of return are r^-₁ and r^-₂. The variances of the stocks' return rates are σ₁² and σ₂². The covariance is Cov[r₁, r₂] = σ₁₂. These two stocks are available to form a portfolio. Derive the weights assigned to each stock in order to achieve a portfolio with the minimum variance.

Q2. Let's return to the data given. What is the minimum variance portfolio formed by all the stocks? You can use a software to solve linear equations.

Data for question 2 -

Table 1 and 2 below provide the standard deviation of individual stock returns and the correlation between them for several common stocks.

Table 1

	Microsoft	Dell	Alaska Air	Southwest Airlines	Ford Motor	Heinz	General Mills
Standard Deviation	35%	47%	38%	32%	53%	19%	17%

Table 2

	Microsoft	Dell	Alaska Air	Southwest Airlines	Ford Motor	Heinz	General Mills
Microsoft	1	0.63	0.24	0.25	0.27	0.17	0.1
Dell	0.63	1	0.19	0.24	0.31	0.12	0.09
Alaska Air	0.24	0.19	1	0.36	0.15	0.26	0.15
Southwest Airlines	0.25	0.24	0.36	1	0.31	0.26	0.22
Ford Motor	0.27	0.31	0.15	0.31	1	0.16	0.05
Heinz	0.17	0.12	0.26	0.26	0.16	1	0.5
General Mills	0.1	0.09	0.15	0.22	0.05	0.5	1

Q3. The information concerning the 1-year co-variances and mean values of the rates of return on five securities is shown in Table 1. The mean values are expressed on a percentage basis, whereas the co-variances are expressed in units of (percent)²/100. For example, the first security has an expected rate of return of 15.1% = 0.151 and a variance of return of 0.023.

(a) Find the minimum variance set formed by these five securities. You can use a software to solve linear equations.

(b) In one r^- - σ diagram, plot the minimum variance set and the five securities. (Your graph should includes one curve and five dots.)

Table 1: Co-variances and mean values of the rates of return on five securities.

Security	Covariance V					r-
1	2.30	0.93	0.62	0.74	-0.23	15.1
2	0.93	1.40	0.22	0.56	0.26	12.5
3	0.62	0.22	1.80	0.78	0.27	14.7
4	0.74	0.56	0.78	3.40	-0.56	9.02
5	-0.23	0.26	0.27	-0.56	2.60	17.68

For question 3, please use excel.