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

Table 2

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.

For question 3, please use excel.