# Modern portfolio theory | Business & Finance homework help

Part B: (22 marks)
Consider a universe of three equities with the following characteristics
i. Security 1: Expected return of μ = 3.00%
ii. Security 2: Expected return of μ = 4.00%
iii. Security 3: Expected return of μ = 5.00%
iv. The inverse of the variance co-variance matrix of security returns V-1 is provided below
0.36 -0.09 0.03
-0.09 0.07 -0.02
0.03 -0.02 0.03
If you were to construct a frontier of efficient portfolios containing these three securities (showing your
work),
1. Determine what the portfolio allocation would be to each security in the cases (8 marks)
i. where portfolio expected return was 4.00% and,
ii. where portfolio expected return was 8.00%
2. For the Global Minimum Variance (GMV) Portfolio determine the following (8 marks),
i. The portfolio allocation of each security,
ii. portfolio standard deviation and
iii. portfolio expected return
3. Using the portfolio with expected return of 8.00% from 1. above and the GMV portfolio
from 2. above, calculate the standard deviation of the efficient portfolio associated with
expected return of 7.00% (6 marks) 