L5 - Optimal Diversification II

Question 1

Langrangian optimisation recap?

Answer 1

1. put in the form max(L) = maximisation conditions + λ(constraint = 0)
2. find FOC
3. solve x and y simultaneously

Question 2

What is the mathematical maximisation problem fund managers are facing?

Answer 2

• Minimise the risk for any given level of return
• subject to some return we are aiming for and that the weights need to sum to 1

Question 3

What is the matrix transformation of the optimisation problem?

Answer 3

• L = 0.5*variance - λ(expected return - desired expected return) - µ(weight matrix - equal 1)
  
  • both terms are the constraints set equal to 0

Question 4

how do you derive the variance in matrix form?

Answer 4

Question 5

Example of mean-variance model used on two assets?

Answer 5

• round to three decimal places

Question 6

How do you derive the minimum variance portfolio?

Answer 6

• minimising the variance without the restriction on the return

Question 7

What is the two-fund separation theory?

Answer 7

• You can combine any two funds in a linear fashion to get any portfolio risk-return that lies on the efficient frontier

Question 8

What is the lagrangian optimisation problem when we consider a risky portfolio and a risk-free asset?

Answer 8

• add to the first constraint (has part of the fund ‘x’ in the risky asset)

Question 9

What is the tangency portfolio for a risk-free and risky asset example?

Answer 9

Question 10

What is an easier way to derive the tangency portfolio?

Answer 10

• all in excess return
  
  • need to know this method and the matrix method as might be asked to do either in the exam

Question 11

how would we then calculate the optimal complete portfolio?

Answer 11

Question 12

Steps for investing without a risk-free asset?

Answer 12

Question 13

Steps for investing with a risk-free asset?

Answer 13

Question 14

Steps for investing on the CAL?

Answer 14