Lecture 4 - Markowitz Portfolio Optimisation Model : Part I

Question 1

What is the Markowitz Model also called?

Answer 1

Mean variance analysis.

Question 2

What are the three steps involved in the Markowitz Model?

Answer 2

1. Identify the risk-return combinations available for the set of risky assets. Also, called portfolio opportunity set.
2. Identify the optimal portfolio of risky assets that result in the steepest CAL. Optimal portfolio of risky assets (P) also has the highest Sharpe ratio.
3. Choose appropriate complete portfolio (C) by mixing the risk free asset with the optimal risky portfolio. The choice of (C) depends on A (the index of risk aversion).

Question 3

In detail, explain step 1 of the Markowitz Model (for many risky assets)?

Answer 3

• Opportunity set of many risky assets.
• Determine the risk-return opportunities available.
• Minimum-variance frontier of risky assets.
• All portfolios that lie on the minimum-variance frontier from the global minimum-variance portfolio and upward provide the best risk-return combinations. Because for a given level of risk a rational investor will always choose points on the efficient frontier as it has the highest expected return.
• Efficient frontier of risky assets is the portion of the frontier that lies above the global minimum-variance portfolio.

Question 4

In detail, explain step 2 of the Markowitz Model (for many risky assets)?

Answer 4

Search for the CAL with the highest Shape ratio (that is, the steepest slope).

Question 5

In detail, explain step 3 of the Markowitz Model (for many risky assets)?

Answer 5

• Choose appropriate complete portfolio (C) using formula to find y*.
• Capital allocation.
• Investors’ degree of risk aversion.
• Indifference curve that is tangent to the CAL(P).
• Tangency point.

Question 6

Individual investors choose the appropriate mix between the optimal risky portfolio P and T-bills (F). Everyone invests in…

Separation property - two independent tasks
Determination of the optimal risky portfolio is purely technical
Allocation of the complete portfolio to risk-free versus the risky portfolio depends on personal preference

Answer 6

P, regardless of their degree of risk aversion.

Question 7

More (less) risk averse investors…

Answer 7

Put less (more) in P

Question 8

What is the separation property/principle?

Answer 8

Portfolio choice can be separated into two independent tasks.
First is determination of the optimal risky portfolio. This is purely technical. All investors in the market would invest in the same identical risky portfolio P.
Second is allocation of the complete portfolio to risk-free versus the risky portfolio depends on personal preference.