Markowitz and Risk Penalty Models

Question 1

What are the assumptions of the Markowitz Model?

Answer 1

1. The investor considers alternatives
2. Investors maximize one period utility
3. Variability of returns is used to estimate risk
4. Investor’s base decisions only on expected returns and risk
5. Investors desire more returns and less risk

Question 2

What did the Markowitz Theory introduce that most people were blind to before?

Answer 2

Comovement

Question 3

Portfolio combinations below the Markowitz frontier are ________ by any combination on the frontier.

Answer 3

dominated

Question 4

Essay Question: Explain the Markowitz Efficient Frontier

Answer 4

The efficient frontier is a mean-variance portfolio optimization model that displays the set of optimal portfolios that offer the highest expected return for a defined level of risk or the lowest risk for a given level of expected return.

In graph form, the frontier looks like this:

Portfolios that lie below the efficient frontier are sub-optimal because they do not provide enough return for the level of risk.

The Markowitz model also shows how optimizing co-movement can reduce risk. It also shows how risk can be eliminated if:
pxy = -1
Wx = σy / (σx + σy)
Wy = 1 - Wx

Question 5

What is the risk penalty model?

Answer 5

The risk penalty model is a mean-variance model describing how investors penalize return based on risk of an investment. The greater the “U” utility the better off an investor will be.

Question 6

What are the 8 assumptions of the CAPM?

Answer 6

1) Investors are Markowitz Efficient Investors

2) You may lend or borrow any amount at the risk free rate.

3) Homogeneous expectations.

4) 1 identical holding period.

5) Fractional Shares

6) No transaction costs or taxes.

7) No inflation or the change in inflation is fully anticipated

8) Capital markets are in equilibrium (all assets are properly priced).

Question 7

What are the 3 basic principles of portfolio theory?

Answer 7

1) Investors avoid risk and must be compensated for it
2) We want to summarize and quantify an investor’s risk preference
3) We cannot evaluate the risk of an asset separate from which the portfolio of which it is a part of

Question 8

What is the risk penalty model?

Answer 8

The risk penalty model is a mean-variance model describing how investors penalize return based on risk of an investment. The greater the “U” utility the better off an investor will be.

Question 9

What is the “A” risk aversion index?

Answer 9

A way to quantify risk that an investor desires.
- Positive A: Risk averse
- 0: Neutral risk
- Negative A: Risk lover