Topic 3

Question 1

Markowitz’ mean variance optimization disadvantages

Answer 1

• Does not work in practice
• Expected returns are usually historical and are not very appropriate
• Optimal weights returned by the optimizer tend to appear extreme
• Optimal weights are extremely sensitive to small changes in the expected returns. If we change expected return for one asset, all the assets change weights significantly.
• “Balance” in weights is ignored.
• Difficult to embed views, and uncertainty surrounding those views.
• No tool to set confidence in changes of expected returns.

Question 2

Black-litterman optimization advantages

Answer 2

• Works in practice
• Derive expected returns from an equilibrium model, such as the international version of the CAPM. Equilibrium will then be the world portfolio
• If we apply our view on expected return, it will change the weight almost only for our targeted asset and cash, rather than everything.
• “Balance” in weights is kept.
• Managers can deviate from the equilibrium outcome by specifying views different than the equilibrium. Views are ‘mixed’ with the equilibrium in the optimization. We should state views by taking in consideration the historical correlations.
• How much views are taken into account depends on the views’ confidence.

Question 3

Methods to compute returns

Answer 3

Average returns lead to very unbalanced portfolio
CAPM better and closer to market weights
Market weights by definition

Question 4

Define implied portfolio with market weights

Answer 4

1. Implied weights: invest in each country according to its market weights
2. Compute volatilities
3. Compute correlation matrix
4. Compute VCV
5. Compute returns by reverse engineering maximisation formula
6. Set risk free rate
7. Compute global gamma
8. Compute gamma for client
9. Compute optimal weights

Question 5

Types of views

Answer 5

• Relative views: Germany will outperform France with 1 percent.
  o In equilibrium, the difference is only 0.04% > Germany more attractive than in equilibrium.
• Absolute views: The excess return on Italy will be 6 percent.
  o In equilibrium, it is 9.78% > Italy relatively less attractive than in equilibrium.

Question 6

Risk aversion

Answer 6

Client 1: gamma = 1, low risk aversion. invest more in risky assets and uses borrowing
Client 2: gamma = 3, high risk aversion, just invest less in risky assets and more in risk-free

Choose gamma as such that the risk premium on developed equities is equal to a specific value (e.g. 4.5%)

Question 7

VCV change as market variance changes.

How to model time-variation in market volatility?

Answer 7

Moving window volatility
Standard GARCH model
Asymetric GARCH model