Dynamic Asset Allocation

This course requires that the student has prior knowledge of financial markets, financial instruments, and derivatives. In particular knowledge about introductory asset allocation; that is, a thorough understanding of the mean-variance analysis. These are all competences acquired in the course Finansiering, investering og virksomhedsstrategi (9161001) which is based on the textbooks:

• David Hillier, Mark Grinblatt and Sheridan Titman: Financial Markets and Corporate Strategy, European Edition, Irwin/McGraw-Hill, 2012.
• Christian R. Flor and Linda S. Larsen: Indledende porteføljevalgsteori, teaching note, latest edition.

Furthermore, the student should be able to explain and apply Itô calculus. A basic understanding of term structure models is also highly recommended. For example, knowledge about the Vasicek and CIR term structure models is expected. The student should also be familiar with numerical methods, like Monte Carlo simulation. These are all competences acquired in the course Derivatives and Risk Management (9427401) which are based on the textbooks:

• John Hull: Options, futures and other derivatives, Pearson, (newest edition).
• Claus Munk: Fixed income modelling, Oxford, 1st edition, (newest edition).

The student should have an elementary background in mathematics and probability theory. In particular, the student should be able to compute expectations, variances, and covariances of random variables whether their distribution is discrete (e.g. binomial) or continuous (e.g. normal).

Finally, it is highly recommended that the student is familiar with vector and matrix notation and know how to solve a system of linear equations. These are all competences acquired in the courses Matematik (9105701) and Statistik (9116001) which are based on the textbooks:

• Knut Sydsaeter and Peter Hammond, Essential Mathematics for Economic Analysis, Pearson Education, 3rd edition 2008.
• Malcow-Møller, N. og Allan Würtz "Indblik i Statistik", latest edition.

1. Decision-making in multi-period models with uncertainty
2. Dynamic programming and stochastic control with a focus on asset allocation (portfolio choice) problem
3. Contrast normative theories with positive (empirical) investor behavior
4. Optimal consumption and investment decisions of individuals, e.g.
   • review of mean-variance analysis
   • dynamic model with constant investment opportunities
   • dynamic model with stochastic interest rates
   • dynamic model with stochastic market price of risk
   • effects of labor income, housing, etc.
   • non-standard utility or information structures may be considere

Demonstrate knowledge about the course’s focus areas enabling the student to:

• Explain the idea of dynamic programming and the derivation of the Bellman equation in discrete-time models and the Hamilton-Jacobi-Bellman equation in continuous-time models of typical financial optimization problems.
• Describe and explain the one-period mean-variance analysis framework for optimal portfolio choice.
• Describe and explain a general and various concrete diffusion-type models for utility-maximizing dynamic consumption and portfolio strategies.
• Solve the associated Hamilton-Jacobi-Bellman equations for the different models considered, interpret and explain the conclusions; discuss and criticize the assumptions behind the models.
• Compare the solutions to diffusion-type models for utility-maximizing dynamic consumption and portfolio strategies to typical investment advice

Demonstrate skills, such that the student is able to:

• Apply the standard Hamilton-Jacobi-Bellmann equation in continuous-time models of typical financial optimization problems
• Analyze and criticize the one-period mean-variance analysis framework for optimal portfolio choice
• Analyze a general diffusion-type model for utility-maximizing dynamic consumption and portfolio strategies, e.g. set up the associated Hamilton-Jacobi-Bellman equation.
• Analyze and criticize various concrete diffusion-type models for utility-maximizing dynamic consumption and portfolio strategies, solve the associated Hamilton-Jacobi-Bellman equations, interpret and explain the conclusions.
• Be able to implement optimal investment strategies numerically
• Discuss and criticize the assumptions made for the applications and interpretation of the results.
• Reflect upon the conclusions obtained by the analysis in the different applications.
  
  

Demonstrate competences, such that the student is able to:

• Independently apply models and theories related to dynamic asset allocation for individual investors.
• Identify a need for further development of the models and theories related to dynamic asset allocation.
• Independently apply dynamic asset allocation theories and models and use this to develop models, in new, but related, topics 
• Use the above knowledge and skills to participate in team work so that the student obtains competences in collaboration and communication.

Example:

Munk, C.: "Dynamic asset allocation", Lecture notes, Copenhagen Business School, newest edition, or similar material.

Articles and additional lecture notes.