ECO421 Asset Pricing

• Topics

  The course covers key economic principles for sound valuation and investment choice, to better understand strengths and weaknesses of popular investments models. An important aim is to increase student sophistication to help avoid naive or inappropriate use of finance models.

  The course sets out by illustrating how difficulties in estimating expected returns cause a need for models for expected returns (like the CAPM), and difficulties in applying portfolio choice models (like that of Markowitz). The course covers the basic principles of rational choice under uncertainty, which provides the foundation for the mean-variance portfolio choice model of Markowitz. We implement the portfolio choice model in R, and use it to develop the Capital Asset Pricing Model (CAPM). The combination of Markowitz and CAPM enables us to derive and implement the more sophisticated and robust Black-Litterman portfolio choice model, which allows us also to incorporate private views on expected returns.

  The consumption-based asset pricing model provides a link between financial markets and macroeconomic quantities, which is useful to build economic intuition. The consumption-based framework allows us to study the determination of the riskless rate (which the CAPM takes as exogenous), and to derive and better understand multi-factor models (like that of Fama and French). The consumption-based framework moreover allows us to develop better economic intuition for the forces that shape asset risk premia.

  A final module covers the relationship between equilibrium and absence of arbitrage opportunities. We study the absence or presence of arbitrage through properties of "pure securities." All assets are shown to be portfolios of pure securities: stocks, bonds, derivatives etc. Popular models like the CAPM and the Black-Scholes-Merton option pricing formula are special instances of the same basic economic framework.

  To keep the mathematics at a minimal level, results are generally formulated in a discrete-time setting, with an emphasis on one-period models. Topics include, but are not limited to

  1. Introduction and models of choice under uncertainty

  • Estimating expected returns: Why we need asset pricing models
  • The link between finance and microeconomics: Investor preferences
  • Measuring risk aversion: absolute and relative risk aversion
  • Basic results of optimal investment choice

  2. Mean-variance portfolio choice/asset allocation and pricing

  • Elementary linear algebra (with illustrations and exercises in R)
  • Mean-variance portfolio choice: the Markowitz model
  • Constrained portfolio choice: Implementation of short sales constraints, and ESG/sustainability constraints at the individual asset level or portfolio level
  • The CAPM
  • Mean-variance portfolio choice with private beliefs: the Black-Litterman model

  3. Consumption-based asset pricing and multi-factor asset pricing models

  • The link between finance and macroeconomics: Asset prices in a pure exchange economy
  • The riskless rate, risk premia, and aggregate consumption/savings
  • Ross' multi-factor asset pricing model (the APT)
  • Understanding linear multi-factor models, like the Fama-French three factor model

  4. Key properties of securities markets

  • Arrow-Debreu securities markets and pure securities
  • Replicating portfolios and the relationship between pure and complex (real world) securities
  • Spanning: Complete versus incomplete markets
  • No-arbitrage conditions and pricing of securities
  • Optimal consumption/investment choice
  • General equilibrium

  5. The "theory of everything"

  • The Fundamental Theorem of Asset Pricing
  • Stochastic discount factors (SDFs)
  • The relationship between pure security prices, SDFs, and option pricing theory
  • The binomial option pricing model

  There may be changes to the above topics, for instance to accommodate student interests, new developments, or current events.

• Learning outcome

  After completing the course, the student:

  Knowledge

  • knows the fundamental theory of portfolio choice and asset pricing
  • understands key simplifying assumptions behind investment models and their ideal use cases
  • understands the roles of the concepts of "equilibrium" and "no arbitrage" in investments
  • understands the roles of spanning and complete markets assumptions (which all models make)
  • understands the relationship between portfolio choice, partial/general equilibrium, and asset prices

  Skills

  • can implement sophisticated portfolio choice models with and without constraints (e.g. short sales or ESG and sustainability requirements)
  • can interpret and correctly apply asset pricing models across various applications (e.g. asset allocation versus capital budgeting/project analysis)
  • is able to discern the important assumptions, features and empirical predictions of investments models
  • can formulate and conduct quantitative analyses

  General competences

  • can implement finance models in R
  • is able to communicate key insights from asset pricing
  • can extract key insights from asset pricing research
  • is able to discuss recent empirical research and current events in financial markets from an asset pricing viewpoint

• Teaching

  Regular lectures, class room discussions, problem solving exercises, and student presentations.

• Recommended prerequisites

  Students without prior knowledge of R should work through the R tutorial posted on the course home page, before the first lecture.

• Required prerequisites

  To take this course you should already have basic insights corresponding to

  • optimization, similar to those obtained in a basic course in mathematics or ECO401,
  • a general understanding of financial markets, similar to those obtained in FIE400.

• Compulsory Activity

  Students must finish between four and six assignments, in groups of up to three students. The number of assignments depends on class interests, needs, and available time. Students must submit an individual self-assessment report for each assignment.

• Assessment

  Individual four hour home exam.

• Grading Scale

  A-F

• Computer tools

  The course uses R to illustrate key concepts and topics. Some of the assignments are designed to be solved with R, but can be solved in other types of software like Excel, Python, or Matlab. R is however the only formally supported software in the course. Students do not need to know R before attending the course, but should work through a short R tutorial—available on the course home page—before the course commences.

• Literature

  Lecture notes.

  Additional readings may be assigned.