Summary: Asset Pricing

Read the summary and the most important questions on Asset Pricing

• 1 Week 1: The Basics

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• 1.1 Portfolio Theory

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• Modern Portfolio Theory (MPT)

  - Given expected returns, risks, and correlations:
  

  • MPT maximizes expected return given a certain level of risk
  • OR
  • MPT minimizes risk given a certain level of expected return 

  
  - Focus on the optimal combination of assets
  

  • Diversification
  • Irrespective of the investor's utility function

• How to form expected returns out of historical returns?

  Assume that historical average risk and returns are representative for the future.

• 1.2 Utility Functions

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• Von Neuman Morgenstern Expected Utility:

  Decision-maker faced with risky outcomes of different choices will behave as if he is maximizing the expected value of some function defined over the potential outcomes --> so, probability-weighted average of utility over the possible outcomes

• Explain the formula: U[W] = aW - b/2V[W] = aW - b/2W^2

  • U[W] describes my utility (happiness) over my wealth
    
  • aW (with a > 0) describes that if I get more wealth, my happiness goes up.
  • -b/2V[W] means that higher risk makes me less happy. 
  • b is the risk aversion factor. The higher b, the heavier the risk factor is taken into account
  • First derivative: a - bW > 0, more wealth makes me more happy
  • Second derivative: -b < 0: the extra wealth makes me less additionally happy

• What can we say about the utility function?

  • If you invest in riskier assets (i.e., the w+ and w- are further apart, there is a bigger discount in utility)
  • The difference in the utility function and actgual utility is the risk premium

• What can we conclude about utility wrt the demand for the market portfolio?

  • Increases with expected return
    
  • Decreases with risk-free rate
  • Decreases with risk
  • Decreases with risk aversion
  • Decreases with wealth (?) -> no, other way around

• 1.3 CAPM

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• What is the empirical translation of the CAPM?

  Alpha should equal the risk free rate!

• 1.4 Fama-MacBeth methodology

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• What are the three testable implications based on the CAPM equation?

  1. The relation between expected return and risk is linear
     
  2. Beta is a complete measure of risk of security i in portfolio m (beta is the only variable that predicts risk, any other measure should not have any predictive power)
  3. Higher risk should be associated with higher expected returns

• What are the assumptions in the CAPM model?

  • Markets are efficient, so prices full reflect available information
  • Investors are risk averse

• Why is it difficult to estimate true beta?

  • For out-of-sample testing (expected returns), need to estimate beta on a pre-testing period.
  • Assume:
  • Beta stays constant for next period
  • Rational expectations: E(r) = r
  • Trade off between stability and length of sample period -> remains arbitrary choice (to lengthy mihgt not be relevant anymore)
  • Error in variables problem: estimated gamma is biased downwards