Summary: Asset Pricing

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  • 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

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