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:
Decisionmaker 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, probabilityweighted 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
 U[W] describes my utility (happiness) over my wealth

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

1.3 CAPM
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What is the empirical translation of the CAPM?
Alpha should equal the risk free rate! 
1.4 FamaMacBeth methodology
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What are the three testable implications based on the CAPM equation?
 The relation between expected
return andrisk islinear Beta is a completemeasure ofrisk ofsecurity i inportfolio m (beta is the only variable that predicts risk, any other measure should not have any predictive power)Higher risk should beassociated with higher expectedreturns
 The relation between expected

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
outof sample testing (expectedreturns ), need toestimate beta on apretesting 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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