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The Flawed Assumptions

This article explores the flawed assumptions in investor agreement and concave utility functions and their implications in pricing risk. It discusses the identification of marginal utility and the failure of utility, expected returns, and volatility agreement. The article also examines the implications of these assumptions in securities' expected returns, mean-variance optimization, optimal asset weights, and portfolio choice.

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The Flawed Assumptions

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  1. The Flawed Assumptions Eric Falkenstein

  2. Implications of the Model Don't Work • Assumptions: investor agreement and concave utility function lead to risk being priced • Implication: Our marginal utility’s covariance with returns is priced as risky • Implication: Something intuitive should be identifiable as our marginal utility • As If! Where else does utility, or agreement on expected returns and volatility, fail?

  3. Securities’ expected returns Mean-variance optimization Securities’ standard deviations Optimal asset weights Securities’ correlations The optimization process Portfolio choice

  4. Mean-Variance Optimization Select {wi} so as to minimize: subject to: (i) E(Rp) > R* (ii) S wi = 1

  5. Result of Optimization Expected Return CAPM, APT, etc. trivial implication Single Optimal Risky Portfolio Rf Standard Deviation Finding Alpha

  6. Agents do not agree • CAPM article originally rejected because the idea that everyone agreed on returns and covariances absurd. Editor changed, paper accepted. • Rubinstein’s aggregation theorem (1974) • Can model market as an individual if they all agree on probabilities and covariances • Can’t model disagreement • Milgrom-Stokey (1982) no trade theorem • Trade if have private information—make gross profits • Grossman-Stiglitz (1980) • Kyle (1985)

  7. Try to Forecast Returns • Fundamental Analysis worthless • Markets efficient: mutual funds do not outperform

  8. Investors Trade Too Much • NYSE turns over 100% per year • Odean and Barber (2000): People turnover 75% of stocks in individual accounts. Highest quintile 250%

  9. Investors have Too Many Funds • Two-fund separation theorem: Investors hold unique optimal risky portfolio • Practice: 1000s of mutual funds and ETFs Less risk averse Expected Return More risk averse ‘the’ market everyone holds Rf Standard Deviation

  10. Not Diversified • Goetzmann and Kumar (2005): >25% have only 1 stock, >50% less than 3, 5-10% have more than 10. • Average portfolio volatility much greater than market for average investor Expected Return Rf Standard Deviation

  11. Home Bias • Should invest in world portfolio • Chan, Covrig, and Ng (2005): Everyone is investing mainly in domestic portfolio • Avoiding easy way to diversify risk • Low covariance with risks from home economy

  12. Basic Idea of Utility • Fundamental to economic reasoning • Marginal Revolution transformed economics c. 1860s • Walras, Jevons, Menger • Pre 1860s ‘classical’ economists: Marx, Smith, Ricardo, Mill • Transformed theory of value

  13. Indifference Curves X Slope = Change in Y/Change in X = MU(Y)/MU(X) U4 U3 U2 U1 X O

  14. Budget Line Y Income = Px Qx + PyQy I/Py Slope = Px/Py X O I/Px

  15. Indifference Curves Y MRS = MUx/MUy= Px/Py a b c U4 U3 d U2 e U1 X O

  16. A change in the price of X: Income and substitution effects Y a b U5 C’ Y1 c Yo U4 c” U3 d U2 e U1 X O Xo X1

  17. Utility Theory and Risk Aversion • Utility not applied between goods, but applied to everything • Von-Neumann-Morgenstern (1944) • EU(x)=prob(x1 )U(x1)+prob(x2 )U(x2 ) • Friedman-Savage (1948) • Risk-averse people prefer less variance

  18. Utility Theory and Risk Aversion

  19. Buy Recommendations exclude low risk firms • Half of all stocks have expected returns below the market • Zero recommendations for firms with expected returns below the market return Buy! Expected Return Who cares? Risk

  20. Utility Extrapolation • Rabin (2000) • Say you reject 50-50 bet to make $11, risking $10 • Then you reject any bet where you lose $100 • Even: • +$100,000,000,000 if heads • -$100 if tails • Comes from global concavity of utility function • W+11th dollar worth less than 10/11 of W-10th dollar • W+11th+21th (W+32nd) dollar worth less than 10/11 of W+11 dollar. So W+32nd dollar worth 10/11*10/115/6 dollar • Etc.

  21. Easterlin’s Paradox (1974) • Within a society, rich people tend to be much happier than poor people. • But, rich societies tend not to be happier than poor societies (or not by much). • As countries get richer, they do not get happier.

  22. Easterlin’s Paradox • Progress and Happiness a Puzzle • Gregg Easterbrook’s The Progress Paradox, • David Myers’s The American Paradox, and • Barry Schwartz’s The Paradox of Choice • Japan: between 1958-1987 per capita income rose 500% • No change in subjective well-being • Knight and Song (2006): Chinese villagers more affected by relative than absolute wealth, compared to their villages • Choose between • World A: $100,000 a year in perpetuity while others earned $90,000 • World B: earn $110,000 while others earned $200,000 • Most prefer World A

  23. Wolfers and Stevenson (2008) • Libertarians love this: • with pure greed, individual self-interest consistent with reciprocal altruism, growth • With pure envy, not • Torture data to confess Japan ‘adjustment’ Still not true for USA

  24. Bad Assumptions • People do not approach the problem of investing as a mean-variance optimization, or factor risk, problem. • Invest based on differing beliefs, • taking lots of idiosyncratic risk when they do, • reaching for absolute return • Necessary and Sufficient Condition for Risk Aversion Wrong • Absurd extrapolations • Incorrect implications for happiness • And, there appear no general priced risk factors

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