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4. Seduced by Symmetry, Smarter by Half

verfasst von : James Ming Chen

Erschienen in: Postmodern Portfolio Theory

Verlag: Palgrave Macmillan US

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Abstract

The capital asset pricing model (CAPM) remains the dominant paradigm in financial risk management—at least among practitioners, if not among scholars.¹ Courts and regulators likewise depend on the CAPM, and in so doing confer legal significance on this model.² Once upon a time, long long ago, “the hegemony of the CAPM” could be attributed “mostly to its apparent ease of applicability and, to a lesser extent, its empirical justifications.”³ The latter excuse, at least, has withered away. Despite evidence that beta is not positively related to returns on stock,⁴ to say nothing of beta’s failure to account for macroeconomic⁵ and idiosyncratic⁶ factors affecting security prices and returns, much of contemporary mathematical finance still hinges on the CAPM. Even Eugene Fama, beta’s leading nemesis, has conceded that “market professionals (and academics) still think about risk in terms of market β.”⁷

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See Haim Levy, The Capital Asset Pricing Model in the 21st Century: Analytical, Empirical, and Behavioral Perspectives 4–5 (2012) (describing the CAPM and its constituent concepts, “particularly beta,” as “probably the most widely employed measures used by academic researchers” and “even more intensively used by investment firms and practitioners”).

See, e.g., In re American Classic Voyages Co., 367 B.R. 500, 513 (D. Del. Bankr. 2007) (“While there are other models to determine equity, CAPM is probably the most widely used” (quoting Peter V. Pantaleo & Barry W. Ridings, Reorganization Value, 51 Bus. Lawyer 419–442, 433 n.52 (1996)); Energy Conservation Standards & Test Procedures for Commercial Heating, Air-Conditioning, and Water-Heating Equipment, 80 Fed. Reg. 42,614, 42,627, 42,637 (July 17, 2015); Petition of the Western Coal Traffic League to Institute a Rulemaking Proceeding to Abolish the Use of the Multi-Stage Discounted Cash Flow Model in Determining the Rairoald Industry’s Cost of Equity Capital, 80 Fed. Reg. 27,281, 27,282 (May 13, 2015).

Philip H. Dybvig & Jonathan E. Ingersoll, Jr., Mean-Variance Theory in Complete Markets, 55 J. Bus. 233–251, 233 (1982).

See Eugene F. Fama & Kenneth R. French, The Cross-Section of Expected Stock Returns, 47 J. Fin. 427–465 (1992); see also Marc R. Reinganum, A New Empirical Perspective on the CAPM, 16 Fin. & Quant. Analysis 439–462 (1981); Seha M. Tinic & Richard R. West, Risk and Return: January vs. the Rest of the Year, 13 J. Fin. Econ. 561–574 (1983).

See Nai-Fu Chen, Richard Roll & Stephen A. Ross, Economic Forces and the Stock Market, 59 J. Bus. 383–403 (1986).

See Josef Lakonishok & Alan C. Shapiro, Stock Returns, Beta, Variance, and Size: An Empirical Analysis, 40:4 Fin. Analysts J. 36–41 (July/Aug. 1986).

Eugene F. Fama, Efficient Capital Markets: II, 46 J. Fin. 1575–1617, 1593 (1991); accord Glenn N. Pettengill, Sridhar Sundaram & Ike Mathur, The Conditional Relation Between Beta and Returns, 30 J. Fin. & Quant. Analysis 101–116, 102 (1995).

Tim Koller, Marc Goedhart & David Wessels, Valuaiton: Measuring and Managing the Value of Companies 261 (5th ed. 2010).

See Javier Estrada, Mean-Semivariance Optimization: A Heuristic Approach, 18 J. Applied Fin. 57–72, 58 (2008).

Id.

AEP Texas North Co. v. Surface Transp. Bd., 609 F.3d 432, 443 (D.C. Cir. 2010); see also id. at 441 (declining to resolve the substantive merits of the CAPM relative to single- and double-stage discounted cash flow and “a model called ‘3-Factor Fama-French’”); cf. City of Los Angeles v. United States Dep’t of Transp., 165 F.3d 972, 977 (D.C. Cir. 1999) (“we do not sit as a panel of referees on a professional economics journal”).

Ravi Jagannathan & Zhenyu Wang, The Conditional CAPM and the Cross-Section of Expected Returns, 51 J. Fin. 3–53, 4 (1996) (footnote omitted).

See Haim Levy, The CAPM Is Alive and Well: A Review and Synthesis, 16 Eur. Fin. Mgmt. 43–71 (2009); cf. Levy, CAPM in the 21st Century, supra note 1, at 22 (describing the CAPM and related models of mean-variance optimization as “still ‘alive and kicking’”).

See, e.g., John Y. Campbell, Andrew W. Lo & A. Craig MacKinlay, The Econometrics of Financial Markets 17, 81, 172, 498 (1997); Felipe M. Aparicio & Javier Estrada, Empirical Distributions of Stock Returns: European Securities Markets, 1990–95, 7 Eur. J. Fin. 1–21 (2001); Geert Bekaert, Claude Erb, Campbell R. Harvey & Tadas Viskanta, Distributional Characteristics of Emerging Market Returns and Asset Allocation, 24:2 J. Portfolio Mgmt. 102–116 (Winter 1998); Pornchai Chunhachinda, Krishnan Dandepani, Shahid Hamid & Arun J. Prakash, Portfolio Selection and Skewness: Evidence from International Stock Markets, 21 J. Banking & Fin. 143–167 (1997); Amado Peiró, Skewness in Financial Returns, 23 J. Banking & Fin. 847–862 (1999).

See, e.g., J. Brian Gray & Dan W. French, Empirical Comparisons of Distributional Models for Stock Index Returns, 17 J. Bus. Fin. & Accounting 451–459 (1990); Stanley J. Kon, Models of Stock Returns—A Comparison, 39 J. Fin. 147–165 (1984); Harry M. Markowitz & Nilufer Usmen, The Likelihood of Various Stock Market Return Distributions, Part 1: Principles of Inference, 13 J. Risk & Uncertainty 207–219 (1996); Harry M. Markowitz & Nilufer Usmen, The Likelihood of Various Stock Market Return Distributions, Part 2: Empirical Results, 13 J. Risk & Uncertainty 221–247 (1996); Terence C. Mills, Modelling Skewness and Kurtosis in the London Stock Exchange FT-SE Index Return Distributions, 44 Statistician 323 – 332 (1995). See generally Terence C. Mills, The Econometric Modelling of Financial Time Series (2d ed. 1999).

See, e.g., Ralph O. Swalm, Utility Theory—Insights into Risk Taking, 44 Harv. Bus. Rev. 123–136 (1966).

See, e.g., Daniel Kahneman & Amos Tversky, Prospect Theory: An Analysis of Decision under Risk, 47 Econometrica 263–292 (1979); Paul Slovic, Psychological Study of Human Judgment: Implications for Investment Decision Making, 27 J. Fin. 779–799 (1972).

See Miles S. Kimball, Precautionary Saving in the Small and in the Large, 58 Econometrica 53–73 (1990); cf. Jørgen Haug, Thorsten Hens & Peter Woehrmann, Risk Aversion in the Large and in the Small, 118 Econ. Letters 310–313 (2013).

See generally Daniel Kahneman, Jack L. Knetsch & Richard H. Thaler, The Endowment Effect, Loss Aversion, and Status Quo Bias, 5 J. Econ. Persp. 193–206 (1991).

United States v. Butler, 297 U.S. 1, 82 (1936).

Paul A. Samuelson, Risk and Uncertainty: A Fallacy of Large Numbers, 98 Scientia 1–6, 2 (1963), reprinted in 1 Collected Scientific Papers of Paul A. Samuelson 153–158 (Joseph E. Stiglitz ed., 1966). For examples of the vast literature responding to Samuelson, see Phillipe J.S. de Brouwer & Freddy van den Spiegel, The Fallacy of Large Numbers Revisited: The Construction of a Utility Function That Leads to the Acceptance of Two Games While One Is Rejected, 1 J. Asset Mgmt. 257–266 (2001); Stephen A. Ross, Adding Risks: Samuelson’s Fallacy of Large Numbers Revisited, 34 J. Fin. & Quant. Analysis 323–339 (1999).

Lewis Grizzard, Gettin’ It On: A Down-Home Treasury 72 (1990); accord Joe Garagiola, It’s Anyone’s Ballgame 109 (1988). Lewis Grizzard (1946–1994) was a humor columnist for the Atlanta Journal-Constitution.

See, e.g., Rob Bauer, Roul Haerden & Roderick Molenaar, Asset allocation in Stable and Unstable Times, 13:3 J. Investing 72–80 (Fall 2004); Malcolm P. Baker & Jeffrey Wurgler, Comovement and Predictable Relations Between Bonds and the Cross-Section of Stocks, 2 Rev. Asset Pricing Stud. 57–87 (2012).

See, e.g., John Drzik, Richard J. Herring & Francis X. Diebold, The New Role of Risk Management: Rebuilding the Model, Knowledge@Wharton, http://knowledge.wharton.upenn.edu/article.cfm?articleid=2268 (June 24, 2009).

Cf. Flannery O’Connor, Everything That Rises Must Converge (1965).

H. Levy & H.M. Markowitz, Approximating Expected Utility by a Function of Mean and Variance, 69 Am. Econ. Rev. 308–317, 314 (1979).

See John Y. Campbell & John Ammer, What Moves the Stock and Bond Markets? A Variance Decomposition for Long-Term Asset Returns, 48 J. Fin. 3–37 (1993); cf. Robert Dubois, Asset Price Trend Theory: Reframing Portfolio Theory from the Ground Up, 16:3 J. Wealth Mgmt. 11–30, 12–13 (Winter 2013) (distinguishing between “risk moderation” through the reduction of “both positive and negative variance” and “risk containment” through “limit[s] [on] negative portfolio variance,” such as “loss-contingent exits”).

See François Longin & Bruno Solnik, Extreme Correlation of International Equity Markets, 56 J. Fin. 649–676, 650–651, 669–670 (2001).

See Martin L. Leibowitz, Anthony Bova & P. Brett Hammond, The Endowment Model of Investing: Return, Risk, and Diversification 235, 265 (2010).

See generally, e.g., Yakov Amihud & Haim Mendelson, The Effects of Beta, Bid-Ask Spread, Residual Risk, and Size on Stock Returns, 44 J. Fin. 479–486 (1989); Seth Klarman & Joseph Williams, Beta, 5 J. Fin. Econ. 117 (1991); Myron Scholes & Joseph Williams, Estimating Betas from Nonsynchronous Data, 5 J. Fin. Econ. 309–327 (1977); Jay Shanken, On the Estimation of Beta Pricing Models, 5 Rev. Fin. Stud. 1–33 (1992).

See generally Paul A. Samuelson, General Proof That Diversification Pays, 2 J. Fin. & Quant. Analysis 1–13 (1967).

See Tennessee Williams, The Catastrophe of Success, in N.Y. Times, Nov. 30, 1947, reprinted in Tennessee Williams, The Glass Menagerie 99–103 (Robert Bray introd., 1999) (1st ed. 1945).

See, e.g., Meir Statman, The Diversification Puzzle, 60:4 Fin. Analysts J. 44–53 (July/Aug. 2004).

See Thierry Post & Haim Levy, Does Risk Seeking Drive Stock Prices? A Stochastic Dominance Analysis of Aggregate Investor Preferences and Beliefs, 18 Rev. Fin. Stud. 925–953 (2005).

See James Chong, Shaun Pfeiffer & G. Michael Phillips, Can Dual Beta Filtering Improve Investor Performance?, 10 J. Personal Fin. 63–86, 74 (2010).

See Frank A. Sortino, Robert van der Meer & Auke Plantinga, The Dutch Triangle, 26:1 J. Portfolio Mgmt. 5–7 (Fall 1999).

Richard C. Grinold & Ronald N. Kahn, Active Portfolio Management: A Quantitative Approach for Producing Superior Returns and Controlling Risk 5 (2d ed. 1999).

See generally id. at 109–46; Thomas H. Goodwin, The Information Ratio, 54:4 Fin. Analysts J. 34–43 (July/Aug. 1998); Francis Gupta, Robertus Prajogi & Eric Stubbs, The Information Ratio and Performance, 26:1 J. Portfolio Mgmt. 33–39 (Fall 1999); Craig Israelsen, A Refinement to the Sharpe Ratio and Information Ratio, 5 J. Asset Mgmt. 423–427 (2005).

William F. Sharpe, Gordon J. Alexander & Jeffrey W. Bailey, Investments 183 (6th ed. 1998).

M.A. Bellelah, M.O. Bellelah, H. Ben Ameur & R. Ben Hafsia, Does the Equity Premium Puzzle Persist During Financial Crisis? The Case of the French Equity Market, Research in Int’l Bus. & Fin. (2015) (preprint at 14) (available at http://dx.doi.org/10.1016/j.ribaf.2015.02.018).

J.E. Lovelock, Gaia: A New Look at Life on Earth 70 (1979); see also Edward O. Wilson, Consilience: The Unity of Knowledge 182–183 (1998) (“[P]rogress in a scientific discipline can be measured by how quickly its founders are forgotten.”); cf. A.N. Whitehead, The Aims of Education and Other Essays 162 (1929) (“A science which hesitates to forget its founders is lost.”).

Levy, CAPM in the 21st Century, supra note 1, at 5.

Jagannathan & Wang, supra note 12, at 4.

Guy Kaplanski, Traditional Beta, Downside Risk Beta and Market Risk Premiums, 44 Q. Rev. Econ. & Fin. 636–653, 637 (2004).

Louis K.C. Chan & Josef Lakonishok, Are Reports of Beta’s Death Premature?, 19:4 J. Portfolio Mgmt. 51–62, 51 (Summer 1993).

See, e.g., Rolf W. Banz, The Relationship Between Return and Market Valuation of Common Stocks, 9 J. Fin. Econ. 3–18 (1981).

See, e.g., S. Basu, Investment Performance of Common Stocks in Relation to Their Price-Earning Ratios: A Test of the Efficient Market Hypothesis, 32 J. Fin. 663–682 (1977); cf. Marc R. Reinganum, Misspecification of Capital Asset Pricing: Empirical Anomalies Based on Earnings’ Yield and Market Values, 9 J. Fin. Econ. 19–46 (1981) (identifying both the size and the value anomalies).

Fama & French, The Cross-Section of Stock Returns, supra note 4, at 464.

See, e.g., Kent Daniel & Sheridan Titman, Evidence on the Characteristics of Cross-Sectional Variation in Stock Returns, 52 J. Fin. 1–33 (1997); Eugene Fama & Kenneth R. French, Size and Book-to-Market Factors in Earnings and Returns, 50 J. Fin. 131–155 (1995).

See generally, e.g., John M. Griffin, Are the Fama and French Factors Global or Country Specific?, 15 Rev. Fin. Stud. 783–803 (2002); Adam Borchert, Lisa Ensz, Joep Knijn, Greg Pope & Aaron Smith, Understanding Risk and Return, the CAPM, and the Fama-French Three-Factor Model (Tuck School of Business Case No. 03–111, supervised by Kent Womack & Ying Zhang) (Dec. 2003) (available at http://ssrn.com/abstract=481881).

See Mark M. Carhart, On Persistence in Mutual Fund Performance, 52 J. Fin. 57–82 (1997); Mark Grinblatt, Sheridan Titman & Russ Wermers, Momentum Investment Strategies, Portfolio Performance, and Herding: A Study of Mutual Fund Behavior, 85 Am. Econ. Rev. 1088–1105 (1995); Narasimhan Jegadeesh & Sheridan Titman, Returns to Buying Winners and Selling Losers: Implications for Market Efficiency, 48 J. Fin. 65–91 (1993).

See Louis K.C. Chan, Narasimhan Jegadeesh & Josef Lakonishok, Momentum Strategies, 51 J. Fin. 1681–1713 (1996).

See K. Geert Rouwenhorst, International Momentum Strategies, 53 J. Fin. 267–284 (1998).

See K. Geert Rouwenhorst, Local Return Factors and Turnover in Emerging Stock Markets, 54 J. Fin. 1439–1464 (1999).

See Cifford S. Asness, Momentum in Japan: The Exception That Proves the Rule, 37:4 J. Portfolio Mgmt. 67–75 (Summer 2011); Andy Chui, Sheridan Titman & K.C. John Wei, Individualism and Momentum Around the World, 65 J. Fin. 361–392 (2010).

See Clifford S. Asness, John M. Liew & Ross L. Stevens, Parallels Between the Cross-Sectional Predictability of Stock and Country Returns, 23:3 J. Portfolio Mgmt. 79–87 (Spring 1997); Clifford S. Asness, Toby J. Moskowitz & Lasse Heje Pedersen, Value and Momentum Everywhere, 58 J. Fin. 929–985 (2013).

See Claude B. Erb & Campbell R. Harvey, The Strategic and Tactical Value of Commodity Futures, 62:2 Fin. Analysts J. 69–97 (March/April 2006) (commodities); Tobias J. Moskowitz, Yao Hua Ooi & Lasse Heje Pedersen, Time Series Momentum, 104 J. Fin. Econ. 228–250 (2012) (futures); John Okunev & Derek White, Do Momentum-Based Strategies Still Work in Foreign Currency Markets? 38 J. Fin. & Quant. Analysis 425–447 (2003) (currencies).

See Adams, Moskowitz & Pedersen, supra note 56, at 939–951 (documenting momentum and value effects in government bonds and value effects in currencies and commodities).

See Joëlle Miffre & Georgios Rallis, Momentum Strategies in Commodity Futures Markets, 31 J. Banking & Fin. 1863–1886 (2007).

See Navin Chopra, Josef Lakonishok & Jay R. Ritter, Measuring Abnormal Performance: Do Stocks Overreact?, 31 J. Fin. Econ. 235–268 (1985); Werner F.M. De Bondt & Richard H. Thaler, Does the Stock Market Overreact?, 40 J. Fin. 793–805 (1985); Andrew W. Lo & A. Craig MacKinlay, When Are Contrarian Profits Due to Stock Market Overreaction?, 3 Rev. Fin. Stud. 175–205 (1990).

See Narasimhan Jegadeesh & Sheridan Titman, Profitability of Momentum Strategies: An Evaluation of Alternative Explanations, 56 J. Fin. 699–720 (2001).

See Eugene F. Fama & Kenneth R. French, Disseccting Anomalies, 63 J. Fin. 1653–1678 (2008); Eugene F. Fama & Kenneth R. French, Multifactor Explanation of Asset Pricing Anomalies, 51 J. Fin. 55–85 (1996); Eugene F. Fama & Kenneth R. French, Size, Value, and Momentum in International Stock Returns, 105 J. Fin. Econ. 457–472 (2012).

See, e.g., Subhrendu Rath & Robert B. Durand, Decomposing the Size, Value and Momentum Premia of the Fama–French–Carhart Four-Factor Model, 132 Econ. Letters 139–141 (2015); cf. Jimmy Liew & Maria Vassalou, Can Book-to-Market, Size and Momentum Be Risk Factors That Predict Economic Growth?, 57 J. Fin. Econ. 221–245 (2000).

See Doron Avramov & Tarun Chordia, Pricing Stock Returns, 82 J. Fin. Econ. 387–415 (2006).

See, e.g., Fischer Black, Beta and Return, 20:1 J. Portfolio Mgmt. 8–18 (Fall 1993); Chan & Lakonishok, supra note 45; A.D. Clare, R. Priestley & S.H. Thomas, Reports of Beta’s Death Are Premature: Evidence from the UK, 22 J. Banking & Fin. 1207–1229 (1998); Kevin Grundy & Burton G. Malkiel, Reports of Beta’s Death Have Been Greatly Exaggerated, 22:3 J. Portfolio Mgmt. 36–44 (Spring 1996).

Jonathan Fletcher, An Examination of the Cross-Sectional Relationship of Beta and Return: UK Evidence, 49 J. Econ. & Bus. 211–221, 220 (1997).

Pettengill, Sundaram & Mathur, supra note 7, at 102.

Giovanni Barone Adesi, Patrick Gagliardini & Giovanni Urga, Testing Asset Pricing Models with Coskewness, 22 J. Bus. & Econ. Stat. 474–485, 474 (2004). On type I and type II errors, see generally Roxy Peck & Jay L. Devore, Statistics: The Exploration and Analysis of Data 464–465 (2011); David Sheskin, Handbook of Parametric and Nonparametric Statistical Procedures 54 (2004).

Barone Adesi, Galiardini & Urga, supra note 68, at 474.

Id. On omitted-variable bias, see generally Jeffrey M. Wooldridge, Omitted Variable Bias: The Simple Case, in Introductory Econometrics: A Modern Approach 89–93 (2009); Kevin A. Clarke, The Phantom Menace: Omitted Variable Bias in Econometric Research, 22 Conflict Mgmt. & Peace Sci. 341–352 (2005).

Eugene F. Fama & Kenneth R. French, The CAPM Is Wanted, Dead or Alive, 51 J. Fin. 1947–1958, 1956 (1996); accord Kaplanski, supra note 44, at 637.

Pettengill, Sundaram & Mathur, supra note 7, at 105.

Nurjannah, Don U.A. Galadegera & Robert Brooks, Conditional Relation Between Systematic Risk and Returns in the Conventional and Downside Frameworks: Evidence from the Indonesian Market, 3 J. Emerging Mkt. Fin. 271–300, 274 (2012).

See generally Daniel Kahneman, Thinking, Fast and Slow 19–105 (2011).

Id. at 19–20.

Id. at 20.

Id. The right answer is 17 × 24 = 408.

Id.

See Keith E. Stanovich & Richard F. West, Individual Differences in Reasoning: Implications for the Rationality Debate, 23 Behav. & Brain Scis. 645–665 (2000); see also In Two Minds: Dual Processes and Beyond (Jonathan St. B. T. Evans & Keith Frankish eds., 2009) (recognizing a similar divide within the dual nature of human thought); Jonathan St. B. T. Evans, Dual-Processing Accounts of Reasoning, Judgment, and Social Cognition, 59 Ann. Rev. Psych. 255–278 (2008) (same).

See Kahneman, Thinking, Fast and Slow, supra note 74, at 20–21, 450.

Id. at 20 (emphasis in original).

Id. at 21 (emphasis in original).

Id.

Id. at 22.

See id.

Id. at 23.

Id. at 42. See generally Martin S. Hagger, Chantelle Wood, Chris Stiff & Nikos L.D. Chatzisarantis, Ego Depletion and the Strength Model of Self-Control: A Meta-Analysis, 136 Psych. Bull. 495–525 (2010).

Kahneman, Thinking, Fast and Slow, supra note 74, at 43.

See generally Matthew T. Gailliot & Roy F. Baumeister, The Physiology of Willpower: Linking Blood Glucose to Self-Control, 11 Personality & Soc. Psych. Rev. 303–327 (2007); Matthew T. Gailliot, Roy F. Baumeister, C. Nathan DeWall, John K. Maner, E. Ashby Plant, Dianne M. Tice, Lauren E. Brewer & Brandon J. Schmeichel, Self-Control Relies on Glucose as a Limited Energy Source: Willpower Is More Than a Metaphor, 92 J. Personality & Soc. Psych. 325–336 (2007); cf. Roy F. Baumeister, W. Scott Simpson, Stephen J. Ware & Daniel S. Weber, The Glucose Model of Mediation: Physiological Bases of Willpower as Important Explanations for Common Mediation Behavior, 15 Pepperdine Dispute Resolution L.J. 377–413 (2015).

Kahneman, Thinking, Fast and Slow, supra note 74, at 21.

Id.

See Haim Levy & Amnon Rapoport, Experimental Tests of the Separation Theorem and the Capital Asset Pricing Model, 7 Am. Econ. Rev. 500–518 (1988); Hersh Shefrin & Meir Statman, Behavioral Portfolio Theory, 35 J. Fin. & Quant. Analysis 127–151, 142 (2000).

See Amos Tversky & Daniel Kahneman, Rational Choice and the Framing of Decisions, 59 J. Bus. S251–S278 (1986); Amos Tversky & Daniel Kahneman, The Framing of Decisions and the Psychology of Choice, 211 Science 453–481 (1981).

See Victor DeMiguel, Lorenzo Garlappi & Raman Uppal, Optimal Versus Naïve Diversification: How Inefficient Is the 1/N Portfolio Design?, 22 Rev. Fin. Stud. 1915–1953 (2009). See generally Shlomo Benartzi & Richard H. Thaler, Naïve Diversification Strategies in Defined Contribution Plans, 91 Am. Econ. Rev. 79–98 (2001).

See Samuel M. Hartzmark, The Worst, the Best, Ignoring All the Rest: The Rank Effect and Trading Behavior, 28 Rev. Fin. Stud. 1024–1059 (2015).

Nicholas Barberis, Ming Huang & Richard H. Thaler, Individual Preferences, Monetary Gambles, and Stock Market Participation: A Case for Narrow Framing, 96 Am. Econ. Rev. 1069–1090, 1084 (2006). See generally Daniel Kahneman, Maps of Bounded Rationality: Psychology for Behavioral Economics, 93 Am. Econ Rev. 1449–1475 (2003).

Titel: Seduced by Symmetry, Smarter by Half
verfasst von: James Ming Chen
Verlag: Palgrave Macmillan US
Buch: Postmodern Portfolio Theory
Print ISBN: 978-1-137-54463-6

Electronic ISBN: 978-1-137-54464-3

Copyright-Jahr: 2016
DOI: https://doi.org/10.1057/978-1-137-54464-3_4