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Modern Portfolio Theory

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Postmodern Portfolio Theory

Abstract

Portfolio theory may be the most fecund intellectual export from quantitative finance to other sciences. Social sciences outside the strictly financial domain have applied portfolio theory to subjects as diverse as regional development,1 social psychology,2 and information retrieval.3 Proper understanding of portfolio theory and its place in finance and cognate sciences begins with a return to the origins of modern portfolio theory. For “the end of all our exploring/Will be to arrive where we started/And know the place for the first time.”4

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Notes

  1. 1.

    See, e.g., Michael E. Conroy, Regional Economic Growth: Diversification and Control (1975); Siddharth Chandra, Regional Economy Size and the Growth-Instability Frontier: Evidence from Europe, 43 J. Regional Sci. 95–122 (2003).

  2. 2.

    See Siddharth Chandra & William G. Shadel, Crossing Disciplinary Boundaries: Applying Financial Portfolio Theory to Model the Organization of the Self-Concept, 41 J. Research in Personality 346–373 (2007).

  3. 3.

    See Jun Wang & Jianhan Zhu, Portfolio Theory of Information Retrieval, in SIGIR’09: Proceedings of the 32nd International ACM SIGIR Conference on Research and Development in Information Retrieval, at 115–123 (2009).

  4. 4.

    Eliot, Burnt Norton, in Four Quartets, 13–22, 13 (Harcourt, Brace & Co. 1971; 1st ed. 1943) (“for history is a pattern/Of timeless moments”).

  5. 5.

    See Edwin J. Elton, Martin J. Gruber, Stephen J. Brown & William N. Goetzmann, Modern Portfolio Theory and Investment Analysis (9th ed. 2014); Edwin J. Elton & Martin J. Gruber, Modern Portfolio Theory, 1950 to Date, 21 J. Banking & Fin. 1743–1759 (1997); Harry M. Markowitz, Portfolio Selection, 7 J. Fin. 77–91, 87–91 (1952).

  6. 6.

    See Harry M. Markowitz, Foundations of Portfolio Theory, 46 J. Fin. 469–477, 469–470 (1991).

  7. 7.

    On risk aversion, see generally Steven Shavell, Foundations of Economic Analysis of Law 52 (2004).

  8. 8.

    See Richard A. Brealy, Stewart C. Myers & Franklin Allen, Principles of Corporate Finance 160–162 (8th ed. 2006).

  9. 9.

    See Eugene F. Fama, Foundations of Finance 361 (1976); Eugene F. Fama & James D. MacBeth, Risk, Return and Equilibrium: Empirical Tests, 81 J. Pol. Econ. 607–636, 624 (1973).

  10. 10.

    See Markowitz, Foundations of Portfolio Theory, supra note 6, at 469–470.

  11. 11.

    See Harry M. Markowitz, Portfolio Selection: Efficient Diversification of Investments 17 (2d ed. 1991) (1st ed. 1959).

  12. 12.

    See William F. Sharpe, Mutual Fund Performance, 39 J. Bus. 119, 123–138 (1966); William F. Sharpe, Adjusting for Risk in Portfolio Performance Measurement. 1:2 J. Portfolio Mgmt. 29–34 (Winter 1975); William F. Sharpe, The Sharpe Ratio, 21:1 J. Portfolio Mgmt. 49–58 (Fall 1994).

  13. 13.

    See http://en.wikipedia.org/wiki/Standard_score.

  14. 14.

    See Mark Levinson, Guide to Financial Markets 145–146 (4th ed. 2006).

  15. 15.

    See Irwin Friend & Marshall Blume, Measure of Portfolio Performance Under Uncertainty, 60 Am. Econ. Rev. 561–575, 565 (1970).

  16. 16.

    See Martin L. Leibowitz, Anthony Bova & P. Brett Hammond, The Endowment Model of Investing: Return, Risk, and Diversification 14 (2010) Michael B. Miller, Mathematics and Statistics for Financial Risk Management 198, 213, 292 (2d ed. 2014); Shannon P. Pratt & Roger J. Grabowski, Cost of Capital: Applications and Examples 305–306 (4th ed. 2010).

  17. 17.

    See http://en.wikipedia.org/wiki/Beta_(finance).

  18. 18.

    See id.

  19. 19.

    William F. Sharpe, A Simplified Model for Portfolio Analysis, 9 Mgmt Sci. 277–293, 281 (1963).

  20. 20.

    See http://en.wikipedia.org/wiki/Sharpe_ratio#Strengths_and_weaknesses.

  21. 21.

    See Jack L. Treynor, How to Rate Management of Investment Funds, 43 Harv. Bus. Rev. 63–75 (1965); http://en.wikipedia.org/wiki/Beta_(finance).

  22. 22.

    See Levinson, supra note 14, at 148.

  23. 23.

    See generally Minder Cheng & Ananth Madhavan, The Dynamics of Leveraged and Inverse Exchange-Traded Funds, 7:4 J. Inv. Mgmt. 43–62 (4th quarter 2009); Patricia Knain Little, Inverse and Leveraged ETFs: Not Your Father’s ETF, 1:1 J. Index Investing 83–89 (Summer 2010).

  24. 24.

    See Chris Tofallis, Investment Volatility: A Critique of Standard Beta Estimation and a Simple Way Forward, 187 Eur. J. Oper. Research 1358–1367, 1361 (2008).

  25. 25.

    See Marie Brière, Kim Oosterlinck & Ariane Szafarz, Virtual Currency, Tangible Return: Portfolio Diversification with Bitcoins 5 (Sept. 2013) (available at http://ssrn.com/abstract=2324780).

  26. 26.

    See David Yermack, Is Bitcoin a Real Currency? An Economic Appraisal 15, 22 (Dec. 2013) (NBER Working Paper No. 19747) (available at http://www.nber.org/papers/w19747).

  27. 27.

    Brière, Oosterlick & Szafarz, supra note 25, at 9.

  28. 28.

    Yermack, supra note 26, at 16.

  29. 29.

    Id. at 15.

  30. 30.

    See generally Scott Plous, The Psychology of Judgment and Decision Making 233 (1993); Maria Lewicka, Confirmation Bias: Cognitive Error or Adaptive Strategy of Action Control?, in Personal Control in Action: Cognitive and Motivational Mechanisms 233–255 (Mirosław Kofta, Gifford Weary & Grzegorz Sedek eds., 1998); Raymond S. Nickerson, Confirmation Bias: A Ubiquitous Phenomenon in Many Guises, 2 Rev. Gen. Psych. 175–220 (1998).

  31. 31.

    See, e.g., Reuben Grinberg, Bitcoin: An Innovative Alternative Digital Currency, 4 Hastings Sci. & Tech. L.J. 160–207 (2011).

  32. 32.

    See, e.g., Jerry Brito, Houman Shadab & Andreal Castillo, Bitcoin Financial Regulation: Securities, Derivatives, Prediction Markets, and Gambling, 16 Colum. Sci. & Tech. L. Rev. 144–221 (2014); J. Scott Colesanti, Trotting Out the White Horse: How the S.E.C. Can Handle Bitcoin’s Threat to American Investors, 65 Syracuse L. Rev. 1–52 (2014).

  33. 33.

    See Levinson, supra note 14, at 148.

  34. 34.

    See id.

  35. 35.

    See, e.g., Fischer Black, Capital Market Equilibrium with Restricted Borrowing, 45 J. Bus. 444 – 455 (1972); Fischer Black, Michael C. Jensen & Myron S. Scholes, The Capital Asset Pricing Model: Some Empirical Tests, in Studies in the Theory of Capital Markets 79–121 (Michael C. Jensen ed., 1972); John Lintner, Security Prices, Risk and Maximal Gains from Diversification, 20 J. Fin. 587–615 (1965); John Lintner, The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets, 73 Rev. Econ. & Stats. 13–37 (1965); Jan Mossin, Equilibrium in a Capital Asset Market, 34 Econometrica 768–783 (1966); William F. Sharpe, Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk, 19 J. Fin. 425–442 (1964); Jack L. Treynor, Toward a Theory of Market Value of Risky Assets, in Asset Pricing and Portfolio Performance: Models, Strategy and Performance Metrics 15–22 (Robert A. Korajczyk ed., 1999); Jack L. Treynor & Fischer Black, Corporate Investment Decisions, in Modern Developments in Financial Management 310–327 (Stewart C. Myers ed., 1976). See generally Bernell K. Stone, Risk, Return, and Equilibrium: A General Single-Period Theory of Asset Selection and Capital Market Equilibrium (1970); Eugene F. Fama & Kenneth R. French, The Capital Asset Pricing Model: Theory and Evidence, 18:3 J. Econ. Persp. 25–46 (Summer 2004).

  36. 36.

    See sources cited supra note 35.

  37. 37.

    Eugene Fama, Risk, Return, and Equilibrium: Some Clarifying Comments, 23 J. Fin. 29– 40, 40 (1968).

  38. 38.

    See Franco Modigliani & Merton Miller, The Cost of Capital, Corporate Finance, and the Theory of Investment, 48 Am. Econ. Rev. 261–297 (1958).

  39. 39.

    See Robert A. Korajczyk, Introduction, in Asset Pricing and Portfolio Performance, supra note 35, at viii, xv.

  40. 40.

    See id.

  41. 41.

    See id.

  42. 42.

    See Philip H. Dybvig & Stephen A. Ross, Differential Information and Performance Measurement Using a Security Market Line, 40 J. Fin. 383–399 (1985).

  43. 43.

    See Korajczyk, supra note 39, at xv.

  44. 44.

    See Sharpe, Capital Asset Prices, supra note 35, at 426–427.

  45. 45.

    See Modigliani & Miller, supra note 38.

  46. 46.

    See Theoretical Framework of Finance, 1 Handbook of Quantitative Finance and Risk Management 3–22, § 1.5, at 10–12 (Cheng-Few Lee, Alice C. Lee & John Lee eds., 2010).

  47. 47.

    See Korajczyk, supra note 39, at xv.

  48. 48.

    See Richard Roll, A Critique of the Asset Pricing Theory’s Tests—Part I: On Past and Potential Testability of the Theory, 4 J. Fin. Econ. 129–176, 136 (1977).

  49. 49.

    See Treynor, supra note 35, at 16–17.

  50. 50.

    See Sharpe, Mutual Fund Performance, supra note 12; Sharpe, Adjusting for Risk, supra note 12.

  51. 51.

    See J.D. Jobson & Bob M. Korkie, Performance Hypothesis Testing with the Sharpe and Treynor Measures. 36 J. Fin. 889–908 (1981); Sharpe, Mutual Fund Performance, supra note 12, at 121–122.

  52. 52.

    See Marvin McClay, The Penalties of Incurring Unsystematic Risk, 4:3 J. Portfolio Mgmt. 31–35, 32 (Spring 1978); Treynor, supra note 21.

  53. 53.

    See Michael C. Jensen, The Performance of Mutual Funds in the Period 1945–1964, 23 J. Fin. 389–416 (1968).

  54. 54.

    United States v. Grinnell Corp., 384 U.S. 563, 570–571 (1966) (defining monopolization under section 2 of the Sherman Act, 15 U.S.C. § 2, as “the willful acquisition or maintenance of [monopoly] power as distinguished from growth or development as a consequence of a superior product, business acumen, or historic accident”).

  55. 55.

    See generally, e.g., Paul H. Cootner, The Random Character of Stock Market Prices (1964); Eugene F. Fama, Efficient Capital Markets: A Review of Theory and Empirical Work, 25 J. Fin. 383–417 (1970); Eugene F. Fama, Efficient Capital Markets II, 46 J. Fin. 1575–1617 (1991); Eugene F. Fama, The Behavior of Stock Market Prices, 38 J. Bus. 34–105 (1965); Lawrence H. Summers, Does the Stock Market Rationally Reflect Fundamental Values?, 41 J. Fin. 591–601 (1986); Eugene F. Fama & Kenneth R. French, The Cross-Section of Expected Stock Returns, 47 J. Fin. 427–465, 427–429 (1992).

  56. 56.

    Richard A. Brealey, Stewart C. Myers & Franklin Allen, Principles of Corporate Finance 330 (10th ed. 2011); accord Amgen Inc. v. Connecticut Retirement Plans & Trust Funds, 133 S. Ct. 1184, 1192 (2013).

  57. 57.

    Basic, Inc. v. Levinson, 485 U.S. 224, 246–247 (1988). Violations of section 10(b) of the Securities and Exchange Act of 1934, 15 U.S.C. § 78j(b), and Securities and Exchange Commission Rule 10b-5, 17 C.F.R. § 240.10b-5, give rise to an implied private cause of action. See, e.g., Blue Chip Stamps v. Manor Drug Stores, 421 U.S. 723, 730 (1975); Amgen, 133 S. Ct. at 1192.

  58. 58.

    See, e.g., James D. Cox, Understanding Causation in Private Securities Lawsuits: Building on Amgen, 66 Vand. L. Rev. 1719–1753, 1732 (2013) (“arguing that “friction in accessing public information” and nontrivial “processing costs” prevent markets from incorporating “all public information … in a security’s price with the same alacrity, or perhaps with any quickness at all”); Donald C. Langevoort, Basic at Twenty: Rethinking Fraud on the Market, 2009 Wis. L. Rev. 151–198, 175 (“Doubts about the strength and pervasiveness of market efficiency are much greater today than they were in the mid-1980s”); Baruch Lev & Meiring de Villiers, Stock Price Crashes and 10b-5 Damages: A Legal, Economic and Policy Analysis, 47 Stan. L. Rev. 7–37, 20–21 (1994).

  59. 59.

    Halliburton Co. v. Erica P. John Fund, Inc., 134 S. Ct. 2398, 2410 (2014); see also Schleicher v. Wendt, 618 F.3d 679, 685 (7th Cir. 2010) (recognizing the fact that “the … price [of a stock] may be inaccurate does not detract from the fact that false statements affect it, and cause loss,” in violation of Basic, Inc. v. Levinson’s fraud on the market rule).

  60. 60.

    Amgen, 133 S. Ct. at 1192; accord Halliburton, 134 S. Ct. at 2411.

  61. 61.

    See Sanford Grossman, On the Efficiency of Competitive Stock Markets Where Trades Have Diverse Information, 31 J. Fin. 573–585 (1978). On the informational content of stock trades, see generally Michael J. Brennan & Patricia J. Hughes, Stock Prices and the Supply of Information, 46 J. Fin. 1665–1691 (1991); Joel Hasbrouck, Measuring the Information Content of Stock Trades, 46 J. Fin. 179–207 (1991); Joel Hasbrouck, The Summary Informativeness of Stock Trades: An Econometric Analysis, 4 Rev. Fin. Stud. 571–595 (1991).

  62. 62.

    See Paul Milgrom & Nancy Stokey, Information, Trade and Common Knowledge, 31 J. Econ. Theory 17–27 (1982).

  63. 63.

    See Andrei Shleifer & Robert Vishny, The Limits of Arbitrage, 52 J. Fin. 35–55 (1997) (identifying barriers that block otherwise risk-free transactions that exploit the mispricing of assets).

  64. 64.

    See Stephen A. Ross, The Arbitrage Theory of Capital Asset Pricing, 13 J. Econ. Theory 341–360 (1976); Stephen A. Ross, A Simple Approach to the Valuation of Risky Streams, 51 J. Bus. 453–475 (1978).

  65. 65.

    See generally Frederick C. Dunbar & Dana Heller, Fraud on the Market Meets Behavioral Finance, 31 Del. J. Corp. L. 455–531, 463–464 (2006).

  66. 66.

    See Paul A. Samuelson, Proof That Properly Anticipated Prices Fluctuate Randomly, 6 Indus. Mgmt. Rev. 41–49 (1965)

  67. 67.

    The Supreme Court’s “fraud on the market” theory “relied upon the ‘semi-strong’ version” of the efficient markets hypothesis. Halliburton Co. v. Erica P. John Fund Inc., 134 S. Ct. 2398, 2420 (2014) (Thomas, J., concurring in the judgment) (citing Lynn A. Stout, The Mechanisms of Market Inefficiency: An Introduction to the New Finance, 28 J. Corp. L. 635–669, 640 & n.24 (2003); Fama, Efficient Capital Markets: A Review of Theory and Empirical Work, supra note 55, at 388).

  68. 68.

    See Andrew W. Lo & Jasmina Hasanhodzic, The Evolution of Technical Analysis: Financial Prediction from Babylonian Tablets to Bloomberg Terminals 150 (2010).

  69. 69.

    See id.

  70. 70.

    See generally Sitabhra Sinha, Arnab Chatterjee, Anirban Chakraborti & Bikas K. Chakrabarti, Econophysics: An Introduction (2011). The interaction between finance and physics has come a long way since Louis Jean-Baptiste Bachelier’s path-breaking books such as Théorie de la Spéculation (1900), Calcul des Probabilités (1912), and Le Jeu, la Chance, et le Hasard (1914). See James Owen Weatherall, The Physics of Wall Street: A Brief History of Predicting the Unpredictable 10–11 (2013) (reporting that Bachelier’s thesis at La Sorbonne was poorly received because he was trying to apply mathematics to a field with which mathematicians of his time were unfamiliar).

  71. 71.

    See Luciano Zunino, Aurelio Fernandez Bariviera, M. Belén Guercio, Lisana B. Martinez & Osvaldo A. Rosso, On the Efficiency of Sovereign Bond Markets, 391 Physica A 4342–4349 (2012); Aurelio Fernandez Bariviera, Luciano Zunino, M. Belén Guercio, Lisana B. Martinez & Osvaldo A. Rosso, Revisiting the European Sovereign Bonds with a Permutation-Information-Theory Approach, 86 Eur. Phys. J. B 509 (2014).

  72. 72.

    See Eugene F. Fama & Kenneth R. French, Luck Versus Skill in the Cross-Section of Mutual Fund Returns, 65 J. Fin. 1915–1947 (2010).

  73. 73.

    See, e.g., Jonathan Brogaard, Terrence Hendershott & Ryan Riordan, High-Frequency Trading and Price Discovery, 27 Rev. Fin. Stud. 2267–2306 (2014); Terrence Hendershott, Charles M. Jones & Albert J. Menkveld, Does Algorithmic Trading Improve Liquidity?, 66 J. Fin. 1–33 (2011); Albert J. Menkveld, High Frequency Trading and the New Market Makers, 16 J. Fin. Mkts. 712–740 (2013); Martin L. Scholtus, Dick J.C. Van Dijk & Bart Frijns, Speed, Algorithmic Trading, and Market Quality Around Macroeconomic News Announcements, 38 J. Banking & Fin. 89–105 (2014).

  74. 74.

    See Eugene F. Fama & Kenneth R. French, Permanent and Temporary Components of Stock Prices, 96 J. Pol. Econ. 246–273 (1988).

  75. 75.

    Benjamin Graham & David L. Dodd, Security Analysis 452 (1st ed. 1934); see also Benjamin Graham, The Intelligent Investor (1st ed. 1949).

  76. 76.

    John Y. Campbell & Robert F. Shiller, Stock Prices, Earnings, and Expected Dividends, 43 J. Fin. 661–676, 666 (1988).

  77. 77.

    Robert J. Shiller, Irrational Exuberance 256 n.19 (3d ed. 2015) (quoting Samuelson). For empirical evidence supporting this dictum, see Randolph Cohen, Christopher Polk & Tuomo Vuolteenaho, The Value Spread, 58 J. Fin. 609–642 (2003); Jeeman Jung & Robert J. Shiller, Samuelson's Dictum and the Stock Market, 43 Econ. Inquiry 221–228 (2005); Tuomo Vuolteenaho, What Drives Firm-Level Stock Return?, 57 J. Fin. 233–264 (2002).

  78. 78.

    See William F. Sharpe, The Arithmetic of Active Management, 47:1 Fin. Analysts J. 7–9, 7 (Jan./Feb. 1991).

  79. 79.

    See Edwin J. Elton & Martin J. Gruber, Investments and Portfolio Performance 382–383 (2011); Steven Roman, Portfolio Management and the Capital Asset Pricing Model 53–67 (2004).

  80. 80.

    See André F. Perold, The Capital Asset Pricing Model, 18 J. Econ. Persp. 3–24, 10–12 (2004).

  81. 81.

    See James Tobin, Liquidity Preference as Behavior Towards Risk, 67 Rev. Econ. Stud. 65–86 (1958); cf. Winston W. Chang, Daniel Hamberg & Junichi Hirata, Liquidity Preference as Behavior Toward Risk Is a Demand for Short-Term Securities—Not Money, 73 Am. Econ. Rev. 420–427 (1983).

  82. 82.

    See David Cass & Joseph E. Stiglitz, The Structure of Investor Preferences and Asset Returns, and Separability in Portfolio Allocation, 2 J. Econ. Theory 122–160 (1970); Robert C. Merton, An Analytic Derivation of the Efficient Portfolio Frontier, 7 J. Fin. & Quant. Analysis 1851–1872 (1972); Stephen A. Ross, Mutual Fund Separation and Financial Theory—The Separating Distributions, 17 J. Econ. Theory 254–286 (1978).

  83. 83.

    See sources cited supra note 55.

  84. 84.

    See Sharpe, Arithmetic of Active Management, supra note 78, at 7–8.

  85. 85.

    See Philip H. Dybvig & Jonathan E. Ingersoll, Jr., Mean-Variance Theory in Complete Markets, 55 J. Bus. 233–251 (1982). On the notion of complete markets, where economic conditions permit the emergence of a set of prices that allow aggregate supplies of every commodity in the economy to satisfy aggregate demand, see generally Kenneth J. Arrow & Gérard Debreu, Existence of an Equilibrium for a Competitive Economy, 22 Econometrica 265–290 (1954).

  86. 86.

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

  87. 87.

    See Lawrence A. Cunningham, From Random Walks to Chaotic Rashes: The Linear Genealogy of the Efficient Capital Markets Hypothesis, 62 Geo. Wash. L. Rev. 546–608, 568–570 (1994).

  88. 88.

    See Sharpe, Arithmetic of Active Management, supra note 78, at 7–8.

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    James Ming Chen

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Chen, J.M. (2016). Modern Portfolio Theory. In: Postmodern Portfolio Theory. Quantitative Perspectives on Behavioral Economics and Finance. Palgrave Macmillan, New York. https://doi.org/10.1057/978-1-137-54464-3_2

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