Postmodern Portfolio Theory

Navigating Abnormal Markets and Investor Behavior

James Ming Chen

• Publisher: Palgrave Macmillan
• Year: 2016
• ISBN:
  9781137544643
• Topic: Economics
• Subtopic: Econometrics
• Index: Economics

This survey of portfolio theory, from its modern origins through more sophisticated, "postmodern" incarnations, evaluates portfolio risk according to the first four moments of any statistical distribution: mean, variance, skewness, and excess kurtosis. In pursuit of financial models that more accurately describe abnormal markets and investor psychology, this book bifurcates beta on either side of mean returns. It then evaluates this traditional risk measure according to its relative volatility and correlation components. After specifying a four-moment capital asset pricing model, this book devotes special attention to measures of market risk in global banking regulation. Despite the deficiencies of modern portfolio theory, contemporary finance continues to rest on mean-variance optimization and the two-moment capital asset pricing model. The term postmodern portfolio theory captures many of the advances in financial learning since the original articulation ofmodern portfolio theory. A comprehensive approach to financial risk management must address all aspects of portfolio theory, from the beautiful symmetries of modern portfolio theory to the disturbing behavioral insights and the vastly expanded mathematical arsenal of the postmodern critique. Mastery of postmodern portfolio theory's quantitative tools and behavioral insights holds the key to the efficient frontier of risk management.

© The Editor(s) (if applicable) and The Author(s) 2016

James Ming ChenPostmodern Portfolio TheoryQuantitative Perspectives on Behavioral Economics and Finance10.1057/978-1-137-54464-3_1

Begin Abstract

1. Finance as a Pattern of Timeless Moments

James Ming Chen¹ 

(1)

College of Law, Michigan State University, East Lansing, Michigan, USA

 

1.1 Introduction

T.S. Eliot, Little Gidding, in Four Quartets 49–59, 58 (Harcourt, Brace & Co. 1971; 1st ed. 1943) (“for history is a pattern/Of timeless moments”).

End Abstract

1.1 Introduction

Quantitative finance traces its roots to modern portfolio theory. Despite the deficiencies of modern portfolio theory, mean-variance optimization nevertheless continues to form the basis for contemporary finance. The term postmodern portfolio theory captures many of the advances in financial learning since the original articulation of modern portfolio theory. A comprehensive approach to financial risk management must address all aspects of portfolio theory, from the beautiful symmetries of modern portfolio theory to the disturbing behavioral insights and the vastly expanded mathematical arsenal of the postmodern critique.

This survey of portfolio theory, from its modern origins through more sophisticated, “postmodern” incarnations, evaluates portfolio risk according to the first four moments of any statistical distribution: mean, variance, skewness, and excess kurtosis. Postmodern Portfolio Theory also evaluates the challenge that prospect theory and behavioral finance pose to portfolio theory and, more broadly, to quantitative finance. The efficient capital markets hypothesis and the conventional two-moment capital asset pricing model now compete with the postmodern alternative of an expanded four-moment capital asset pricing model and its behavioral extensions. Mastery of postmodern portfolio theory’s quantitative tools and behavioral insights holds the key to the efficient frontier of risk management.

This book proceeds in four parts. Part 1 introduces portfolio theory. Chapter 2 expounds modern portfolio theory as a framework for assessing risk-adjusted financial returns. Conventional mean-variance analysis, the foundation of modern portfolio theory, emphasizes expected return, standard deviation, and beta. These quantitative measures are drawn from the lower moments of statistical distributions.

Chapter 3 outlines new approaches to portfolio theory that account for market abnormalities and investor behavior. The foundational theory of contemporary finance is riddled not only with mistakes in measurement, but also with mistakes in perception. At its most ambitious, the postmodern critique seeks ways to account for the destructive potential of systemic coordination and cascades. At its most modest, postmodern portfolio theory respects fundamental limits on human knowledge.

Parts 2 and 3 pursue the postmodern agenda for risk management by emphasizing asymmetry in finance and the higher statistical moments of financial returns. This book’s approach to postmodern portfolio theory emphasizes single-sided statistical moments, the statistical notions of skewness and kurtosis, and behavioral responses to these decidedly abnormal financial phenomena. Beginning with a bifurcation of beta on either side of mean returns, Part 2 of this book tours financial and behavioral space in search of a mathematically cogent account of risk on either side of mean returns. After a brief exploration of time series models that measure asymmetry in volatility alongside intertemporal changes in volatility, Part 3 specifies a four-moment capital asset pricing model based upon a Taylor series expansion of log returns.

Part 4 devotes additional attention to the problem of fat tails and kurtosis risk in finance. It does so by examining the treatment of value-at-risk and expected shortfall as measures of market risk in the trading book of financial institutions observing the Basel Accords on international banking regulation. Risk management, even when undertaken by some of the world’s largest financial institutions under central bank supervision, cannot fully escape mathematically dictated limitations on economic forecasting.

Part 1
Perpetual Possibility in a World of Speculation: Portfolio Theory in Its Modern and Postmodern Incarnations

© The Editor(s) (if applicable) and The Author(s) 2016

James Ming ChenPostmodern Portfolio TheoryQuantitative Perspectives on Behavioral Economics and Finance10.1057/978-1-137-54464-3_2

Begin Abstract

2. Modern Portfolio Theory

James Ming Chen¹

(1)

College of Law, Michigan State University, East Lansing, Michigan, USA

2.1 Mathematically Informed Risk Management

2.2 Measures of Risk; the Sharpe Ratio

2.3 Beta

2.4 The Capital Asset Pricing Model

2.5 The Treynor Ratio

2.6 Alpha

2.7 The Efficient Markets Hypothesis

2.8 The Efficient Frontier

End Abstract

2.1 Mathematically Informed Risk Management

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

Modern portfolio theory offers a mathematically informed approach to financial risk management.⁵ Modern portfolio theory assumes that investors are rationally risk averse.⁶ Given two portfolios with the same expected return, investors prefer the less risky one.⁷ Although idiosyncratic risks are hard to identify, let alone manage, diversification reduces the systemic risk that market forces will swamp an entire portfolio of highly correlated assets.⁸ Reward follows risk:⁹ though a riskier investment is not necessarily more rewarding, modern portfolio theory does predict that an investor will demand a higher expected return in exchange for accepting greater risk.¹⁰ A direct, positive relationship between risk and return is canonical to conventional theories of finance.

2.2 Measures of Risk; the Sharpe Ratio

Measures of risk abound within modern portfolio theory. Harry Markowitz’s original formulation used the volatility of returns, as measured by their standard deviation, as a proxy for risk.¹¹ William Sharpe proposed a measure of “reward to variability” that relied squarely on standard deviation:¹²

where R represents expected return, R _f represents the return from a risk-free baseline such as Treasury bonds, and σ represents standard deviation. The Sharpe ratio bears an obvious resemblance to the definition of a standard score in ordinary statistics:¹³

2.3 Beta

An alternative measure for risk, beta, compares returns on an individual asset or a portfolio of assets with returns realized from a broader benchmark, based on the entirety or at least some significant portion of the financial market.¹⁴ The beta of an asset within a portfolio measures the (1) the covariance between the rate of return on the asset and the rate of return on the portfolio as a whole (2) divided by the variance of returns on the portfolio.¹⁵ More formally:

Beta may be most intuitively understood by relation to standard statistical measures of correlation. Pearson’s r is the standard measure of correlation between two sets of data. When specified for an entire population rather than a sample, Pearson’s correlation coefficient is designated as ρ(x, y):

By contrast, beta is a measure of covariance. For any two sets of data, represented by independent variable x and dependent variable y, beta for y is the ratio of the covariance between the two data sets to the variance of x:

The mathematical relationship between beta and Pearson’s correlation coefficient c...

Table of contents

• Cover
• Frontmatter
• 1. Finance as a Pattern of Timeless Moments
• 1. Perpetual Possibility in a World of Speculation: Portfolio Theory in Its Modern and Postmodern Incarnations
• 2. Bifurcating Beta in Financial and Behavioral Space
• 3. Τέσσερα, Τέσσερα: Four Dimensions, Four Moments
• 4. Managing Kurtosis: Measures of Market Risk in Global Banking Regulation
• Backmatter