Second and higher moments of fundamentals: A literature review

• Published date: 01 January 2020
• Author: Qin Emma Wang,Ivilina Popova,Betty Simkins,Yuecheng Jia
• Date: 01 January 2020
• DOI: http://doi.org/10.1111/eufm.12215

DOI: 10.1111/eufm.12215

EUROPEAN

FINANCIAL MANAGEMENT

ORIGINAL ARTICLE

Second and higher moments of fundamentals:

A literature review

Yuecheng Jia

1

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Ivilina Popova

2

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Betty Simkins

3

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Qin Emma Wang

4

1

Chinese Academy of Finance and

Development, Chinese Academy of

Finance and Development, Central

University of Finance and Economics,

Beijing, China

2

Department of Finance and Economics,

Texas State University, San Marcos, Texas

3

Department of Finance, Spears School of

Business, Oklahoma State University,

Stillwater, Oklahoma

4

Department of Finance, Spears School of

Business, Oklahoma State University,

Tulsa, Oklahoma

Correspondence

Ivilina Popova, Department of Finance

and Economics, Texas State University,

San Marcos, TX 78666.

Email: ip12@txstate.edu

Abstract

This literature review outlines the recent progress in

fundamental second and higher moments of research.

We survey the moments’existence, formation, and

financial market and macroeconomic implications.

Research shows that time‐varying volatility and non‐

Gaussian shocks exist throughout all measures of

fundamentals at both the micro‐and macro levels. In

addition, the granular network among firms helps

explain the origin of fundamental second and higher

moments. Empirical evidence shows that the moments

have strong predictive power on asset prices and

macroeconomic variables. We also highlight several

areas where more research is needed to better under-

stand the moments.

KEYWORDS

fundamental higher moments, fundamental second moments,

granular network, non‐Gaussian shocks, time‐varying volatility

JEL CLASSIFICATION

G12

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INTRODUCTION

In this paper, we review the fast‐growing literature on the macroeconomic and financial market

implications of fundamental second and higher order moments. In particular, we review the

literature on consumption‐based long‐run risk with related disaster models, consumption‐based

habit formation papers, production‐based pricing models, and granularity‐networks papers. We

Eur Financ Manag. 2020;26:216–237.wileyonlinelibrary.com/journal/eufm216

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© 2019 John Wiley & Sons Ltd

We are grateful for helpful comments from John Doukas (the editor), one anonymous referee, and Russ Simkins for

helpful comments. We are solely responsible for any remaining errors.

focus mainly on equity and options markets. We consider fundamentals the qualitative and

quantitative information that contributes to the economic well‐being and subsequent financial

valuation of a firm, security, or currency. The second and higher‐order moments investigated

include volatility, skewness, andthe lumpiness of the shocks to the economicvariables of interest.

At the micro level, we focus on firm profitability, earnings, assets, and growth—which are

underlying factors that can capture or affect a firm’s business operations and future prospects. At

the macro level, we focus on consumption growth, gross domestic product (GDP) growth,

aggregate earnings, and inflation—which are benchmarks of the whole economy. Fundamentals

at both the micro and macro levels contain information on the economy and, thus, stock prices.

We start our literature review in Section 2 with empirical evidence documenting that

fundamentals, at both the firm and aggregate levels, contain time‐varying volatility, non‐

Gaussian shocks, and skewness. Next, we survey theory and models rationalizing the

informational content of the second and higher moments in Sections 3 and 4, respectively. We

then move on to the theoretical framework and empirical results for the predictive power of

the second and higher moments of fundamentals on macroeconomic quantity variables and

asset prices in Section 5. The last section concludes the paper and provides directions for future

research.

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EXISTENCE AND VARIATION OF FUNDAMENTAL

SECOND AND HIGHER MOMENTS

In this section, we summarize the evidence and measures from both theoretical and empirical

works that document fundamental second and higher moments dynamics. For an economic

quantity variable to be meaningful, it should have sufficient variation in the cross‐section and

time series. Fundamental second and higher moments satisfy this condition.

Empirical research supports the predictive power of firm fundamentals on the cross‐section

of stock returns and the time series of aggregate stock market returns. These studies find

that individual stock return is high when asset growth is low, gross profitability is high, and the

return on equity is high. They also find that the aggregate stock market return in excess of the

short‐term interest rate is high when the dividend‐price ratio and earnings‐price ratio are high.

The Appendix summarizes representative studies and publications on fundamentals related

market returns and their predictors.

We first survey the literature on time‐varying volatility of fundamentals at the macro level.

We then describe literature that demonstrates non‐Gaussian shocks to fundamentals. Next, we

survey the literature on the skewness and lumpiness of aggregate fundamentals.

1

Table 1

summarizes representative papers documenting fundamental second and higher moments at

the macro level.

For fundamentals at the micro level, we cover the literature on the volatility of operating

cash flows and earnings and then describe the literature on the skewness of gross profit and

earnings. Table 2 summarizes representative papers documenting fundamental second and

higher moments at the micro level.

1

Our concept of second and higher moments of fundamentals at the macro level refers to the time series second and higher moments (volatility and skewness)

of shocks to economic quantity variables of interest. This is distinct from the other uncertainty measures, such as parameter uncertainty, learning, robust

control, and ambiguity.

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