The negative relationship between the cross-section of expected returns and lagged idiosyncratic volatility. The German stock market 1990-2016

Table of Contents

1 Introduction

2 Literature

3 Data

4 Methodology

5 Results

5.1 Estimating Idiosyncratic Volatility

5.2 Patterns in Average Returns January 1990 - June 2016

5.3 Patterns in Average Returns January 2003 - June 2016

6 Conclusion

7 Appendix

7.1 Portfolio Strategies January 1990 - June 2016

7.2 Portfolio Strategies January 2003 - June 2016

Research Objectives and Thematic Focus

The primary objective of this paper is to empirically investigate the existence of the "Idiosyncratic Volatility Puzzle" within the German stock market for the period from January 1990 to June 2016, specifically examining whether a negative relationship exists between lagged idiosyncratic volatility and the cross-section of expected stock returns.

• Analysis of idiosyncratic volatility estimation methods and their impact on portfolio returns.
• Testing of various portfolio construction strategies, including different estimation and holding periods.
• Examination of the effects of value-weighting versus equal-weighting schemes on portfolio performance.
• Robustness checks using sub-period analysis (2003–2016) and controlling for firm size through double-sorting procedures.

Excerpt from the Book

Summary of Chapters

1 Introduction: This chapter outlines the research motivation, specifically addressing the failure of the CAPM to explain stock return variations and introducing the concept of the Idiosyncratic Volatility Puzzle.

2 Literature: This section provides a comprehensive review of previous empirical and theoretical studies regarding idiosyncratic volatility, including seminal works by Fama and MacBeth, Ang et al., and Bali and Cakici.

3 Data: This chapter describes the sample selection criteria for stocks from the Frankfurt Stock Exchange (General and Prime Standard) and the use of the Fama-French three-factor model.

4 Methodology: This section details the statistical methods used to estimate idiosyncratic volatility and the procedures for constructing and testing quintile portfolios.

5 Results: This chapter presents the empirical findings regarding idiosyncratic volatility estimation, return patterns for different sample periods, and the impact of controlling for firm size.

6 Conclusion: This chapter summarizes the main findings, confirming that the Idiosyncratic Volatility Puzzle is present in the German market when controlled for size, and discusses the implications of the results.

7 Appendix: This section contains additional tables detailing the results of alternative portfolio strategies for both the full sample and the 2003–2016 sub-period.

Keywords

Idiosyncratic Volatility, Asset Pricing, German Stock Market, Fama-French Three-Factor Model, Portfolio Construction, CAPM, Risk Premium, Size Effect, Jensen’s Alpha, Return Reversals, Market Efficiency, Diversification, Equity Returns, Financial Econometrics, Investment Strategies

Frequently Asked Questions

What is the core subject of this paper?

The paper investigates the "Idiosyncratic Volatility Puzzle," which is the phenomenon where stocks with high past idiosyncratic volatility exhibit abnormally low expected returns, specifically testing its presence in the German stock market.

What are the primary themes analyzed?

The research focuses on the relationship between idiosyncratic volatility and expected returns, the impact of different portfolio weighting schemes, and the influence of firm size on these findings.

What is the main research question?

The primary question is whether the negative relationship between cross-sectional expected returns and lagged idiosyncratic volatility, as observed in US and international markets, can also be identified in the German stock market.

Which methodology is employed?

The paper uses the Fama-French three-factor model to estimate idiosyncratic volatility and constructs quintile portfolios based on these estimates, followed by statistical tests to analyze Jensen's alphas and raw returns.

What does the main body of the work cover?

The main body covers a literature review of asset pricing models, data screening procedures for the Frankfurt Stock Exchange, detailed methodological descriptions for volatility estimation, and extensive empirical testing across various strategies and sub-periods.

What are the key terms that characterize this work?

Key terms include Idiosyncratic Volatility, Asset Pricing, Fama-French Three-Factor Model, and Portfolio Construction.

How does this study differ from the work of Ang et al. (2006)?

While this study follows the basic methodology of Ang et al. (2006), it focuses exclusively on the German market and applies additional robustness checks, such as size-controlled double-sorting, which revealed the puzzle in this specific context.

Why is the sub-period 2003–2016 analyzed separately?

The sub-period is analyzed to address potential noise and survivorship bias present in the early sample years (1990–2002) and to provide enough data points for reliable double-sorted portfolio constructions.

What is the significance of the "size control" finding?

Controlling for size is significant because it disentangles the influence of small-cap stocks, revealing that the idiosyncratic volatility puzzle is specifically present for the German market when firm size is taken into account.