Andreas Johansson
RISK FACTORS AND THEIR BOOTSTRAPS
HIDDEN RISKS AND HOW TO CAPTURE THE RISK-PREMIA
Andreas Johansson RISK FACTORS AND THEIR BOOTSTRAPS
ISBN 978-91-7731-194-2
DOCTORAL DISSERTATION IN FINANCE
STOCKHOLM SCHOOL OF ECONOMICS, SWEDEN 2021
RISK FACTORS AND THEIR BOOTSTRAPS
“Characterizing the Tail-Risk of Factor Mimicking Portfolios” establishes that there exist non-linear and complex dependencies in the higher moments, in the crash-risk, of equity returns.
``Smart Beta Made Smart’’ investigates if we can replicate theoretical risk factors using publically available mutual funds and exchange-traded funds.
``How to find Yggdrasil in the forest? Estimation uncertainty and the issue of detecting godlike-performance’’ examine the power properties of the Sharpe ratio and Jensen’s alpha.
ANDREAS JOHANSSON holds a B.Sc. in Economics, B.Sc. in Statistics, and a M.Sc. in Statistics from Uppsala University. He is a researcher at the Department of Finance at Stockholm School of Economics (SSE) and the Swedish House of Finance (SHoF) in Sweden. His main research fields are asset pricing, econometrics, and risk management.
Andreas Johansson
RISK FACTORS AND THEIR BOOTSTRAPS
HIDDEN RISKS AND HOW TO CAPTURE THE RISK-PREMIA
Andreas Johansson RISK FACTORS AND THEIR BOOTSTRAPS
ISBN 978-91-7731-194-2
DOCTORAL DISSERTATION IN FINANCE
STOCKHOLM SCHOOL OF ECONOMICS, SWEDEN 2021
RISK FACTORS AND THEIR BOOTSTRAPS
“Characterizing the Tail-Risk of Factor Mimicking Portfolios” establishes that there exist non-linear and complex dependencies in the higher moments, in the crash-risk, of equity returns.
``Smart Beta Made Smart’’ investigates if we can replicate theoretical risk factors using publically available mutual funds and exchange-traded funds.
``How to find Yggdrasil in the forest? Estimation uncertainty and the issue of detecting godlike-performance’’ examine the power properties of the Sharpe ratio and Jensen’s alpha.
ANDREAS JOHANSSON holds a B.Sc. in Economics, B.Sc. in Statistics, and a M.Sc. in Statistics from Uppsala University. He is a researcher at the Department of Finance at Stockholm School of Economics (SSE) and the Swedish House of Finance (SHoF) in Sweden. His main research fields are asset pricing, econometrics, and risk management.
Risk Factors and their Bootstraps
Hidden Risks and How to Capture the Risk-premia Andreas Johansson
Akademisk avhandling
som för avläggande av ekonomie doktorsexamen vid Handelshögskolan i Stockholm framläggs för offentlig granskning onsdagen den 19 maj 2021, kl 10.00,
Swedish House of Finance, Drottninggatan 98, Stockholm
Risk factors and their bootstraps
Hidden risks and how to capture the risk-premia.
Andreas Johansson
Dissertation for the Degree of Doctor of Philosophy, Ph.D., in Finance
Stockholm School of Economics, 2021
Risk factors and their bootstraps
© SSE and Andreas Johansson, 2021 ISBN 978-91-7731-194-2 (printed) ISBN 978-91-7731-195-9 (pdf)
This book was typeset by the author using LATEX.
Front cover photo: © Robert Kneschke, Shutterstock.com, 2021 Printed by: BrandFactory, Gothenburg, 2021
Keywords: intertemporal dependency, risk factors, skewness, kurtosis, bootstrap, smart beta, daily flows, sharpe ratio, alpha, estimation uncertainty, power
To everyone who has supported me
Foreword
This volume is the result of a research project carried out at the Department of Finance at the Stockholm School of Economics (SSE).
This volume is submitted as a doctoral thesis at SSE. In keeping with the policies of SSE, the author has been entirely free to conduct and present his research in the manner of his choosing as an expression of his own ideas.
SSE is grateful for the financial support provided by the The Swedish Bank Research Foundation, Jan Wallander Foundation, and Louis Fraenckels Foundation which has made it possible to carry out the project.
Göran Lindqvist Per Strömberg
Director of Research Professor and Head of the Stockholm School of Economics Department of Finance
Stockholm School of Economics
Acknowledgements
I’m forever grateful to all the people who have made the completion of this dissertation possible.
First, I’m grateful to my supervisor Michael Halling. He has always been there to support and guide me throughout this journey, keeping me focused on the goal of becoming a solid researcher.
Second, I thank my co-authors Riccardo Sabbatucci and Andrea Tamoni, which have given me a masterclass in doing research of the highest quality. I’m so grateful for the trust they have bestowed on me.
Finally, I’m thankful to Jungsuk Han, who gave me his time and support throughout the program. Not just when I was his teaching assistant but also when I had questions about potential research topics.
Additionally, the faculty has been very supportive and helpful. Magnus Dahlquist was always open to discussing potential research projects. Adrien d’Avernas drilled me before the job-market and finally made me dive into machine learning. Per Strömberg guided me through the non-research-paper-related questions, e.g., how to approach conferences and discuss papers.
The administration has also been key for me completing this dissertation. Anneli Sandbladh always helped me out whenever I had questions about everything from funding to coffee. She was always there, happily helping me out and making the whole journey so much smoother. Jenny Wahlberg helped me out with the course administration and was always available when I had questions about administrative tasks. Hedvig Mattson could quickly resolve any technical issues and often saved me from hours of work by pointing me to the "correct" person. I cannot thank you all enough for making my Ph.D. run smoothly and for making the Ph.D. journey so much more enjoyable.
Then there are a ton of people who have not been directly involved in my Ph.D., but they have been essential for keeping my sanity and inspiring me to push forward during the most stressful parts of the Ph.D.
First, Mahamadi Ouoba, who has been my friend and my moral support throughout the program. Without your drive, passion, and openness to discuss the intricacies of becoming a Doctor, the program would not have been as enjoyable. I am also glad that I got the opportunity to know and spend the last couple of years with the other Ph.D.
viii RISK FACTORS AND THEIR BOOTSTRAPS
candidates in my cohort. Especially Xingyu Zhu, who kept my sanity in check during the job-market and helped me sort through rough ideas throughout the program.
Second, I’m also grateful for my office mates—especially Jieying Li, who made me look forward to going to the office early in the program. I still miss your energy in the office! Markus Ibert was a great inspiration and was always open to discuss research topics, even when I had no clue what I was talking about. Yingjie Qi happily discussed everything from research to kids while demonstrating an unfaltering work ethic. Felix Wilke always brought his sharp mind to every discussion; too bad that the "virus" didn’t give me more opportunities to pick his mind.
Finally, a big thank you to everyone who has made this journey so much more enjoyable by grabbing lunch or just sitting down over a cup of coffee; Yue Tang, Laszlo Sajtos, Alberto Allegrucci, Ivika Jäger, Yavor Kovachev, Anastasia Girshina, Rustem Sadykov, and Katarina Warg.
Also, a big thank you to the great teachers who gave me the confidence and the skills to pursue my research agenda; Jörgen Weibull, Tomas Björk, Albert S. (Pete) Kyle, Pär Mårtensson, and Peter Schotman. I am also grateful to all my students, who have kept my skillset well-polished and up to date.
Last but not least, thanks to my loving family. Especially my wife, Rebecca Tingvall, who has been there during the highs and the lows and with an unfaltering belief in me. I wouldn’t be here without my family’s never-ending love and support.
A big thank you to all of you!
Stockholm, March 20, 2021 Andreas Johansson
Contents
Introduction 1
1 Tail-Risk of Factor Mimicking Portfolios 5
1.1 Theoretical Setup . . . 9
1.2 Empirical Results . . . 13
1.3 Conclusion . . . 23
1.A Appendix . . . 25
1.B References . . . 37
2 Smart Beta Made Smart 41 2.1 Introduction . . . 42
2.2 Literature Review . . . 46
2.3 Data . . . 48
2.4 Descriptive Statistics . . . 50
2.5 Fund classification . . . 54
2.6 Empirical Results . . . 62
2.7 Replicating Factors “by Name” . . . 73
2.8 Conclusion . . . 76
2.A Appendix . . . 85
2.B References . . . 101
3 How to find Yggdrasil in the forest? 107 3.1 Data and Method . . . 110
3.2 Results . . . 115
3.3 Simulations . . . 124
3.4 Conclusion . . . 129
3.A References . . . 131
Introduction
This doctoral thesis is a collection of three independent empirical papers in finance concerning risk-adjusted returns. Under an assumption of a highly efficient market, an investment’s expected returns should be directly related to the investment riskiness.
However, it is often hard to detect and pinpoint your portfolio’s risks in practice.
The first paper, "Characterizing the Tail-Risk of Factor Mimicking Portfolios,"
proposes a new and simple approach of detecting auto-correlation, not just in the first moments but in any statistical moment. By generalizing the variance ratio test of Lo and Mackinlay (1988) to include higher statistical moments, I establish a strong and significant intertemporal dependency in equity returns. Moreover, the dependency structure I unveil is non-linear and complex, implying a term-structure in the crash-risk, the tail-risk, of equity returns. Consequently, depending on which horizon and which risk-factor we are exposed to, the crash risk might increase or decrease as we extend our holding period.
Hence, we need to be careful when extrapolating a short-run risk estimate to a longer horizon.
In the second paper, “Smart Beta Made Smart” (joint with Riccardo Sabbatucci and Andrea Tamoni), we construct synthetic and tradable risk factors using optimal combinations of large and liquid mutual funds and ETFs. Using these synthetic portfolios, we show that investors cannot use mutual funds and ETFs to capture the risk-premia of the most commonly used risk factors. We also propose an empirical approach, using a minimum statistical distance methodology, to classify funds into different strategies. We also show that investors are more likely to put money into funds by their names instead of their actual holdings. And institutional investors seem to do better on average than retail investors, mostly due to more options in the type of funds available. The results have direct implications on how we evaluate portfolio managers and the cross-sectional return anomalies.
The final paper, “How to find Yggdrasil in the forest? Estimation uncertainty and the issue of detecting godlike-performance,” I show that in most real-life situations, we will have too few observations to make a distinction between two different investments with any confidence, even ex-post. Due to the low signal-to-noise ratio in equity returns, it is hard to detect if one investment outperforms another using the Sharpe ratio or the alpha. Therefore, we need to be extremely careful when comparing two investments over
2 RISK FACTORS AND THEIR BOOTSTRAPS
a short time period. Ten years is too short of a time period to distinguish one investment from another unless we believe double digits alpha is common.
INTRODUCTION 3
References
Lo, A. W. and A. C. Mackinlay (1988). “Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification test.” In:The Review of Financial Studies 1.1, pp. 41–66.
