Investment horizon in the CAPM: A comparison of a wavelet-based decomposition and the fractal regression

• Název práce v češtině: Investiční horizont v CAPM: Porovnání vlnkové dekompozice a fraktálové regrese
• Název v anglickém jazyce: Investment horizon in the CAPM: A comparison of a wavelet-based decomposition and the fractal regression
• Klíčová slova: CAPM, oceňování aktiv, víceškálová analýza, vlnky, fraktálová regrese
• Klíčová slova anglicky: CAPM, asset pricing, multiscale analysis, wavelets, fractal regression
• Akademický rok vypsání: 2019/2020
• Typ práce: diplomová práce
• Jazyk práce: angličtina
• Ústav: Institut ekonomických studií (23-IES)
• Vedoucí / školitel: prof. PhDr. Ladislav Krištoufek, Ph.D.
• Řešitel: skrytý - zadáno vedoucím/školitelem
• Datum přihlášení: 03.06.2020
• Datum zadání: 03.06.2020
• Datum a čas obhajoby: 15.09.2021 09:00
• Místo konání obhajoby: Opletalova - Opletalova 26, O314, Opletalova - místn. č. 314
• Datum odevzdání elektronické podoby: 22.07.2021
• Datum proběhlé obhajoby: 15.09.2021
• Oponenti: Mgr. Lukáš Vácha, Ph.D.

Seznam odborné literatury

List the most important papers you are going to use (specify at least 5 relevant references).

Black, Fischer (1993). ‘Beta and Return’. The Journal of Portfolio Management 20 (1), pp. 8–18. doi: 10.3905/jpm.1993.409462.

Gençay, Ramazan, Selçuk, Faruk and Whitcher, Brandon (2003). ‘Systematic risk and timescales’. Quantitative Finance 3 (2), pp. 108–116. doi: 10.1088/1469-7688/3/2/305.

Gençay, Ramazan, Selçuk, Faruk and Whitcher, Brandon (2005). ‘Multiscale systematic risk’. Journal of International Money and Finance 24 (1), pp. 55–70. issn: 0261-5606. doi: 10.1016/j.jimonfin.2004.10.003.

In, Francis and Kim, Sangbae (2012). An Introduction to Wavelet Theory in Finance: A Wavelet Multiscale Approach.World Scientific Publishing Company. isbn: 9789814397834.

Kristoufek, L. (2015). Detrended fluctuation analysis as a regression framework: Estimating dependence
at different scales. Physical Review E, 91, 022802.

Kristoufek, L., & Ferreira, P. (2018). Capital asset pricing model in Portugal: Evidence from fractal
regressions. Portuguese Economic Journal, 17(3), 173–183.

Tilfani, Oussama, Ferreira , Paulo & Boukfaoui My Youssef El (2020) Multiscale optimal portfolios using CAPM fractal regression: estimation for emerging stock markets, Post-Communist Economies, 32:1, 77-112, DOI: 10.1080/14631377.2019.1640983

Percival, Donald B. and Walden, Andrew T. (2000). Wavelet Methods for Time Series Analysis. Cambridge University Press. isbn: 0-521-64068-7. doi: 10.1017/cbo9780511841040.

Sharpe, William F. (1964). ‘Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk’. The Journal of Finance 19 (3), p. 425. doi: 10.2307/2977928.

Předběžná náplň práce v anglickém jazyce

Motivation:
Why is it important to work on this specific topic? Refer to previous literature related to your topic. Try to read your motivation to some of your colleagues and see if they find it interesting.

The capital asset pricing model presented by Sharpe (1964) influences practitioners and academics for decades. It tries to explain the risk-return relationship in a simple way. Investors use it to evaluate the riskiness of their portfolios and it helps them to take the right investment decisions. Despite numerous critiques, it has become one of the cornerstones of the modern portfolio theory.

Multiscale extensions of the CAPM (e.g. Gençay, Selçuk and Whitcher 2005 and Tilfani, Ferreira and Boukfaoui 2020) can discover new information about risk-return relationship, which is hidden to traditional methods. In addition, such extension has very straightforward interpretation of investment horizon. Investors have different investment horizons and, as they all meet in the financial markets, they influence it in a slightly different way. The extension of the original model with investment horizon also responds to some of the critiques of the CAPM and such relationship is in line with assumption of the fractal market hypothesis.

Increasing number of publications try to extend the CAPM with investment horizon using advanced mathematical methods like Fourier transform, wavelets, or fractals. Such models seem to provide with promising results, but further research on this topic is still required to fully understand the extended models. For example, majority of papers focuses on only one way and it is unclear how successful different methodologies are in bringing the investment horizon into the model.

The thesis will try to bring some clarity into this topic by estimating the multiscale CAPM by two different frameworks. One is based on wavelet decomposition, which is becoming quite common in asset pricing, and other based on detrend fluctuation analysis, which has been applied in asset pricing only very recently. The goal to verify whether both methods leads to the same conclusions about scale-specific riskiness of selected assets.

Overall, the topic of multiscale beta is very up-to-date and, given the popularity of asset pricing models, investors and researchers could benefit from any progress in this area.
Hypotheses:
1. Wavelet-based methods captures some scale-specific relationship in the CAPM
2. Fractal regression captures some scale-specific relationship in the CAPM
3. Results of wavelet-based methods and fractal regression leads to the same scale-specific conclusion about riskiness of an asset
Methodology:
Explain in detail how you plan to test each hypothesis. Include a concrete description of the material you are going to work with (e.g., data sources).

I will need return from selected market(s) and the risk-free rate for that market. These data are obtainable from public sources and databases available at our institute. Then, I will apply the two methods to estimate the CAPM at different scales. Finally, I interpret its results and compare whether the interpretation about riskiness of given asset is consistent for both methods.

First, I will use the maximal overlap discrete wavelet transform to obtain wavelet and scaling coefficients, which extracts high and low frequency movement from the data. Then I will apply the ordinary OLS framework to estimate the beta and standard errors based on the coefficients from previous step. This methodology is based on e.g. Gençay, Selçuk and Whitcher (2005).

Second, I will estimate the CAPM using fractal regression framework proposed by Kristoufek (2015). I expect to follow the methodology of e.g. Kristoufek and Ferreira (2018) or Tilfani, Ferreira and Boukfaoui (2020). In this framework, the beta is obtained through detrend fluctuation analysis and the standard errors are calculated using bootstrap.

Lastly, I will verify whether results for both methods lead to the same conclusion about riskiness of an asset. The nature of results will not be suitable for a proper statistical testing, but both methods allows me to verify whether an asset is rather defensive or aggressive at given frequency band.
Expected Contribution:
What new do you plan to bring to the current discussion in the academic literature? How could your results be used in practice?

The thesis will evaluate two promising methods of incorporating the investment horizon into the CAPM. Although some papers on the multiscale CAPM have been already published, they focus on one method only and they do not offer any comparison of above-mentioned methods. It is currently unclear how a choice of different methodology influences results and conclusions about scale-specific risk-return relationship captured by the CAPM.

The thesis contributes to the current literature with such comparison as well as original results of estimation, which may be of interest for other researchers and practitioners. Despite numerous publications on the CAPM, the thesis focuses on a very specific part of asset pricing which is not well documented yet. To increase the credibility of the results and to facilitate future research in this area, I will focus on making the results easily reproducible.
Outline:
The expected structure of your thesis (try to be specific).
1) Introduction
2) Literature review
3) Methodology
a. CAPM
b. Wavelet-based decomposition
c. Fractal regression
4) Empirical part
a. Data description
b. Wavelet-based decomposition
c. Fractal regression
5) Conclusion