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Are realized moments useful for stock market returns analysis?
Název práce v češtině: Jsou realizované momenty užitečné pro analýzu výnosů akcií?
Název v anglickém jazyce: Are realized moments useful for stock market returns analysis?
Klíčová slova: Realizované momenty, skloněnost, špičatost, oceňování aktiv, akciové trhy
Klíčová slova anglicky: realized moments, skewness, kurtosis, asset pricing, stock market
Akademický rok vypsání: 2016/2017
Typ práce: diplomová práce
Jazyk práce: angličtina
Ústav: Institut ekonomických studií (23-IES)
Vedoucí / školitel: doc. PhDr. Jozef Baruník, Ph.D.
Řešitel: skrytý - zadáno vedoucím/školitelem
Datum přihlášení: 05.06.2017
Datum zadání: 05.06.2017
Datum a čas obhajoby: 19.06.2019 09:00
Místo konání obhajoby: Opletalova - Opletalova 26, O206, Opletalova - místn. č. 206
Datum odevzdání elektronické podoby:01.04.2019
Datum proběhlé obhajoby: 19.06.2019
Oponenti: prof. Ing. Evžen Kočenda, M.A., Ph.D., DSc.
Kontrola URKUND:
Seznam odborné literatury
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Andersen, T., Bollerslev, T., Diebold, F., & Ebens, H. (2001). The distribution of realized stock return volatility. Journal of Financial Economics, 43-76.
Andersen, T., Bollerslev, T., Diebold, F., & Labys, P. (2001). The Distribution of Realized Exchange Rate Volatility. Journal of the American Statistical Association, 96(453), 42-55.
Andersen, T., Bollerslev, T., Diebold, F., & Labys, P. (2003). Modeling and Forecasting realized volatility. Econometrica, 71(2), 529-626.
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Bakshi, G., Kapadia, N., & Madan, D. (2003). Stock return characteristics, skew laws, and the differential pricing of individual equity options. Review of Financial Studies, 16(1), 101-143.
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Bonato, M. (2011). Robust estimation of skewness and kurtosis in distributions with infinite higher moments. Finance Research Letters 8, 8(2), 77-87.
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Předběžná náplň práce v anglickém jazyce
It has been a never-ending struggle to understand the properties of stock returns and be able to forecast their future development. From simple AR and MA models, through GARCH and their fractionally integrated versions, to intra-day data based models such as HAR, researchers and investors alike have been trying to analyze and forecast the behavior of returns. The question of stock return properties is of the utmost importance when it comes to portfolio or risk management.

This thesis aims to gain further understanding of stock returns on two different levels: 1) Further understand distributional properties of returns – so far, there have been various attempts to forecast future returns and future volatility. This thesis aims to explore whether it is possible to predict also realized skewness and kurtosis and gain additional insights into the distribution of returns. 2) Establish, whether current realized skewness or kurtosis can be used in forecasts of future returns or volatility, and whether disregarding skewness and kurtosis has a detrimental effect on the quality of such predictions.

The intuition behind the use of skewness and kurtosis in the financial market modelling is, that volatility should not be the only measure of risk on the market. Two distributions with same mean and variance might have completely different kurtosis: thus, when speaking about returns, the two distributions also carry a different amount of risk as a high kurtosis increases the uncertainty about the actual returns. Moreover, the distribution of returns need not be symmetric, thus making positive returns more or less likely than negative returns. Thus, additional knowledge about two moments might be very helpful in investors’ decision making.

The current literature - such as Amaya et al (2015) or Chang et al (2013) - mostly focused on cross-sectional analysis of returns and their realized moments. It is the goal of this thesis to address also the time-series forecasting of future returns using the realized moments.

Furthermore, Corsi and Reno (2009) use HAR with heterogeneous leverage and jumps to model volatility. It seems natural to ask, whether inclusion of realized skewness and kurtosis in the model would have a significant positive impact on the said model performance.


1. Hypothesis #1: realized moments can be used to forecast future returns.
2. Hypothesis #2: current realized moments are not independent of past realized moments
3. Hypothesis #3: higher kurtosis should be compensated by higher expected return
4. Hypothesis#4: realized moments improve HAR’s performance in 1 day ahead volatility forecasting
5. Hypothesis #5: realized moments improve HAR’s performance in multi-period volatility forecasts


The current plan is to use 5-minute intraday data for 29 most liquid US companies spanning the years 2005-2015. This dataset includes information about the prices in each of the time intervals. From this information, log returns will be calculated and subsequently used to calculate the realized measures.

The above-mentioned measures will be used for the analysis of stock market returns as described in the Motivation section of this proposal. The individual time series will be modelled using these measures and the validity of the models will be evaluated using the out of sample forecast together with a benchmarking against some of the other techniques used in financial time-series modelling, such as ARIMA or HAR for log-returns and GARCH or HAR for volatility. Where applicable, robust statistical methods shall be used to verify the estimation results. While the robust methods in time-series setting might not be wide-spread, there have been some applications even in the volatility modelling (Croux et al. (2011))

One additional possible technique to model the joint fluctuation of returns, volatility, skewness and kurtosis might be a VAR model, but I will have to explore this option further in the process of working on the thesis.
Expected Contribution:
This thesis hope to provide further insights into the behavior of stock market returns. If the results of the research suggest that the realized measures are useful for the analysis of stock returns, these measures might be used for investment decisions and risk management. Otherwise, it will be evident that some different approaches should be explored.


1. Introduction
2. Literature Review
3. Data
4. Methodology
5. Results
6. Conclusion
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