Vlastnosti 1/N portfólia
| Thesis title in thesis language (Slovak): | Vlastnosti 1/N portfólia |
|---|---|
| Thesis title in Czech: | Vlastnosti 1/N portfolia |
| Thesis title in English: | Properties of 1/N portfolio |
| Key words: | 1/N portfolio|Bayesovská statistika|Frekventistická statistika|Oceňování a zajišťování |
| English key words: | 1/N portfolio|Bayesian statistics|Frequentist statistics|Pricing and hedging |
| Academic year of topic announcement: | 2023/2024 |
| Thesis type: | Bachelor's thesis |
| Thesis language: | slovenština |
| Department: | Department of Probability and Mathematical Statistics (32-KPMS) |
| Supervisor: | doc. RNDr. Jan Večeř, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 09.04.2024 |
| Date of assignment: | 10.04.2024 |
| Confirmed by Study dept. on: | 18.06.2024 |
| Date and time of defence: | 03.09.2024 08:30 |
| Date of electronic submission: | 15.07.2024 |
| Date of submission of printed version: | 15.07.2024 |
| Date of proceeded defence: | 03.09.2024 |
| Opponents: | doc. RNDr. Ing. Miloš Kopa, Ph.D. |
| Guidelines |
| The objective of this thesis is to investigate the connection between the 1/N portfolio strategy and the notion of the uninformative prior within Bayesian statistics. This investigation posits each asset as a probabilistic model, each with its unique state price density. When investors allocate their portfolio equally across assets, known as the 1/N portfolio, it symbolically mirrors the selection of an uninformative prior in Bayesian terms. This thesis will delve into the nuances of this connection, specifically how the equally weighted portfolio strategy aligns with the concept of prior distribution and its subsequent influence on the posterior distribution in Bayesian statistics.
Furthermore, the study will juxtapose the 1/N portfolio against a portfolio that mimics the asset yielding the highest return, resembling a frequentist approach to model selection. This comparison aims to examine the hypothesis that both Bayesian and frequentist portfolio strategies converge asymptotically. To empirically validate these theoretical insights, the thesis will employ simulations using real-world data sets, such as a collection of major currencies (e.g., G10) or a set of significant assets (e.g., Dow Jones Industrial Average). Through these simulations, the thesis seeks to provide a comprehensive understanding of how Bayesian and frequentist perspectives manifest in portfolio management, particularly in the context of asset allocation and model selection. |
| References |
| DeMiguel, V., Garlappi, L., & Uppal, R. (2009). Optimal Versus Naive Diversification: How Inefficient is the 1/N Portfolio Strategy? Review of Financial Studies, 22(5), 1915-1953.
Benartzi, S., & Thaler, R. H. (2001). Naive Diversification Strategies in Defined Contribution Saving Plans. American Economic Review, 91(1), 79-98. Vecer, J. (2024). Principles of Bayesian Portfolio Selection, CRC Press, forthcoming. Hastie, T., Tibshirani, R., & Friedman, J. (2009). The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer Series in Statistics. Springer, New York, NY. Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed.). Chapman and Hall/CRC. Malkiel, B. G. (2020). A Random Walk Down Wall Street: The Time-Tested Strategy for Successful Investing (12th ed.). W. W. Norton & Company. Ang, A. (2014). Asset Management: A Systematic Approach to Factor Investing. Oxford University Press. Berger, J. O. (1985). Statistical Decision Theory and Bayesian Analysis (2nd ed.). Springer Series in Statistics. Springer-Verlag, New York, NY. Hahn, E. D., & Greenland, A. (2020). Bayesian Methods for Management and Business: Pragmatic Solutions for Real Problems. Wiley. Greenberg, E. (2012). Introduction to Bayesian Econometrics (2nd ed.). Cambridge University Press. Hilpisch, Y. (2018). Python for Finance: Mastering Data-Driven Finance. O'Reilly Media. |
| Preliminary scope of work |
| Tato práce zkoumá paralelu mezi strategií portfolia 1/N a konceptem neinformativního apriorního rozdělení v bayesovské statistice, a to analýzou, jak se toto přístup porovnává s frekventistickým výběrem modelu prostřednictvím empirických simulací na datech skutečných aktiv. |
| Preliminary scope of work in English |
| This thesis explores the parallel between the 1/N portfolio strategy and the concept of an uninformative prior in Bayesian statistics, analyzing how this approach compares to frequentist model selection through empirical simulations on real-world asset data. |