Portfolio Selection with Probabilistic Utility, Bayesian Statistics, and Markov Chain Monte Carlo
AbstractWe propose a novel portfolio selection approach that manages to ease some of the problems that characterise standard expected utility maximisation. The optimal portfolio is no longer defined as the extremum of a suitably chosen utility function: the latter, instead, is reinterpreted as the logarithm of a probability distribution for optimal portfolios and the selected portfolio is defined as the expected value with respect to this distribution. A further theoretical aspect is the adoption of a Bayesian inference framework. We find that this approach has several attractive features, when comparing it to the standard maximisation of expected utility. We remove the over-pronounced sensitivity on external parameters that plague optimisation procedures and obtain a natural and self consistent way to account for uncertainty in knowledge and for personal views. We test the proposed method against traditional expected utility maximisation, using artificial data to simulate finite-sample behaviour, and find superior performance of our procedure. All numerical integrals are carried out by using Markov Chain Monte Carlo, where the chains are generated by an adapted version of Hybrid Monte Carlo. We present numerical results for a portfolio of eight assets using historical time series running from January 1988 to January 2002.
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Bibliographic InfoPaper provided by EconWPA in its series Finance with number 0211003.
Length: 27 pages
Date of creation: 19 Nov 2002
Date of revision: 28 Nov 2002
Note: Type of Document - Postscript; prepared on PC; to print on HP/PostScript/Franciscan monk; pages: 27 ; figures: within article. 27 pages, Postscript, figures included
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Bayesian Statistics; Estimation Risk; Finite Sample; Markov Chain Monte Carlo; Portfolio Selection;
Find related papers by JEL classification:
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
- C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
This paper has been announced in the following NEP Reports:
- NEP-ALL-2002-11-28 (All new papers)
- NEP-CFN-2002-11-28 (Corporate Finance)
- NEP-CMP-2002-11-28 (Computational Economics)
- NEP-FIN-2002-11-28 (Finance)
- NEP-IFN-2002-11-28 (International Finance)
- NEP-RMG-2002-11-28 (Risk Management)
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