Coherent Asset Allocation and Diversification in the Presence of Stress Events

Rebonato, Riccardo and Denev, Alexander (2011): Coherent Asset Allocation and Diversification in the Presence of Stress Events.

Abstract

We propose a method to integrate frequentist and subjective probabilities in order to obtain a coherent asset allocation in the presence of stress events. Our working assumption is that in normal market asset returns are sufficiently regular for frequentist statistical techniques to identify their joint distribution, once the outliers have been removed from the data set. We also argue, however, that the exceptional events facing the portfolio manager at any point in time are specific to the each individual crisis, and that past regularities cannot be relied upon. We therefore deal with exceptional returns by eliciting subjective probabilities, and by employing the Bayesian net technology to ensure logical consistency. The portfolio allocation is then obtained by utility maximization over the combined (normal plus exceptional) distribution of returns. We show the procedure in detail in a stylized case.

• Item Type: MPRA Paper
• Language: English
• Keywords: Stress tests, asset allocation, Bayesian Networks
• Subjects: G - Financial Economics > G1 - General Financial Markets > G11 - Portfolio Choice ; Investment Decisions

References

Bank of International Settlements (BIS), (2009), Principles for Sound Stress Testing and Supervision — Consultative Paper, January 2009, latest version May 2009 Black, F and Litterman, R, (1992), Global Portfolio Optimization, Financial Analysts Journal, September 1992, pp. 28-43 Bouchaud, J-P, Potter, M, (2000, 2004), Theory of Financial Risk — From Statistical Physics to Risk Management, Cambridge University Press, Cambridge, UK Ceria, S., Stubbs R.A. (2004), Incorporating Estimation Errors into Portfolio Selection: Robust Efficient Frontiers, Axioma Inc. Technical Report Cherubini, U, Luciano, E, Vecchiato, W, (2004), Copula Methods in Finance, John Wiley & sons, Chicester Cochrane, J, (2004), Asset Pricing, Princeton University Press, Princeton, NJ Connor, G, Goldberg L R, Korajczyk R A, (2010), Portfolio Risk Analysis, Princenton University Press, Princeton, NJ de Kluyver, C, A, Moskowitz, H, (1984), Assessing Scenario Probabilities Via Goal Programming, Management Science, Vol 30, (March 1984), No 3, 273-278 Efron B, Tibshirani R, (1986), Bootstrap Methods for Standard Errors, Confidnce Intervals and Other Measures of Statistical Accuracy, Statistical Sceince, Vol 1, number 1, 54-75 El-Erian M A, (2010), Looking Ahead, Journal of Portfolio Management, Vol 36. No 2, Winter 2010, Page 4 Frydman R, Goldberg M D, (2007), Imperfect Knowledge Economics: Exchange Rates and Risk, Princeton University Press, Princeton, NJ Frydman R, Goldberg M D, (2009), Financial Markets and the State: Long Swings, Risk and the Scope of Regulation, Capitalism and Society, Vol 4, Issue 2, Article 2, available at: http://www.bepress.com/cas/vol4/iss2/art2, last accessed 20th November, 2009, Berkeley Electronic Press Davidson P, (2010), Risk and Uncertainty, in The Economic Crisis and the State of Economics, Skidelski and Wigstroem, Editors, Palgrave, Macmillan, New York Engle, R, (2009), Anticipating Correlations: A New Paradigm for Risk Management, Princeton Univeristy Press, Princeton, NJ Ferguson, T S, (1961), On the Rejection of Outliers, in Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability,pp. 253–287. Friedman, M, (1953), Essays in Positive Economics, University of Chicago press, Chicago, IL Garside, G R, Rhodes, P C, Holmes, D E, (1999), The Efficient Estimation of Missing Information in Causal Inverted Multiway Trees, Knowledge-Based Systems, 12, 101—111 Genest, C, Remillard, B, Beaudoin D, (2009), Goodness-of-Fit Tests for Copulas: A Review and Power Study, Insurance: Mathematics and Economics, Volume 44, issue 2, April 2009, 199-213 Gilio, A, (1995), Probabilistic Consistency of Conditional Probability Bounds, Lecture Notes in Computer Science, Vol 945, 200-209 Grubbs, F E, (1969), Procedures for Detecting Outlying Observations in Samples, Technometrics, 11, 1, 1-21. Kole, E, Koedijk K, Verbeek M, (2007), Selecting Copulas for Risk Management, Journal of Banking & Finance, Vol. 31, number 8, pag. 2405-2423 Kwiatkowski, J, Rebonato, R, (2010), A Coherent Aggregation Framework for Stress Testing and Scenario Analysis, accepted for publication in Applied Mathematical Finance Malevergne, Y, Sornette, D, (2001), Testing the Gaussian Copula Hypothesis for Financial Assets Dependences, Finance 0111003, EconWPA Mantegna, R N, Stanley, H E, (2000), An Introduction to Econophysics — Correlations and Complexity in Finance, Cambridge University Press, Cambridge, UK Markham, M J, Rhodes, P C, (1999), Maximixing Entropy to Deduce an Initial Probability Distribution for a Causal Network, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, Vol 7, No 1, 63-80 Markowitz, H, (1959, 1991), Portfolio Selection, Blackwell, Oxford Markowitz, H, (1987), Mean-Variance Analysis in Portfolio Choice and Capital Markets, Blackwell, Oxford Merton R, (1971), Optimum Consumption and Portfolio Rules in a Continuous Time Model, Journal of Economic Theory, 3, 373-413 Meucci, A, (2007), Risk and Asset Allocation, Springer Finance, Berlin Moore, A, (2001), Bayes Nets for Representing and Reasoning About Uncertainty, CarnegieMellon University, http://www.autonlab.org/tutorials/bayesnet09.pdf, last accessed 18th August, 2009 Moskowitz, H, Sarin, R K, (1983), Improving the Consistency of Conditional Probability Assessment for Forecasting and Decision Making, Management Science, Vol 29, No 6, (June 1983), 735-749 Olmo J.(2009), Extreme Value Theory Filtering Techniques for Outlier Detection, City University Economics Discussion Papers No 09/09 Potters, M, (2010), Lessons from Statistical Finance, in The Economic Crisis and the State of Economics, Skidelski and Wigstroem, Editors, Palgrave, Macmillan, New York Pearl, J , (2009), Causality, 2nd edition, Cambridge University Press, Cambridge, UK Rebonato, R, (2010a), Coherent Stress Testing — A Bayesian Approach to Financial Stress, John Wiley, Chichester Rebonato, R, (2010b), A Bayesian Approach to Stress Testing and Scenario Analysis, Journal of Investment Management, Vol. 8, No. 3, (2010), pp. 1—13 Rebonato, R (2010c), A Bayesian Approach to Coherent Stress Testing, in Rethinking Risk Measurement, Klaus Bloeker Editor, Incisive Media, London Rebonato, R, Chen J, (2009), Evidence for State Transition and Altered Serial Co-dependence in US$ Interest Rates, Quantitative Finance, vol 9, No 3, April 2009, 259-278 Rebonato, R, Gaspari V, (2006), Analysis of Drawdowns and Drawups in the US Interest-Rate Market, Quantitative Finance, 6(4), 297-326 Rebonato, R, Jaeckel, P, (1999), The Most General Methodology to Create a Valid Correlation Matrix for Risk Management and Option Pricing Purposes, Journal of Risk, Vol 2, Number 2, Winter 1999/2000, 17-28 Rochet, J-C, (2010), The Future of Banking Regulation, Chapter 3 in Balancing the Banks - Global Lessons from the Financial Crisis, M Dewatripont, J-C Rochet and J Tirole, Princeton University Press, Princeton, NJ Samuleson P, (1969), Lifetime Portfolio Selection by Dynamic Stochastic Programming, Review of Economics and Statistics, 51, 239-246 Schluter, C, Trede M, (2002), Identifying Multiple Outliers in Heavy-Tailed Distributions with an Application to Market Crashes, Journal of Empirical Finance Vol. 15, issue 4, 700-713 Schramm, M, Fronhoefer, B, (2005), Completing Incomplete Bayesian Networks, in G. Kern-Isberner, W. Roedder, and F. Kulmann (Eds.): WCII 2002, LNAI 3301, pp. 200—218, Springer-Verlag, Berlin Heidelberg. Sornette, D, (2004), Critical Phenomena in Physical Sciences, Springer Verlag, Berlin Sornette, D and Johansen, A, (2001), Significance of Log-Periodic Precursors to Financial Crashes, Quantitative Finance, Vol 1, 452-471 Tzani, R, and Polychronakos A P, (2008), Correlation Breakdown, Copula Credit Models and Arbitrage, GARP Risk Review, December 2008, 27-37 Tverski, A, Kahneman, D, (1979), Causal Schemata in Judgments under Uncertainty, in Progress in Social Psychology, M. Fishbein (Ed.), Lawrence Erlbaum Associates, Hillsdale, 1979 Williamson, J, (2005), Bayesian Nets and Causality — Philosohpical and Computational Foundations, Oxford University Press, Oxford