Bayesian inference of the multi-period optimal portfolio for an exponential utility. (English) Zbl 1435.62104
The paper consider a very interesting problem – the multi-period optimal portfolio for an exponential utility. The stochastic representations for the optimal portfolio weights under both priors are presented which are used to derive the corresponding estimates for the weights together with covariance matrix as well as to prove the posterior asymptotic normality. In empirical study twelve stocks are examined, namely, Barclays, Glaxo Smith Kline, Standard Life, Marks and Spencer, Burberry Group plc, HSBC, Lloyds Banking, NEXT plc, Rolls-Royce Holding, The Sage Group, Tesco plc. and Unilever. The paper describes the behaviour of them.
Reviewer: Rózsa Horváth-Bokor (Budakalász)
MSC:
| 62F15 | Bayesian inference |
| 62E15 | Exact distribution theory in statistics |
| 62H12 | Estimation in multivariate analysis |
| 91B24 | Microeconomic theory (price theory and economic markets) |
| 62P20 | Applications of statistics to economics |
Keywords:
Bayesian estimation; credible sets; multi-period optimal portfolio; posterior predictive distribution; stochastic representationSoftware:
BayesDAReferences:
| [1] | Aguilar, O.; West, M., Bayesian dynamic factor models and portfolio allocation, J. Bus. Econom. Statist., 18, 338-357 (2000) |
| [2] | Ando, T., Bayesian portfolio selection using a multifactor model, Int. J. Forecast., 25, 550-566 (2009) |
| [3] | Avramov, D.; Zhou, G., Bayesian portfolio analysis, Ann. Rev. Financial Econ., 2, 25-47 (2010) |
| [4] | Bai, J.; Shi, S., Estimating high dimensional covariance matrices and its applications, Ann. Econ. Finance, 12, 199-215 (2011) |
| [5] | Barry, C., Portfolio analysis under uncertain means, variances, and covariances, J. Finance, 29, 515-522 (1974) |
| [6] | Basak, S.; Chabakauri, G., Dynamic mean-variance asset allocation, Rev. Financ. Stud., 23, 2970-3016 (2010) |
| [7] | Bauder, D.; Bodnar, R.; Bodnar, T.; Schmid, W., Bayesian estimation of the efficient frontier, Scand. J. Stat., 46, 802-830 (2019) · Zbl 1433.62085 |
| [8] | Bernardo, J. M.; Smith, A. F.M., Bayesian Theory (2000), Wiley · Zbl 0943.62009 |
| [9] | Bodnar, T.; Dette, H.; Parolya, N., Testing for independence of large dimensional vectors, Ann. Statist., 47, 2977-3008 (2019) · Zbl 1436.60018 |
| [10] | Bodnar, T.; Dmytriv, S.; Parolya, N.; Schmid, W., Tests for the weights of the global minimum variance portfolio in a high-dimensional setting, IEEE Trans. Signal Process., 67, 4479-4493 (2019) · Zbl 1543.91094 |
| [11] | Bodnar, T.; Mazur, S.; Okhrin, Y., Bayesian estimation of the global minimum variance portfolio, European J. Oper. Res., 256, 292-307 (2017) · Zbl 1395.91395 |
| [12] | Bodnar, T.; Mazur, S.; Podgórski, K., Singular inverse wishart distribution and its application to portfolio theory, J. Multivariate Anal., 143, 314-326 (2016) · Zbl 1328.62313 |
| [13] | Bodnar, T.; Okhrin, Y., On the product of inverse Wishart and normal distributions with applications to discriminant analysis and portfolio theory, Scand. J. Statist., 38, 311-331 (2011) · Zbl 1246.62132 |
| [14] | Bodnar, T.; Parolya, N.; Schmid, W., A closed-form solution of the multi-period portfolio choice problem for a quadratic utility function, Ann. Oper. Res., 229, 121-158 (2015) · Zbl 1358.91088 |
| [15] | Bodnar, T.; Parolya, N.; Schmid, W., On the exact solution of the multi-period portfolio choice problem for an exponential utility under return predictability, European J. Oper. Res., 246, 528-542 (2015) · Zbl 1346.91261 |
| [16] | Bodnar, T.; Schmid, W., A test for the weights of the global minimum variance portfolio in an elliptical model, Metrika, 67, 2, 127-143 (2008) · Zbl 1433.91150 |
| [17] | Bodnar, T.; Schmid, W., Econometrical analysis of the sample efficient frontier, Eur. J. Finance, 15, 317-335 (2009) |
| [18] | Bodnar, T.; Schmid, W., On the exact distribution of the estimated expected utility portfolio weights: Theory and applications, Statist. Risk Model., 28, 319-342 (2011) · Zbl 1229.91352 |
| [19] | Brandt, M., Portfolio choice problems, (Ait-Sahalia, Y.; Hansen, L., Handbook of Financial Econometrics, volume 1 (2010), Tools and Techniques, North Holland), 269-336 |
| [20] | Brandt, M.; Santa-Clara, W., Dynamic portfolio selection by augmenting the asset space, J. Finance, 61, 2187-2217 (2006) |
| [21] | Brown, S., Optimal Portfolio Choice under Uncertainty: A Bayesian Approach (1976), University of Chicago, (Ph.D. thesis) |
| [22] | Çanakoğlu, E.; Özekici, S., Portfolio selection in stochastic markets with exponential utility functions, Ann. Oper. Res., 166, 281-297 (2009) · Zbl 1163.91374 |
| [23] | Carlin, B. P.; Louis, T. A., Bayes and Empirical Bayes Methods for Data Analysis (2000), Chapman & Hall/CRC · Zbl 1017.62005 |
| [24] | DasGupta, A., (Asymptotic Theory of Statistics and Probability. Asymptotic Theory of Statistics and Probability, Springer Texts in Statistics (2008), Springer) · Zbl 1154.62001 |
| [25] | Elton, E. J.; Gruber, M. J., On the optimality of some multiperiod portfolio selection criteria, J. Bus., 47, 231-243 (1974) |
| [26] | Frost, P.; Savarino, J., An empirical Bayes approach to efficient portfolio selection, J. Financ. Quant. Anal., 21, 293-305 (1986) |
| [27] | Gelman, A.; Carlin, J. B.; Stern, H. S.; Rubin, D. B., Bayesian Data Analysis, volume 2 (2014), Chapman & Hall/CRC Boca Raton: Chapman & Hall/CRC Boca Raton FL, USA · Zbl 1279.62004 |
| [28] | Gibbons, M. R.; Ross, S. A.; Shanken, J., A test of the efficiency of a given portfolio, Econometrica, 57, 1121-1152 (1989) · Zbl 0679.62097 |
| [29] | Givens, G. H.; Hoeting, J. A., Computational Statistics (2012), John Wiley & Sons |
| [30] | Gupta, A.; Nagar, D., Matrix Variate Distributions (2000), Chapman and Hall/CRC: Chapman and Hall/CRC Boca Raton · Zbl 0935.62064 |
| [31] | Gupta, A.; Varga, T.; Bodnar, T., Elliptically Contoured Models in Statistics and Portfolio Theory (2013), Springer · Zbl 1306.62028 |
| [32] | Isserlis, L., On a formula for the product-moment coefficient of any order of a normal frequency distribution in any number of variables, Biometrika, 12, 134-139 (1918) |
| [33] | Klein, R.; Bawa, V., The effect of estimation risk on optimal portfolio choice, J. Financ. Econ., 3, 215-231 (1976) |
| [34] | Kotz, S.; Nadarajah, S., Multivariate \(t\) Distributions and their Applications (2004), Cambridge University Press: Cambridge University Press Cambridge, United Kingdom · Zbl 1100.62059 |
| [35] | Li, D.; Ng, W.-L., Optimal dynamic portfolio selection: Multiperiod mean-variance formulation, Math. Finance, 10, 387-406 (2000) · Zbl 0997.91027 |
| [36] | Markowitz, H., Portfolio selection, J. Finance, 7, 77-91 (1952) |
| [37] | Markowitz, H., Portfolio Selection: Efficient Diversification of Investments (1959), John Wiley: John Wiley New York |
| [38] | Mathai, A. M.; Provost, S. B., Quadratic Forms an Random Variables (1992), Marcel Dekker: Marcel Dekker New York · Zbl 0792.62045 |
| [39] | Merton, R. C., Lifetime portfolio selection under uncertainty: the continuous time case, Rev. Econ. Stat., 50, 247-257 (1969) |
| [40] | Meyer, C. D., Matrix Analysis and Applied Linear Algebra (2000), SIAM · Zbl 0962.15001 |
| [41] | Mossin, J., Optimal multiperiod portfolio policies, J. Bus., 41, 215-229 (1968) |
| [42] | Muirhead, R. J., Aspects of Multivariate Statistical Theory (1982), Wiley: Wiley New York · Zbl 0556.62028 |
| [43] | Okhrin, Y.; Schmid, W., Distributional properties of portfolio weights, J. Econometrics, 134, 235-256 (2006) · Zbl 1420.91430 |
| [44] | Pástor, L., Portfolio selection and asset pricing models, J. Finance, 55, 179-223 (2000) |
| [45] | Pástor, L.; Stambaugh, R. F., Comparing asset pricing models: an investment perspective, J. Financ. Econ., 56, 335-381 (2000) |
| [46] | Pennacchi, G. G., Theory of Asset Pricing (2008), Pearson/Addison-Wesley Boston |
| [47] | Polson, N. G.; Tew, B. V., Bayesian portfolio selection: An empirical analysis of the S&P 500 index 1970-1996, J. Bus. Econom. Statist., 18, 164-173 (2000) |
| [48] | Rachev, S. T.; Hsu, J. S.J.; Bagasheva, B. S.; Fabozzi, F. J., Bayesian Methods in Finance (2008), Wiley: Wiley New Jersey |
| [49] | Samuelson, P. A., Lifetime portfolio selection by dynamic stochastic programming, Rev. Econ. Stat., 51, 239-246 (1969) |
| [50] | Sekerke, M., Bayesian Risk Management: A Guide to Model Risk and Sequential Learning in Financial Markets (2015), Wiley: Wiley New Jersey |
| [51] | Shanken, J., On the estimation of beta-pricing models, Rev. Financ. Stud., 5, 1-33 (1992) |
| [52] | Shanken, J.; Zhou, G., Estimating and testing beta pricing models: Alternative methods and their performance in simulations, J. Financ. Econ., 84, 40-86 (2007) |
| [53] | Sun, D.; Berger, J., Objective Bayesian analysis for the multivariate normal model, (Bernardo, J. M.; Bayarri, M. J.; Berger, J. O.; Dawid, A. P.; Heckerman, D.; Smith, A. F.M.; West, M., Bayesian Statistics, volume 8 (2007), Oxford: University Press), 525-547 · Zbl 1252.62030 |
| [54] | Winkler, R. L., Bayesian models for forecasting future security prices, J. Financ. Quant. Anal., 8, 387-405 (1973) |
| [55] | Winkler, R. L.; Barry, C. B., A Bayesian model for portfolio selection and revision, J. Finance, 30, 179-192 (1975) |
| [56] | Zellner, A., An Introduction to Bayesian Inference in Econometrics (1971), John Wiley: John Wiley New York · Zbl 0246.62098 |
| [57] | Zellner, A.; Ando, T., A direct Monte Carlo approach for Bayesian analysis of the seemingly unrelated regression model, J. Econometrics, 159, 33-45 (2010) · Zbl 1431.62295 |
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