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Portfolio Choice and Estimation Risk. A Comparison of Bayesian to Heuristic Approaches*

Published online by Cambridge University Press:  17 April 2015

Herold Ulf  and
Maurer Raimond
Herold Ulf
Affiliation:
Metzler Investment GmbH and Johann Wolfgang Goethe University, Frankfurt/Main, Germany, Grosse Gallusstr. 18, 60311 Frankfurt/Main, Germany, Tel.: +49 69 2104 1138, Email: [email protected]
Maurer Raimond
Affiliation:
Johann Wolfgang Goethe University, Frankfurt/Main, Germany Faculty of Business and Economics, Department of Finance, Senckenberganlage 31-33 (Uni-PF 58), 60054 Frankfurt/Main, Germany, Tel.: +49 69 798 25227, Email: [email protected]
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Abstract

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Estimation risk is known to have a huge impact on mean/variance optimized portfolios, which is one of the primary reasons to make standard Markowitz optimization unfeasible in practice. This issue has attracted new interest in the last years, and several approaches to incorporate estimation risk into portfolio selection have been developed only recently. In this article, we review these approaches as well as some older ones and compare them in an empirical out-of-sample study. The approaches can be classified along two criteria. First, we can differentiate heuristic approaches (restricting portfolio weights and employing simulation techniques) and those based on Bayesian statistics (shrinking the portfolios towards a pre-determined target). Second, the assumptions about the return-generating process differ, either assuming returns to be IID distributed or to be partly predictable. The central result of our empirical study is that all of the IID approaches, whether they account for estimation risk or not, are not superior to simple investment strategies like holding the market portfolio. A risk-adjusted outperformance is possible only if sample means are substituted with conditional expected return estimates. Furthermore, the Bayesian approaches reduce turnover and stabilize portfolio weights.

Keywords

Portfolio selectionestimation riskpredictive regressions
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 36 , Issue 1 , May 2006 , pp. 135 - 160
Copyright
Copyright © ASTIN Bulletin 2006

Footnotes

*

The authors profited from the comments of two anonymous referees. The authors also thank Thanh H. Vo for excellent research assistance. This research project was supported by the German Investment and Asset Management Association and the E-finance lab at the Goethe-University Frankfurt.

References

Ang, A. and Bekaert, G. (2003) Stock return predictability: Is it there?, Working Paper Columbia University.Google Scholar
Banz, R.W. (1997) Editorial: Zero correlation between theory and practice in financial economics?, Finanzmarkt und Portfoliomanagement 11, 383–391.Google Scholar
Barry, C.B. (1974) Portfolio analysis under uncertain means, variances, and covariances, Journal of Finance 29, 515–522.CrossRefGoogle Scholar
Beller, K.R., Kling, J.L. and Levinson, M.J. (1998) Are industry stock returns predictable?, Financial Analysts Journal 54, September/October, 42–57.CrossRefGoogle Scholar
Best, M. and Grauer, R. (1991) On the sensitivity of mean variance efficient portfolios to changes in asset means. Some analytical and computational results, The Review of Financial Studies 4, No. 2, 315–342.CrossRefGoogle Scholar
Black, F. and Litterman, R. (1992) Global Portfolio Optimization, Financial Analysts Journal, September/October, 8–43.Google Scholar
Campbell, J.Y. (1987) Stock returns and the term structure, Journal of Financial Economics 18, 373–399.CrossRefGoogle Scholar
Campbell, J.Y. and Shiller, R.J. (1988) Stock prices, earnings, and expected dividends, Journal of Finance 43, 661–676.CrossRefGoogle Scholar
Campbell, J.Y. and Viceira, L.M. (2002) Strategic asset allocation, Clarendon Lectures in Economics: Oxford University Press.CrossRefGoogle Scholar
Chen, N., Roll, R. and Ross, S.A. (1986) Economic forces and the stock market, Journal of Business 59, 383–403.CrossRefGoogle Scholar
Chopra, V. and Ziemba, W.T. (1993) The effect of errors in means, variances, and covariances on optimal portfolio choice, Journal of Portfolio Management 19, 6–11.CrossRefGoogle Scholar
Chopra, V.K., Hensel, C.R. and Turner, A.L. (1993) Massaging mean/variance inputs: Returns from alternative global investment strategies in the 1980s, Management Science 39, 845–855.CrossRefGoogle Scholar
Cochrane, J.H. (1999) Portfolio advice for a multifactor world, in: Federal Reserve Bank of Chicago Economic Perspectives 23, No. 3, 59–78 Google Scholar
Connor, G. (1997) Sensible return forecasting for portfolio management, in: Financial Analysts Journal 53, September/October, 44–51.CrossRefGoogle Scholar
DeMiguel, V., Garlappi, L. and Uppal, R. (2005) How inefficient is the 1/N asset allocation strategy?, Working Paper.Google Scholar
Doan, T., Litterman, R. and Sims, C. (1984) Forecasting and conditional projecting using realistic prior distributions, Econometric Reviews 3, 1–100.CrossRefGoogle Scholar
Efron, B. (1979) Bootstrap methods: Another look at the jackknife, Annals of Statistics 7, 1–26.CrossRefGoogle Scholar
Eichhorn, D., Gupta, F. and Stubbs, E. (1998) Using constraints to improve the robustness of asset allocation, Journal of Portfolio Management 24, Spring, 41–48.CrossRefGoogle Scholar
Fama, E.F. (1991) Efficient capital markets: II, Journal of Finance 46, 1575–1617.CrossRefGoogle Scholar
Fama, E.F. and French, K. (1988) Dividend yields and expected stock returns, Journal of Financial Economics 22, 3–25.CrossRefGoogle Scholar
Fama, E.F. and French, K. (1989) Business conditions and expected returns on stocks and bonds, Journal of Financial Economics 25, 23–49.CrossRefGoogle Scholar
Fama, E.F. and Schwert, G.W. (1977) Asset returns and inflation, Journal of Financial Economics 5, 15–146.CrossRefGoogle Scholar
Ferson, W.E. and Harvey, C.R. (1991) The variation of economic risk premiums, Journal of Political Economy 99, 385–415.CrossRefGoogle Scholar
Ferson, W.E. and Harvey, C.R. (1993) The risk and predictability of international equity returns, Review of Financial Studies 6, 527–566.CrossRefGoogle Scholar
Fletcher, J. (1997) An investigation of alternative estimators of expected returns in mean-variance analysis, Journal of Financial Research 20, 129–143.CrossRefGoogle Scholar
Fletcher, J. and Hillier, J. (2001) An examination of resampled portfolio efficiency, Financial Analysts Journal 57, September/October, 66–74.CrossRefGoogle Scholar
Frost, P. and Savarino, J. (1986) An empirical Bayes approach to efficient portfolio selection, Journal of Financial and Quantitative Analysis 21, 293–305.CrossRefGoogle Scholar
Frost, P. and Savarino, J. (1988) For better performance: Constrain portfolio weights, Journal of Portfolio Management 14, 29–34.CrossRefGoogle Scholar
Goyan, A. and Welsch, I. (2003) Predicting the equity premium with dividend ratios, Management Science 49, 639–654.Google Scholar
Grauer, R. and Hakansson, N. (1995) Stein and CAPM estimators of the means in asset allocation, International Review of Financial Analysis 4, 35–66.CrossRefGoogle Scholar
Grauer, R. and Shen, F. (2000) Do constraints improve portfolio performance?, Journal of Banking and Finance 24, 1253–1274.CrossRefGoogle Scholar
Green, R. and Hollifield, B. (1992) When will mean-variance efficient portfolios be well diversified?, Journal of Finance 47, 1785–1809.CrossRefGoogle Scholar
Grinold, R.C. and Easton, K.K. (1998) Attribution of performance and holdings, in: Mulvey, J.M./Ziemba, W.T. (ed.) Worldwide asset and liability modeling, Cambridge, 87–113.Google Scholar
Harvey, C.R. (1995) Predictable risk and returns in emerging markets, Review of Financial Studies 8, 773–816.CrossRefGoogle Scholar
Herold, U. (2003) Portfolio construction with qualitative inputs, Journal of Portfolio Management 29, 61–72.CrossRefGoogle Scholar
Herold, U. and Maurer, R. (2003) Bayesian asset allocation and U.S. domestic bias, Financial Analysts Journal 59, November/December, 54–65.CrossRefGoogle Scholar
Herold, U. and Maurer, R. (2004) Tactical asset allocation and estimation risk, Financial Markets and Portfolio Management 18, 39–57.CrossRefGoogle Scholar
Hodrick, R.J. (1992) Dividend yields and expected stock returns, Review of Financial Studies 3, 357–386.CrossRefGoogle Scholar
Jagannathan, R. and Ma, T. (2003) Risk reduction in large portfolios: Why imposing the wrong constraints helps, Journal of Finance 58, 1651–1683.CrossRefGoogle Scholar
Jobson, J.D. and Korkie, B.M. (1981a) Performance hypothesis testing with the Sharpe and Treynor measures, Journal of Finance 36, 888–908.CrossRefGoogle Scholar
Jobson, J.D. and Korkie, B.M. (1981b) Putting Markowitz theory to work, Journal of Portfolio Management 7, 70–74.CrossRefGoogle Scholar
Jorion, P. (1985) International portfolio diversification with estimation risk, Journal of Business 58, 259–278.CrossRefGoogle Scholar
Jorion, P. (1986) Bayes-Stein estimation for portfolio analysis, Journal of Financial and Quantitative Analysis 21, 279–292.CrossRefGoogle Scholar
Jorion, P. (1991) Bayesian and CAPM estimators of the mean: Implications for portfolio selection, Journal of Banking and Finance 15, 717–727.CrossRefGoogle Scholar
Jorion, P. (1992) Portfolio optimization in practice, Financial Analysts Journal January/February 48, 68–74.CrossRefGoogle Scholar
Kahn, R.N., Roulet, J. and Tajbakhsh, S. (1996) Three steps to global asset allocation, Journal of Portfolio Management 22, 23–31.CrossRefGoogle Scholar
Keim, D. and Stambaugh, R. (1986) Predicting returns in the stock and bond markets, Journal of Financial Economics 17, 357–390.CrossRefGoogle Scholar
Klein, R. and Bawa, V. (1976) The effect of estimation risk on optimal portfolio choice, in: Journal of Financial Economics 3, 215–231.CrossRefGoogle Scholar
Klemkosky, R. and Bharati, R. (1995) Time-varying expected returns and asset allocation, in: Journal of Portfolio Management 21, Summer, 80–87.CrossRefGoogle Scholar
Litterman, R. (1986) Forecasting with Bayesian vector autoregressions – Five years of experience, Journal of Business and Economics Statistics 4, 25–38.Google Scholar
Lo, A. (2002) The statistics of Sharpe ratio, Financial Analysts Journal 58, July/August, 36–52.CrossRefGoogle Scholar
Markowitz, H. (1959) Portfolio selection: Efficient diversification of investments, Cambridge.Google Scholar
Michaud, R.O. (1989) The Markowitz optimization enigma: Is ‘optimized’ optimal?, Financial Analysts Journal 45, January/February, 31–42.CrossRefGoogle Scholar
Michaud, R.O. (1998) Efficient asset management, Harvard Business School Press, Boston.Google Scholar
Pastor, L. (2000) Portfolio selection and asset pricing models, in: Journal of Finance 55, 179–223.CrossRefGoogle Scholar
Pastor, L. and Stambaugh, R.F. (1999) Costs of equity capital and model mispricing, in: Journal of Finance 54, 67–121.CrossRefGoogle Scholar
Pastor, L. and Stambaugh, R.F. (2000) Comparing asset pricing models: An investment perspective, Journal of Financial Economics 56, 335–381.CrossRefGoogle Scholar
Rey, D. (2003) Stock market predictability: Is it there?“ A critical review, University of Basel, WWZ Working Paper No. 12-03.Google Scholar
Scherer, B. (2002) Portfolio resampling: Review and critique, Financial Analysts Journal 58, November/December, 98–109.CrossRefGoogle Scholar
Solnik, B. (1993) The performance of international asset allocation strategies using conditioning information, Journal of Empirical Finance 1, 33–55.CrossRefGoogle Scholar
Stein, C. (1955) Inadmissibility of the usual estimator for the mean of a multivariate normal distribution, Proceeding of the 3rd Berkely Symposium on Probability and Statistics 1, Berkely: University of California Press.Google Scholar
Tiao, G.C. and Zellner, A. (1964a) Bayes’ Theorem and the use of prior knowledge in regression analysis, Biometrika 51, 219–230.CrossRefGoogle Scholar
Tiao, G.C. and Zellner, A. (1964b) On the Bayesian estimation of multivariate regression, Journal of the Royal Statistical Society 26, Series B, N277–285.Google Scholar
Todd, R. (1984) Improving economic forecasting with Bayesian vector autoregression, Federal Reserve Bank of Minneapolis Quarterly Review 8, 18–29.Google Scholar
Wang, Z. (2001) A shrinkage approach to asset allocation using asset-pricing models, Working Paper Columbia University.Google Scholar
Zellner, A. (1971) An introduction to Bayesian inference in econometrics, New York: Wiley.Google Scholar
Zellner, A. (1986) On assessing prior distributions and Bayesian regression analysis using g-prior distributions, in: Goel, P./Zellner, A. (ed.) Bayesian inference and decision techniques – Essays in honour of Bruno de Finetti, North Holland, Chapter 15, 233–243.Google Scholar
Zellner, A. and Chetty, K. (1965) Prediction and decision problems in regression models from the Bayesian point of view, Journal of the American Statistical Association 60, 608–616.CrossRefGoogle Scholar