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Optimal Asset Allocation with Factor Models for Large Portfolios

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Author Info
M. Hashem Pesaran ()
Paolo Zaffaroni ()

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Abstract

This paper characterizes the asymptotic behaviour, as the number of assets gets arbitrarily large, of the portfolio weights for the class of tangency portfolios belonging to the Markowitz paradigm. It is assumed that the joint distribution of asset returns is characterized by a general factor model, with possibly heteroskedastic components. Under these conditions, we establish that a set of appealing properties, so far unnoticed, characterize traditional Markowitz portfolio trading strategies. First, we show that the tangency portfolios fully diversify the risk associated with the factor component of asset return innovations. Second, with respect to determination of the portfolio weights, the conditional distribution of the factors is of second-order importance as compared to the distribution of the factor loadings and that of the idiosyncratic components. Third, although of crucial importance in forecasting asset returns, current and lagged factors do not enter the limit portfolio returns. Our theoretical results also shed light on a number of issues discussed in the literature regarding the limiting properties of portfolio weights such as the diversifiability property and the number of dominant factors.

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Publisher Info
Paper provided by CESifo Group Munich in its series CESifo Working Paper Series with number CESifo Working Paper No. 2326.

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Date of creation: 2008
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Handle: RePEc:ces:ceswps:_2326

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Related research
Keywords: asset allocation; large portfolios; factor models; diversification;

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Find related papers by JEL classification:
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions
C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation and Testing
C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Other Model Applications
G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

References listed on IDEAS
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  1. Huberman, Gur, 1982. "A simple approach to arbitrage pricing theory," Journal of Economic Theory, Elsevier, vol. 28(1), pages 183-191, October. [Downloadable!] (restricted)
  2. King, Mervyn & Sentana, Enrique & Wadhwani, Sushil, 1994. "Volatility and Links between National Stock Markets," Econometrica, Econometric Society, vol. 62(4), pages 901-33, July. [Downloadable!] (restricted)
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  3. Gabriele Fiorentini & Enrique Sentana & Neil Shephard, 2004. "Likelihood-Based Estimation of Latent Generalized ARCH Structures," Econometrica, Econometric Society, vol. 72(5), pages 1481-1517, 09. [Downloadable!] (restricted)
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  4. Chamberlain, Gary, 1983. "Funds, Factors, and Diversification in Arbitrage Pricing Models," Econometrica, Econometric Society, vol. 51(5), pages 1305-23, September. [Downloadable!] (restricted)
  5. M. Hashem Pesaran & Allan Timmermann, 1995. "Predictability of Stock Returns: Robustness and Economic Significance," University of California at San Diego, Economics Working Paper Series 95-19, Department of Economics, UC San Diego.
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  6. Grinblatt, Mark & Titman, Sheridan, 1987. "The Relation between Mean-Variance Efficiency and Arbitrage Pricing," Journal of Business, University of Chicago Press, vol. 60(1), pages 97-112, January. [Downloadable!] (restricted)
  7. Chamberlain, Gary & Rothschild, Michael, 1983. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Econometrica, Econometric Society, vol. 51(5), pages 1281-304, September. [Downloadable!] (restricted)
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  8. Connor, Gregory, 1984. "A unified beta pricing theory," Journal of Economic Theory, Elsevier, vol. 34(1), pages 13-31, October. [Downloadable!] (restricted)
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  11. Sentana, Enrique, 2004. "Factor representing portfolios in large asset markets," Journal of Econometrics, Elsevier, vol. 119(2), pages 257-289, April. [Downloadable!] (restricted)
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  12. Aguilar, Omar & West, Mike, 2000. "Bayesian Dynamic Factor Models and Portfolio Allocation," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(3), pages 338-57, July.
  13. Mario Forni & Marc Hallin & Marco Lippi & Lucrezia Reichlin, 2000. "The Generalized Dynamic-Factor Model: Identification And Estimation," The Review of Economics and Statistics, MIT Press, vol. 82(4), pages 540-554, November. [Downloadable!] (restricted)
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  14. Diebold, Francis X & Nerlove, Marc, 1989. "The Dynamics of Exchange Rate Volatility: A Multivariate Latent Factor Arch Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(1), pages 1-21, Jan.-Mar.. [Downloadable!] (restricted)
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  15. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December. [Downloadable!] (restricted)
  16. Green, Richard C & Hollifield, Burton, 1992. " When Will Mean-Variance Efficient Portfolios Be Well Diversified?," Journal of Finance, American Finance Association, vol. 47(5), pages 1785-809, December. [Downloadable!] (restricted)
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  17. Kandel, Shmuel & Stambaugh, Robert F, 1996. " On the Predictability of Stock Returns: An Asset-Allocation Perspective," Journal of Finance, American Finance Association, vol. 51(2), pages 385-424, June. [Downloadable!] (restricted)
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  18. Connor, Gregory & Korajczyk, Robert A. & Linton, Oliver, 2006. "The common and specific components of dynamic volatility," Journal of Econometrics, Elsevier, vol. 132(1), pages 231-255, May. [Downloadable!] (restricted)
  19. Jeff Fleming, 2001. "The Economic Value of Volatility Timing," Journal of Finance, American Finance Association, vol. 56(1), pages 329-352, 02. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Jianqing Fan & Jingjin Zhang & Ke Yu, 2008. "Asset Allocation and Risk Assessment with Gross Exposure Constraints for Vast Portfolios," Quantitative Finance Papers 0812.2604, arXiv.org. [Downloadable!]
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