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Arbitrage Pricing Theory, the Stochastic Discount Factor and Estimation of Risk Premia from Portfolios

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  • M. Hashem Pesaran
  • Ron P. Smith

Abstract

The arbitrage pricing theory (APT) attributes differences in expected returns to exposure to systematic risk factors. Two aspects of the APT are considered. Firstly, the factors in the statistical asset pricing model are related to a theoretically consistent set of factors defined by their conditional covariation with the stochastic discount factor (SDF) used to price securities within inter-temporal asset pricing models. It is shown that risk premia arise from non-zero correlation of observed factors with SDF and the pricing errors arise from the correlation of the errors in the statistical model with SDF. Secondly, the estimates of factor risk premia using portfolios are compared to those obtained using individual securities. It is shown that in the presence of pricing errors consistent estimation of risk premia requires a large number of not fully diversified portfolios. Also, in general, it is not possible to rank estimators using individual securities and portfolios in terms of their small sample bias.

Suggested Citation

  • M. Hashem Pesaran & Ron P. Smith, 2021. "Arbitrage Pricing Theory, the Stochastic Discount Factor and Estimation of Risk Premia from Portfolios," CESifo Working Paper Series 9001, CESifo.
    • Handle: RePEc:ces:ceswps:_9001
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    References listed on IDEAS

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    1. Ang, Andrew & Liu, Jun & Schwarz, Krista, 2020. "Using Stocks or Portfolios in Tests of Factor Models," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 55(3), pages 709-750, May.
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    10. M. Hashem Pesaran & Ron P. Smith, 2021. "Factor Strengths, Pricing Errors, and Estimation of Risk Premia," CESifo Working Paper Series 8947, CESifo.
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    Cited by:

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    2. Feng, Long & Lan, Wei & Liu, Binghui & Ma, Yanyuan, 2022. "High-dimensional test for alpha in linear factor pricing models with sparse alternatives," Journal of Econometrics, Elsevier, vol. 229(1), pages 152-175.

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    More about this item

    Keywords

    arbitrage pricing theory; stochastic discount factor; portfolios; factor strength; identification of risk premia; two-pass regressions; Fama-MacBeth;
    All these keywords.

    JEL classification:

    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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