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

29 Pages Posted: 16 Apr 2021

See all articles by M. Hashem Pesaran

M. Hashem Pesaran

University of Southern California - Department of Economics

Ron Smith

Birkbeck College

Date Written: 2021

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.

JEL Classification: C380, G120

Suggested Citation

Pesaran, M. Hashem and Smith, Ron P., Arbitrage Pricing Theory, the Stochastic Discount Factor and Estimation of Risk Premia from Portfolios (2021). CESifo Working Paper No. 9001, Available at SSRN: https://ssrn.com/abstract=3827614 or http://dx.doi.org/10.2139/ssrn.3827614

M. Hashem Pesaran (Contact Author)

University of Southern California - Department of Economics ( email )

3620 South Vermont Ave. Kaprielian (KAP) Hall 300
Los Angeles, CA 90089
United States

Ron P. Smith

Birkbeck College ( email )

Malet Street
London WC1E 7HX
United Kingdom
+44 207 631 6413 (Phone)
+44 207 631 6416 (Fax)

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