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Multivariate regression tests of the arbitrage pricing theory: The instrumental-variables approach

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Abstract

This article expands the theoretical basis upon which empirical testing of the arbitrage pricing theory (APT) rests. Specifically, it specifies linear restrictions for worlds in which the APT holds. These restrictions may, in principle, be tested. Since the regressors in the model are only “noisy” proxies for a specific linear transformation of the factors or mimicking portfolios, testing regressions suffer from an errors-in-variables problem. The standard econometric treatment for this problem is the instrumental-variables approach. A size-based example is employed to compare the test results derived from the instrumental-variables approach to those obtained via the ordinary least squares (OLS) method. The results from both methods cannot reject a two-factor APT for the size-sorted portfolio sample.

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References

  • Black, F., “Capital Market Equilibrium with Restricted Borrowing.”Journal of Business 45, 444–454 (July 1972).

    Article  Google Scholar 

  • Brown, S. and M. Weinstein, “A New Approach to Testing Asset Pricing Models: The Bilinear Paradigm.”Journal of Finance 38, 711–743 (June 1983).

    Google Scholar 

  • Burmeister, Edwin and Marjorie McElroy, “Joint Estimation of Factor Sensitivities and Risk Premia for the Arbitrage Pricing Theory.”Journal of Finance 63, 721–733 (July 1988).

    Google Scholar 

  • Burmeister, Edwin and Marjorie McElroy, “The Residual Market Factor, the APT, and Mean-Variance Efficiency.”Review of Quantitative Finance and Accounting 1, 27–49 (January 1991).

    Google Scholar 

  • Chamberlain, G. and M. Rothschild, “Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets.”Econometrica 51, 1281–1304 (September 1983).

    Google Scholar 

  • Chen N. and J. Ingersoll, “Exact Pricing in Linear Factor Models with Infinitely Many Assets: A Note.”Journal of Finance 38, 985–988 (June 1983).

    Google Scholar 

  • Connor, G., “A Unified Beta Pricing Theory.”Journal of Economic Theory 34, 13–31, (December 1984).

    Article  Google Scholar 

  • Gibbons, M. “Multivariate Tests of Financial Models: A New Approach.”Journal of Financial Economics 10, 3–27 (January 1982).

    Article  Google Scholar 

  • Grinblatt, M. and S. Titman, “The Relation Between Mean-Variance Efficiency and Arbitrage Pricing.”Journal of Business 60, 97–112 (January 1987).

    Article  Google Scholar 

  • Huberman, G. and S. Kandel, “A Size Based Stock Returns Model.” Manuscript, University of Chicago (October 1985).

    Google Scholar 

  • Huberman, G. and S. Kandel, “Mean-Variance Spanning.”Journal of Finance 42, 873–888 (September 1987).

    Google Scholar 

  • Huberman, G., S. Kandel, and R. Stambaugh, “Mimicking Portfolios and Exact Arbitrage Pricing.”Journal of Finance 42, 1–9 (March 1987).

    Google Scholar 

  • Ingersoll, J. Jr., “Some Results in the Theory of Arbitrage Pricing.”Journal of Finance 39, 1021–1039 (September 1984).

    Google Scholar 

  • Jobson, J. and B. Korkie, “Some Tests of Linear Asset Pricing with Multivariate Normality.”Canadian Journal of Administrative Science 2, 114–138 (June 1985).

    Google Scholar 

  • Lehmann, B. and D. Modest, “The Empirical Foundations of the Arbitrage Pricing Theory.”Journal of Financial Economics 21, 213–254 (1988).

    Article  Google Scholar 

  • Leamer, E.,Specification Searches: Ad Hoc Inference with Nonexperimental Data. New York: John Wiley and Sons, Inc. (1978).

    Google Scholar 

  • Lintner, J., “The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets.”Review of Economics and Statistics 47, 13–27 (February 1965).

    Article  Google Scholar 

  • McElroy, Marjorie and Edwin Burmeister, “Arbitrage Pricing Theory as a Restricted Nonlinear Multiple Regression Model: ITNLSUR Estimates.”Journal of Business and Economic Statistics 6, 29–42 (January 1988).

    Article  Google Scholar 

  • Merton, R., “An Intertemporal Capital Asset Pricing Model.”Econometrica 41, 867–887 (September 1973).

    Google Scholar 

  • Nelson, C. and R. Startz, “The Distribution of the Instrumental Variables Estimator and Its t-Ratio when the Instrument is a Poor One.” Working paper, Department of Economics, University of Washington (May 1988).

  • Nelson, C. and R. Startz, “Some Further Results on the Exact Small Sample Properties of the Instrumental Variable Estimator.” Working paper, Department of Economics, University of Washington (May 1988).

  • Roll, R. and S. Ross, “An Empirical Investigation of the Arbitrage Pricing Theory.”Journal of Finance 35, 1073–1103 (December 1980).

    Google Scholar 

  • Ross, S., “The Arbitrage Theory of Capital Asset Pricing.”Journal Economic Theory 13, 341–360 (December 1976).

    Article  Google Scholar 

  • Sargan, D.Lectures on Advanced Econometric Theory. New York: Basil Blackwell (1988).

    Google Scholar 

  • Shanken, Jay, “The Arbitrage Pricing Theory: Is It Testable?”Journal of Finance 37, 1129–1140 (December 1982).

    Google Scholar 

  • Shanken, Jay, “Multi-Beta or Equilibrium-APT?: A Reply.”Journal of Finance 40, 1189–1196 (September 1985).

    Google Scholar 

  • Shanken, Jay, “Multivariate Proxies and Asset Pricing Relations: Living with the Roll Critique.”Journal of Financial Economics 18, 91–110 (March 1987).

    Article  Google Scholar 

  • Sharpe, W. “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk.”Journal of Finance 19, 425–442 (September 1964).

    Google Scholar 

  • Wei, K.C., “An Asset-Pricing Theory Unifying the CAPM and APT.”Journal of Finance 43, 881–892 (September 1988).

    Google Scholar 

  • Wei, K.C., “The Arbitrage Pricing Theory versus the Generalized Intertemporal Capital Asset Pricing Model: Theory and Empirical Evidence.” Unpublished dissertation, University of Illinois (1984).

  • Zellner, A., “An Efficient Method of Estimating Seemingly Unrelated Regressions and Tests for Aggregation Bias,”Journal of the American Statistical Association 67, 348–368 (1962).

    Article  Google Scholar 

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The authors appreciate the helpful comments of Edwin Burmeister, Raymond Chiang, Steve Pruitt, participant at the 1989 Western Finance Association annual meetings, Indiana University, and University of Miami, and especially Shmuel Kandel.

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John Wei, K.C., Lee, CF. & Chen, A.H. Multivariate regression tests of the arbitrage pricing theory: The instrumental-variables approach. Rev Quant Finan Acc 1, 191–208 (1991). https://doi.org/10.1007/BF02409672

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