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Residual Risk Revisited

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  • Bruce N. Lehmann

Abstract

The Capital Asset Pricing Model in conjunction with the usual market model assumptions implies that well-diversified portfolios should be mean variance efficient and ,hence, betas computed with respect to such indices should completely explain expected returns on individual assets. In fact, there is now a large body of evidence indicating that the market proxies usually employed in empirical tests are not mean variance efficient. Moreover, there is considerable evidence suggesting that these rejections are in part a consequence of the presence of omitted risk factors which are associated with nonzero risk premia in the residuals from the single index market model. Consequently, the idiosyncratic variances from the one factor model should partially reflect exposure to these omitted sources of systematic risk and,hence, should help explain expected returns. There are two plausible explanations for the inability to obtain statistically reliable estimates of a linear residual risk effect in the previous literature:(1) nonlinearity of the residual risk effect and (2) the inadequacy of the statistical procedures employed to measure it.The results presented below indicate that the econometric methods employed previously are the culprits. Pronounced residual risk effects are found in the whole fifty-four year sample and in numerous five year subperiods as well when weighted least squares estimation is coupled with the appropriate corrections for sampling error in the betas and residual variances of individual security returns. In addition, the evidence suggests that it is important to take account of the nonnormality and heteroskedasticity of security returns when making the appropriate measurement error corrections in cross-sectional regressions. Finally, the results are sensitive to the specification of the model for expected returns.

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  • Bruce N. Lehmann, 1986. "Residual Risk Revisited," NBER Working Papers 1908, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:1908
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    Cited by:

    1. Altonji, Joseph G & Segal, Lewis M, 1996. "Small-Sample Bias in GMM Estimation of Covariance Structures," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 353-366, July.
    2. Gonzalez-Rivera, Gloria, 1996. "Time-varying risk The case of the American computer industry," Journal of Empirical Finance, Elsevier, vol. 2(4), pages 333-342, February.
    3. Hui Guo & Robert Savickas, 2003. "Does idiosyncratic risk matter: another look," Working Papers 2003-025, Federal Reserve Bank of St. Louis.
    4. Hui Guo & Jason Higbee, 2006. "Market timing with aggregate and idiosyncratic stock volatilities," Working Papers 2005-073, Federal Reserve Bank of St. Louis.
    5. Andrew Ang & Robert J. Hodrick & Yuhang Xing & Xiaoyan Zhang, 2006. "The Cross‐Section of Volatility and Expected Returns," Journal of Finance, American Finance Association, vol. 61(1), pages 259-299, February.
    6. Liow, Kim Hiang & Addae-Dapaah, Kwame, 2010. "Idiosyncratic risk, market risk and correlation dynamics in the US real estate investment trusts," Journal of Housing Economics, Elsevier, vol. 19(3), pages 205-218, September.
    7. Guo, Hui & Savickas, Robert, 2006. "Idiosyncratic Volatility, Stock Market Volatility, and Expected Stock Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 43-56, January.
    8. Angelidis, Timotheos & Tessaromatis, Nikolaos, 2008. "Idiosyncratic volatility and equity returns: UK evidence," International Review of Financial Analysis, Elsevier, vol. 17(3), pages 539-556, June.
    9. Antoniou, Antonios & Zhao, Huainan & Zhou, Bilei, 2009. "Corporate debt issues and interest rate risk management: Hedging or market timing?," Journal of Financial Markets, Elsevier, vol. 12(3), pages 500-520, August.
    10. Nusret Cakici & Isil Erol & Dogan Tirtiroglu, 2014. "Tracking the Evolution of Idiosyncratic Risk and Cross-Sectional Expected Returns for US REITs," The Journal of Real Estate Finance and Economics, Springer, vol. 48(3), pages 415-440, April.
    11. Cotter, John & Sullivan, Niall O' & Rossi, Francesco, 2015. "The conditional pricing of systematic and idiosyncratic risk in the UK equity market," International Review of Financial Analysis, Elsevier, vol. 37(C), pages 184-193.
    12. Stephan Süss, 2012. "The pricing of idiosyncratic risk: evidence from the implied volatility distribution," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 26(2), pages 247-267, June.
    13. Stivers, Christopher T., 2003. "Firm-level return dispersion and the future volatility of aggregate stock market returns," Journal of Financial Markets, Elsevier, vol. 6(3), pages 389-411, May.
    14. Gregory Connor & Sheng Li, 2009. "Market Dispersion and the Profitability of Hedge Funds," Economics Department Working Paper Series n2000109.pdf, Department of Economics, National University of Ireland - Maynooth.
    15. Hui Guo & Robert Savickas, 2006. "Aggregate idiosyncratic volatility in G7 countries," Working Papers 2004-027, Federal Reserve Bank of St. Louis.
    16. Driscoll, John & Kraay, Aart, 1995. "Spatial correlations in panel data," Policy Research Working Paper Series 1553, The World Bank.
    17. Nicholas Barberis & Ming Huang, 2001. "Mental Accounting, Loss Aversion, and Individual Stock Returns," NBER Working Papers 8190, National Bureau of Economic Research, Inc.
    18. Larry G. Epstein & Martin Schneider, 2008. "Ambiguity, Information Quality, and Asset Pricing," Journal of Finance, American Finance Association, vol. 63(1), pages 197-228, February.
    19. Kryzanowski, Lawrence & Switzer, Lorne & Jiang, Li, 1995. "Stock market crash behavior of screen-sorted portfolios," International Review of Economics & Finance, Elsevier, vol. 4(3), pages 227-244.
    20. Bruce N. Lehmann, 1992. "Empirical Testing of Asset Pricing Models," NBER Working Papers 4043, National Bureau of Economic Research, Inc.

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