Skip to main content
SpringerLink
Log in

Three Alternative Methods in Testing Capital Asset Pricing Model

  • Chapter
  • First Online:
Financial Econometrics, Mathematics and Statistics

  • 2986 Accesses

Abstract

Following the previous chapter, we show how three alternative errors-in-variable models can be used to test the capital asset pricing model. These three methods include the grouping method, the instrumental variable method, and the maximum likelihood method. In addition, we discuss how the errors-in-variable model can improve the capital asset pricing model tests at the individual stock level.

This chapter is an update and expansion of Chap. 3 of Chen’s Ph.D. dissertation (2011).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Chapter 7 provides a detailed explanation of the underestimation of beta risk and the overestimation of other risk factors without measured error.

  2. 2.

    For the Kenneth French’s website, please see http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html.

  3. 3.

    We filter out those financial institutions and utility firms based on the historical Standard Industrial Code (SIC) available from COMPUSTAT. When a firm’s historical SIC is unavailable for a particular year, the next available historical SIC is applied instead. When a firm’s historical SIC is unavailable for a particular year and all the years after, we use the current SIC from COMPUSTAT as a substitute.

Bibliography

  • Ahn, D. H., Conrad, J., & Dittmar, R. F. (2009). Basis assets. Review of Financial Studies, 22, 5133–5174.

    Google Scholar 

  • Aït-Sahalia, Y, Parker, J. A., & Yogo, M. (2004). Luxury goods and the equity premium. Journal of Finance, 59, 2959–3004.

    Google Scholar 

  • Acharya, V. V., & Pedersen, L. H. (2005). Asset pricing with liquidity risk. Journal of Financial Economics, 77, 375–410.

    Google Scholar 

  • Bansal, R., Dittmar, R. F., & Lundblad, C. T. (2005). Consumption, dividends, and the cross section of equity returns. Journal of Finance, 60, 1639–1672.

    Google Scholar 

  • Banz, R. W. (1981). The relationship between return and market value of common stocks. Journal of Financial Economics, 9, 3–18.

    Article  Google Scholar 

  • Black, F. (1972). Capital market equilibrium with restricted borrowing. Journal of Business, 45, 444–455.

    Article  Google Scholar 

  • Black, F., Jensen, M. C., & Scholes, M. (1972). The capital asset pricing model: Some empirical tests. In M. C. Jensen (Ed.). Studies in the theory of capital markets. Praeger.

    Google Scholar 

  • Blume, M. E., & Friend, I. (1973). A new look at the capital asset pricing model. Journal of Finance, 28, 19–33.

    Google Scholar 

  • Brennan M. J., & Zhang, Y. H. (2018). Capital asset pricing with a stochastic horizon. Journal of Financial and Quantitative Analysis, forthcoming.

    Google Scholar 

  • Brennan, M. J. (1970). Taxes, market valuation and corporate financial policy. National Tax Journal, 23, 417–427.

    Google Scholar 

  • Brennan, M. J. (1979). The pricing of contingent claims in discrete time models. The Journal of Finance, 34, 53–68.

    Article  MathSciNet  Google Scholar 

  • Brennan, M. J., Wang, A. W., & Xia, Y. (2004). Estimation and test of a simple model of intertemporal capital asset pricing. The Journal of Finance, 59, 1743–1775.

    Google Scholar 

  • Brown, S. J., & Warner, J. B. (1980). Measuring security price performance. Journal of Financial Economics, 8, 205–258.

    Google Scholar 

  • Campbell, J. Y., & Vuolteenaho, T. (2004). Bad beta, good beta. American Economic Review, 94, 1249–1275.

    Google Scholar 

  • Campbell, J. Y., Giglio, S., Polk, C., & Turley, R. (2018). An intertemporal CAPM with stochastic volatility, Journal of Financial Economics, 128, 207–233.

    Google Scholar 

  • Carhart, M. M. (1997). On persistence in mutual fund performance. Journal of Finance, 52, 57–82.

    Article  Google Scholar 

  • Cartwright, P. A., & Lee, C. F. (1987). Time aggregation and the estimation of the market model: empirical evidence, Journal of Business and Economic Statistics, 5, 131–143.

    Google Scholar 

  • Cederburg, S., & O’Doherty, M. S. (2015). Asset-pricing anomalies at the firm level. Journal of Econometrics, 186, 113–128.

    Google Scholar 

  • Chen, H. Y. (2011). Momentum strategies, dividend policy, and asset pricing test. Ph.D. dissertation, State University of New Jersey, Rutgers.

    Google Scholar 

  • Chen, P. J., Chen, S. S., Lee, C. F., & Shih, Y. C. (2014). The evolution of capital asset pricing models. Review of Quantitative Finance and Accounting, 42(3), 415–448.

    Google Scholar 

  • Cheng, P. L., & Grauer, R. R. (1980). An alternative test of the capital asset pricing model. American Economic Review, 70, 660–671.

    Google Scholar 

  • Chordia, T., & Shivakumar, L. (2006). Earnings and price momentum. Journal of Financial Economics, 80, 627–656.

    Google Scholar 

  • Cochrane, J. H. (1996). A cross-sectional test of an investment-based asset pricing model. Journal of Political Economy, 104, 572–621.

    Article  Google Scholar 

  • Durbin, J. (1954). Errors in variables. Review of the International Statistical Institute, 22, 23–32.

    Article  MathSciNet  Google Scholar 

  • Dybvig, P. H., & Ross, S. A. (2003). Arbitrage, state prices and portfolio theory. In Constantinides, G., Stulz, R. M., & Harris, M. (Ed.). Handbook of the economic of finance (North Holland).

    Google Scholar 

  • Fabozzi, F. J., & Francis, J. C. (1978). Beta as a random coefficient. Journal of Financial and Quantitative Analysis, 13, 101–116.

    Google Scholar 

  • Fama, E. F. (1998). Market efficiency, long-term returns, and behavioral finance. Journal of Financial Economics, 49, 283–306.

    Google Scholar 

  • Fama, E. F., & French, K. R. (1992). The cross-section of expected stock returns. Journal of Finance, 47, 427–465.

    Google Scholar 

  • Fama, E. F., & MacBeth, J. D. (1973). Risk, return, and equilibrium: Empirical tests. Journal of Political Economy, 81, 607–636.

    Google Scholar 

  • Gibbons, M. R. (1982). Multivariate tests of financial models: A new approach. Journal of Financial Economics, 10, 2–27.

    Article  Google Scholar 

  • Gilbert, T., Hrdlicka, C., Kalodimos, J., & Siegel, S. (2014). Daily data is bad for beta: Opacity and frequency-dependent betas. The Review of Asset Pricing Studies, 4, 78–117.

    Google Scholar 

  • Graham, J. R., Harvey, C. R., & Puri, M. (2015). Capital allocation and delegation of decision-making authority within firms. Journal of Financial Economics, 115(3), 449–470.

    Google Scholar 

  • Gu, S., Kelly, B., & Xiu, D. (2018). Empirical asset pricing via machine learning. Working paper, University of Chicago.

    Google Scholar 

  • Hansen, L. P., Heaton, J. C., & Li, N. (2008). Consumption strikes back? Measuring long-run risk. Journal of Political Economy, 116, 260–302.

    Google Scholar 

  • Harvey, C. R., Liu, Y., & Zhu, H. (2016). … and the cross-section of expected returns. Review of Financial Studies, 29, 5–68.

    Google Scholar 

  • Harvey, C. R. (2017). Presidential address: The scientific outlook in Financial Economics. The Journal of Finance, 72, 1399–1440.

    Article  Google Scholar 

  • Heaton, J., & Lucas, D. (2000). Portfolio choice and asset prices: The importance of entrepreneurial risk. Journal of Finance, 55, 1163–1198.

    Google Scholar 

  • Jacobs, K., & Wang, K. Q. (2004). Idiosyncratic consumption risk and the cross section of asset returns. The Journal of Finance, 59, 2211–2252.

    Google Scholar 

  • Jagannathan, R., & Wang, Z. (1993). The CAPM is alive and well. Staff report 165, Federal Reserve Bank of Minneapolis.

    Google Scholar 

  • Jagannathan, R., & Wang, Z. (1996). The conditional CAPM and the cross-section of expected returns. Journal of Finance, 51, 3–53.

    Google Scholar 

  • Jagannathan, R., & Wang, Z. (1998). An asymptotic theory for estimating beta-pricing models using cross-sectional regression. Journal of Finance, 53, 1285–1309.

    Google Scholar 

  • Jagannathan, R., Skoulakis, G., & Wang, Z. (2009). The analysis of the cross section of security returns. In Aït-Sahalia, Y., & Hansen, L. (Ed.). Handbook of financial econometrics (North-Holland) Vol. 2, pp. 73–134.

    Google Scholar 

  • Jarque, C. M., & Bera, A. K. (1987). A test for normality of observations and regression residuals. International Statistical Review, 55, 163–172.

    Google Scholar 

  • Jegadeesh, N., Noh, J., Pukthuanghong, K., Roll, R., & Wang, J. L. (2018). Empirical tests of asset pricing models with individual assets: Resolving the errors-in-variables bias in risk premium estimation. Journal of Financial Economics (forthcoming).

    Google Scholar 

  • Johnston, M. (1997). Econometric method. New York, NY: McGraw-Hill.

    Google Scholar 

  • Kim, D. (1995). The errors in the variables problem in the cross-section of expected stock returns. Journal of Finance, 50, 1605–1634.

    Article  Google Scholar 

  • Kim, D. (1997). A reexamination of firm size, book-to-market, and earnings price in the cross-section of expected stock returns. Journal of Financial and Quantitative Analysis, 32, 463–489.

    Article  Google Scholar 

  • Kim, D. (2010). Issues related to the errors-in-variables problems in asset pricing tests. In C. F. Lee, A. C. Lee, & J. Lee (Ed.). Handbook of quantitative finance and risk management. Berlin: Springer.

    Google Scholar 

  • Lee, C. F. (1973). Errors-in-variables estimation procedures with applications to a capital asset pricing model. State University of New York at Buffalo.

    Google Scholar 

  • Lee, C. F., (1976). Investment horizon and the functional form of the capital asset pricing model, The Review of Economics and Statistics, 58, 356–363.

    Article  Google Scholar 

  • Lee, C. F. (1977). Performance measure, systematic risk, and errors-in-variables estimation method. Journal of Economics and Business, 122–127.

    Google Scholar 

  • Lee, C. F. (1984). Random coefficient and errors-in-variables models for beta estimates: Methods and applications. Journal of Business Research, 12, 505–516.

    Article  Google Scholar 

  • Lee, C. F., & Chen, S. N. (1979). A random coefficient model for reexaming risk decomposition method and risk-return relationship test. Financial Review, 14, 65–65.

    Google Scholar 

  • Lee, C. F., & Jen, F. C. (1978). Effects of measurement errors on systematic risk and performance measure of a portfolio. Journal of Financial and Quantitative Analysis, 13, 299–312.

    Google Scholar 

  • Lee, C. F., Wu, C. & John Wei, K. C. (1990). The heterogeneous investment horizon and the capital asset pricing model: theory and implications. Journal of Financial and Quantitative Analysis 25, 361–376.

    Google Scholar 

  • Lee, C. F., Wei, K. C., & Chen, H. Y. (2015). Multi-factor, multi-indicator approach to asset pricing: Methods and empirical evidence. In C. F. Lee & J. Lee (Ed.). Handbook of financial econometrics and statistics. Singapore: Springer.

    Google Scholar 

  • Li, Q., Vassalou, M., & Xing, Y. (2006). Sector investment growth rates and the cross section of equity returns. Journal of Business, 79, 1637–1665.

    Google Scholar 

  • Lintner, J. (1965). The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. Review of Economics and Statistics, 47, 13.

    Article  Google Scholar 

  • Litzenberger, R. H., & Ramaswamy, K. (1979). The effects of personal taxes and dividends on capital asset prices: Theory and empirical evidence. Journal of Financial Economics, 7, 163–195.

    Google Scholar 

  • MacKinlay, A. C., & Richardson, M. (1991). Using gerneralized methods of moments to test mean-variance efficiency. Journal of Finance, 46, 511–527.

    Google Scholar 

  • Mossin, J. (1966). Equilibrium in a capital asset market. Econometrica, 34, 768–783.

    Article  Google Scholar 

  • Parker, J. A., & Julliard, C. (2005). Consumption risk and the cross section of expected returns. Journal of Political Economy, 113, 185–222.

    Google Scholar 

  • Pástor, Ľ., & Stambaugh, R. F. (2003). Liquidity risk and expected stock returns. Journal of Political Economy, 111, 642–685.

    Google Scholar 

  • Petersen, M. A. (2009). Estimating standard errors in finance panel data sets: Comparing approaches. Review of Financial Studies, 22, 435–480.

    Google Scholar 

  • Petkova, R. (2006). Do the Fama-French factors proxy for innovations in predictive variables? The Journal of Finance, 61, 581–612.

    Article  MathSciNet  Google Scholar 

  • Reinganum, M. R. (1981). Misspecification of capital asset pricing: Empirical anomalies based on earnings’ yields and market values. Journal of Financial Economics, 9, 19–46.

    Article  MathSciNet  Google Scholar 

  • Roll, R. (1969). Bias in fitting the Sharpe model to time series data. Journal of Financial and Quantitative Analysis, 4, 271–289.

    Article  Google Scholar 

  • Roll, R. (1977). A critique of the asset pricing theory’s tests Part I: On past and potential testability of the theory. Journal of Financial Economics, 4, 129–176.

    Article  Google Scholar 

  • Shanken, J. (1992). On the estimation of beta-pricing models. Review of Financial Studies, 5, 1–33.

    Article  Google Scholar 

  • Sharpe, W. F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk. Journal of Finance, 19, 425–442.

    Google Scholar 

  • Vassalou, M. (2003). News related to future GDP growth as a risk factor in equity returns. Journal of Financial Economics, 68, 47–73.

    Article  Google Scholar 

  • Wald, A. (1940). The fitting of straight lines if both variables are subject to error. Annals Mathematical Statistics, 11, 284, 300.

    Article  MathSciNet  Google Scholar 

  • Xiao Y. Y., Tang, Y. S. & Lee, C. F. (2019). Impact of time aggregation on beta value and R square estimations under additive and multiplicative assumptions: Theoretical results and empirical evidence, Handbook of Financial Econometrics, Mathematics, Statistics, and Technology, World Scientific, Singapore, forthcoming.

    Google Scholar 

  • Yogo M. (2006). A consumption-based explanation of expected stock returns. Journal of Finance, 61, 539–580.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Finance and Economics, Rutgers Business School, Rutgers University, Piscataway, NJ, USA

    Cheng-Few Lee

  2. Department of Finance, National Chengchi University, Taipei, Taiwan

    Hong-Yi Chen

  3. Center for PBBEF Research, Morris Plains, NJ, USA

    John Lee

Authors
  1. Cheng-Few Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hong-Yi Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. John Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Cheng-Few Lee .

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Science+Business Media, LLC, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Lee, CF., Chen, HY., Lee, J. (2019). Three Alternative Methods in Testing Capital Asset Pricing Model. In: Financial Econometrics, Mathematics and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-9429-8_8

Download citation

Publish with us

Policies and ethics

Search

Navigation