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Time varying betas and the unconditional distribution of asset returns


  • C. J. Adcock
  • M. Ceu Cortez
  • M. J. Rocha Armada
  • F. Silva


This paper draws attention to the fact that under standard assumptions the time varying betas model cannot capture the dynamics in beta. Conversely, evidence of time variation in beta using this model is equivalent to non-normality in the unconditional distribution of asset returns. Using the multivariate normal as a model for the joint distribution of returns on market indices and predetermined information variables, it is shown how to capture skewness and kurtosis in the unconditional distributions of asset returns. Under the assumptions of the model, asset returns are unconditionally distributed as an extended quadratic form (EQF) in normal variables. Expressions are given for the moment generating function and for the computation of the distribution and density functions. The market-timing model is derived formally using this model. The properties of bias when the standard linear betas model is used to estimate alpha when the correct model is the EQF are also investigated. It is shown that a different time varying betas model can arise as a consequence of portfolio selection. It is also shown that the predetermined information variables have the potential to account for the time series properties of returns, including heterogeneity of variance. An empirical study applies the model to returns on 46 UK bond funds. An analysis of the residuals shows that the model described in this paper is able to capture the dynamics of alpha and beta and properly account for other features of the time series of returns for 28 of these funds, of which 15 exhibit time variation in beta. The study reports the effect of the EQF model on the computation of VaR and CVaR and bias in the estimation of alpha.

Suggested Citation

  • C. J. Adcock & M. Ceu Cortez & M. J. Rocha Armada & F. Silva, 2012. "Time varying betas and the unconditional distribution of asset returns," Quantitative Finance, Taylor & Francis Journals, vol. 12(6), pages 951-967, November.
  • Handle: RePEc:taf:quantf:v:12:y:2012:i:6:p:951-967 DOI: 10.1080/14697688.2010.544667

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    References listed on IDEAS

    1. Michael C. Jensen, 1968. "The Performance Of Mutual Funds In The Period 1945–1964," Journal of Finance, American Finance Association, vol. 23(2), pages 389-416, May.
    2. Russ Wermers, 2000. "Mutual Fund Performance: An Empirical Decomposition into Stock-Picking Talent, Style, Transactions Costs, and Expenses," Journal of Finance, American Finance Association, vol. 55(4), pages 1655-1703, August.
    3. Boney, Vaneesha & Comer, George & Kelly, Lynne, 2009. "Timing the investment grade securities market: Evidence from high quality bond funds," Journal of Empirical Finance, Elsevier, vol. 16(1), pages 55-69, January.
    4. Lehmann, Bruce N & Modest, David M, 1987. " Mutual Fund Performance Evaluation: A Comparison of Benchmarks and Benchmark Comparisons," Journal of Finance, American Finance Association, vol. 42(2), pages 233-265, June.
    5. Glassman, Debra A. & Riddick, Leigh A., 2006. "Market timing by global fund managers," Journal of International Money and Finance, Elsevier, vol. 25(7), pages 1029-1050, November.
    6. Pastor, Lubos & Stambaugh, Robert F., 2002. "Mutual fund performance and seemingly unrelated assets," Journal of Financial Economics, Elsevier, vol. 63(3), pages 315-349, March.
    7. Juan C. Matallín-Sáez, 2006. "Seasonality, Market Timing and Performance Amongst Benchmarks and Mutual Fund Evaluation," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 33(9-10), pages 1484-1507.
    8. Luis Ferruz Agudo & Maria Vargas Magallon & Jose Sarto, 2006. "Evaluation of performance and conditional information: the case of Spanish mutual funds," Applied Financial Economics, Taylor & Francis Journals, vol. 16(11), pages 803-817.
    9. Luis Miguel Doncel & Pilar Grau-Carles & Jorge Sainz, 2009. "On the long-term behavior of mutual fund returns," Quantitative Finance, Taylor & Francis Journals, vol. 9(6), pages 653-660.
    10. Ferson, Wayne E & Schadt, Rudi W, 1996. " Measuring Fund Strategy and Performance in Changing Economic Conditions," Journal of Finance, American Finance Association, vol. 51(2), pages 425-461, June.
    11. George Comer, 2006. "Hybrid Mutual Funds and Market Timing Performance," The Journal of Business, University of Chicago Press, vol. 79(2), pages 771-798, March.
    12. Edelen, Roger M., 1999. "Investor flows and the assessed performance of open-end mutual funds," Journal of Financial Economics, Elsevier, vol. 53(3), pages 439-466, September.
    13. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 33(1), pages 125-132.
    14. Jiang, George J. & Yao, Tong & Yu, Tong, 2007. "Do mutual funds time the market? Evidence from portfolio holdings," Journal of Financial Economics, Elsevier, vol. 86(3), pages 724-758, December.
    15. Bruce N. Lehmann & David M. Modest, 1985. "Mutual Fund Performance Evaluation: A Comparison of Benchmarks and Benchmark Comparisons," NBER Working Papers 1721, National Bureau of Economic Research, Inc.
    16. Warther, Vincent A., 1995. "Aggregate mutual fund flows and security returns," Journal of Financial Economics, Elsevier, vol. 39(2-3), pages 209-235.
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    Cited by:

    1. José Soares Da Fonseca, 2016. "Euro area stock markets performance comparison and its dependence on macroeconomic variables," International Journal of Monetary Economics and Finance, Inderscience Enterprises Ltd, vol. 9(3), pages 245-266.
    2. Matthias Raddant & Friedrich Wagner, 2016. "Phase transition in the S&P stock market," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 11(2), pages 229-246, October.
    3. Rocha Armada, Manuel J. & Sousa, Ricardo M. & Wohar, Mark E., 2015. "Consumption growth, preference for smoothing, changes in expectations and risk premium," The Quarterly Review of Economics and Finance, Elsevier, vol. 56(C), pages 80-97.
    4. José Soares da Fonseca, 2014. "Linkages and Performance Comparison among Eastern Europe Stock Markets," Notas Económicas, Faculty of Economics, University of Coimbra, issue 39, pages 73-83, June.

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