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Investment Horizon Dependent CAPM: Adjusting beta for long-term dependence


  • Carlos León


  • Karen Leiton


  • Alejandro Reveiz



Financial basics and intuition stresses the importance of investment horizon for risk management and asset allocation. However, the beta parameter of the Capital Asset Pricing Model (CAPM) is invariant to the holding period. Such contradiction is due to the assumption of long-term independence of financial returns; an assumption that has been proven erroneous. Following concerns regarding the impact of the long-term dependence assumption on risk (Holton, 1992), this paper quantifies and fixes the CAPM´s bias resulting from this abiding -but flawed- assumption. The proposed procedure is based on Greene and Fielitz (1980) seminal work on the application of fractional Brownian motion to CAPM, and on a revised technique for estimating time-series´ fractal dimension with the Hurst exponent (León and Vivas, 2010; León and Reveiz, 2011a). Using a set of 85 stocks from the S&P100, this paper finds that relaxing the long-term independence assumption results in significantly different estimations of beta. According to three tests herein implemented with a 99% confidence level, more than 60% of the stocks exhibit significantly different beta parameters. Hence, expected returns are biased; on average, the bias is about ± 60bps for a contemporary one-year investment horizon. Thus, as emphasized by Holton (1992), risk is a two-dimensional quantity, with holding period almost as important as asset class. The procedure herein proposed is valuable since it parsimoniously achieves an investment horizon dependent CAPM.

Suggested Citation

  • Carlos León & Karen Leiton & Alejandro Reveiz, 2012. "Investment Horizon Dependent CAPM: Adjusting beta for long-term dependence," BORRADORES DE ECONOMIA 009909, BANCO DE LA REPÚBLICA.
  • Handle: RePEc:col:000094:009909

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    References listed on IDEAS

    1. Oscar Becerra & Luis Fernando Melo, 2008. "Medidas De Riesgo Financiero Usando Cópulas: Teoría Y Aplicaciones," BORRADORES DE ECONOMIA 004523, BANCO DE LA REPÚBLICA.
    2. Nikolay Nenovsky & S. Statev, 2006. "Introduction," Post-Print halshs-00260898, HAL.
    3. Sigridur Benediktsdottir & Chiara Scotti, 2009. "Exchange rates dependence: what drives it?," International Finance Discussion Papers 969, Board of Governors of the Federal Reserve System (U.S.).
    4. Orlov, Alexei G., 2009. "A cospectral analysis of exchange rate comovements during Asian financial crisis," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 19(5), pages 742-758, December.
    5. Meltem Gulenay Chadwick & Fatih Fazilet & Necati Tekatli, 2012. "Common Movement of the Emerging Market Currencies," Working Papers 1207, Research and Monetary Policy Department, Central Bank of the Republic of Turkey.
    6. repec:sae:ecolab:v:16:y:2006:i:2:p:1-2 is not listed on IDEAS
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    Cited by:

    1. León, Carlos & Leiton, Karen & Pérez, Jhonatan, 2014. "Extracting the sovereigns’ CDS market hierarchy: A correlation-filtering approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 415(C), pages 407-420.
    2. Carlos León, 2012. "Implied probabilities of default from Colombian money market spreads: The Merton Model under equity market informational constraints," Borradores de Economia 743, Banco de la Republica de Colombia.

    More about this item


    CAPM; Hurst exponent; long-term dependence; fractional Brownian motion; asset allocation; investment horizon.;

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • G20 - Financial Economics - - Financial Institutions and Services - - - General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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