Investment horizon dependent CAPM: Adjusting beta for long-term dependence
AbstractFinancial 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
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Bibliographic InfoPaper provided by Banco de la Republica de Colombia in its series Borradores de Economia with number 730.
Date of creation: Aug 2012
Date of revision:
CAPM; Hurst exponent; long-term dependence; fractional Brownian motion; asset allocation; investment horizon. Classification JEL: G12; G14; G32; G20; C14;
Other versions of this item:
- 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.
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-09-03 (All new papers)
- NEP-CFN-2012-09-03 (Corporate Finance)
- NEP-ECM-2012-09-03 (Econometrics)
- NEP-FMK-2012-09-03 (Financial Markets)
- NEP-RMG-2012-09-03 (Risk Management)
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- Carlos Eduardo Léon Rincón & Karen Juliet Leiton & Jhonatan Pérez Villalobos, 2013.
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- Carlos Eduardo León Rincón & Karen Julieth Leiton & Jhonatan Perez Villalobos, 2013. "Extracting the sovereigns’ CDS market hierarchy: a correlation-filtering approach," Borradores de Economia 766, Banco de la Republica de Colombia.
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- Carlos León, 2012. "Implied probabilities of default from Colombian money market spreads: The Merton Model under equity market informational constraints," BORRADORES DE ECONOMIA 010075, BANCO DE LA REPÚBLICA.
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