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Capital Asset Pricing with a Stochastic Horizon

Published online by Cambridge University Press:  24 October 2018

Michael J. Brennan  and
Yuzhao Zhang
Michael J. Brennan
Affiliation:
Brennan, michaelbrennan830@gmail.com, University of California–Los Angeles Anderson School and Manchester University
Yuzhao Zhang*
Affiliation:
Zhang, yzhang@business.rutgers.edu, Rutgers University Business School
*
Zhang (corresponding author), yzhang@business.rutgers.edu
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Abstract

In this paper we present empirical tests of an extended version of the capital asset pricing model (CAPM) that replaces the single-period horizon with a probability distribution over different horizons. Adopting a simple parameterization of the probability distribution of the length of the horizon, we estimate the parameters of the distribution as well as the parameters of the CAPM. We find that the extended model is not rejected for several different samples of common stocks, and for these samples it outperforms not only the standard CAPM but also the Fama–French (1993) 3-factor model. The probability distribution over horizon dates varies over time with the New York Stock Exchange (NYSE) turnover rate. We also find that returns satisfy the Euler equation of a representative financial institution that holds the market portfolio and has horizon probabilities estimated from 13F filings.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 55 , Issue 3 , May 2020 , pp. 783 - 827
Copyright
Copyright © Michael G. Foster School of Business, University of Washington 2018

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Footnotes

This paper has benefited greatly from the comments and suggestions of Jennifer Conrad (the editor) and Joost Driessen (the referee). We also thank John Campbell, Jay Shanken, William Sharpe, Grigor Vilkov, Yan Xu, and participants in seminars at Tilburg University, Erasmus University, and the Stockholm School of Economics, as well as Jonathan Lewellen, our discussant at the Western Finance Association, for comments and suggestions on an earlier version of this paper.

References

Abel, A. B.; Eberly, J. C.; and Panageas, S.. “Optimal Inattention to the Stock Market with Information Costs and Transactions Costs.” Econometrica, 81 (2013), 1455–1481.Google Scholar
Adrian, T.; Etula, E.; and Muir, T.. “Financial Intermediaries and the Cross-Section of Asset Returns.” Journal of Finance, 69 (2014), 2555–2596.Google Scholar
Ameriks, J., and Zeldes, S. P.. “How Do Household Portfolio Shares Vary with Age?” Working Paper, Columbia University (2004).Google Scholar
Amihud, Y., and Mendelson, H.. “Asset Pricing and the Bid–Ask Spread.” Journal of Financial Economics, 17 (1986), 223–249.Google Scholar
Beber, A.; Driessen, J.; and Tuijp, P.. “Pricing Liquidity Risk with Heterogeneous Investment Horizons.” Working Paper, Tilburg University (2011).Google Scholar
Black, F.; Jensen, M. C.; and Scholes, M.. “The Capital Asset Pricing Model: Some Empirical Tests.” In Studies in the Theory of Capital Markets, Jensen, M. C., ed. New York: Praeger (1972), 79–121.Google Scholar
Boguth, O.; Carlson, M.; Fisher, A.; and Simutin, M.. “Horizon Effects in Average Returns: The Role of Slow Information Diffusion.” Review of Financial Studies, 29 (2016), 2241–2281.Google Scholar
Brennan, M. J., and Copeland, T. E.. “Beta Changes Around Stock Splits: A Note.” Journal of Finance, 43 (1988), 1009–1014.Google Scholar
Brennan, M. J.; Jegadeesh, N.; and Swaminathan, B.. “Investment Analysis and the Adjustment of Prices to Common Information.” Review of Financial Studies, 6 (1993), 799–824.Google Scholar
Brennan, M. J., and Wang, A.. “The Mispricing Return Premium.” Review of Financial Studies, 23 (2010), 3437–3468.Google Scholar
Brunnermeier, M. K., and Nagel, S.. “Do Wealth Fluctuations Generate Time-Varying Risk Aversion? Micro-Evidence on Individuals’ Asset Allocation.” American Economic Review, 98 (2008), 713–736.Google Scholar
Brunnermeier, M. K., and Sannikov, Y.. “A Macro-Economic Model with a Financial Sector.” American Economic Review, 104 (2014), 379–421.Google Scholar
Calvet, L. E.; Campbell, J. Y.; and Sodini, P.. “Fight or Flight? Portfolio Rebalancing by Individual Investors.” Quarterly Journal of Economics, 124 (2009), 301–346.Google Scholar
Campbell, J. Y., and Vuolteenaho, T.. “Bad Beta, Good Beta.” American Economic Review, 94 (2004), 1249–1275.Google Scholar
Chien, Y.; Cole, H.; and Lustig, H.. “Is the Volatility in the Market Price of Risk due to Intermittent Portfolio Rebalancing?” American Economic Review, 102 (2012), 2859–2896.Google Scholar
Cohen, R. B.; Polk, C.; and Vuolteenaho, R.. “The Price is (Almost) Right.” Journal of Finance, 64 (2009), 2739–2782.Google Scholar
Constantinides, G. M.“Capital Market Equilibrium with Transaction Costs.” Journal of Political Economy, 94 (1986), 842–862.Google Scholar
Davis, M. H. A., and Norman, A. R.. “Portfolio Selection with Transaction Costs.” Mathematics of Operations Research, 15 (1990), 676–713.Google Scholar
Dimson, E.“Risk Measurement When Shares are Subject to Infrequent Trading.” Journal of Financial Economics, 7 (1979), 197–226.Google Scholar
Duffie, D., and Sun, T. S.. “Transactions Costs and Portfolio Choice in a Discrete-Continuous Time Setting.” Journal of Economic Dynamics and Control, 14 (1990), 33–51.Google Scholar
Fama, E. F., and French, K. R.. “The Cross-Section of Expected Stock Returns.” Journal of Finance, 47 (1992), 427–465.Google Scholar
Fama, E. F., and French, K. R.. “Common Risk Factors in the Returns on Stock and Bonds.” Journal of Financial Economics, 33 (1993), 3–56.Google Scholar
Fama, E. F., and French, K. R.. “Multifactor Portfolio Efficiency and Multifactor Asset Pricing.” Journal of Financial and Quantitative Analysis, 31 (1996), 441–465.Google Scholar
Fama, E. F., and French, K. R.. “Dissecting Anomalies with a Five-factor Model.” Review of Financial Studies, 29 (2016), 69–103.Google Scholar
Fama, E. F., and MacBeth, J. D.. “Risk, Return, and Equilibrium: Empirical Tests.” Journal of Political Economy, 81 (1973), 607–636.Google Scholar
Ghysels, E.; Santa-Clara, P.; and Valkanov, R.. “Predicting Volatility: Getting the Most Out of Return Data Sampled at Different Frequencies.” Journal of Econometrics, 131 (2006), 59–95.Google Scholar
Gilbert, T.; Hrdlicka, C.; Kalodimos, J.; and Siegel, S.. “Daily Data is Bad for Beta: Opacity and Frequency-Dependent Betas.” Review of Asset Pricing Studies, 4 (2014), 78–117.Google Scholar
Graham, J. R., and Harvey, C. R.. “Theory and Practice of Corporate Finance: Evidence from the Field.” Journal of Financial Economics, 60 (2001), 187–243.Google Scholar
Handa, P.; Kothari, S. P.; and Wasley, C.. “The Relation Between Return Interval and Betas: Implications for the Size Effect.” Journal of Financial Economics, 23 (1989), 79–100.Google Scholar
Handa, P.; Kothari, S. P.; and Wasley, C.. “Sensitivity of Multivariate Tests of the Capital Asset-Pricing Model to the Return Measurement Interval.” Journal of Finance, 48 (1993), 1543–1551.Google Scholar
Hawawini, H.“Why Beta Shifts as the Return Interval Changes.” Financial Analysts Journal, 39 (1983), 73–77.Google Scholar
He, Z.; Kelly, B.; and Manela, A.. “Intermediary Asset Pricing: New Evidence from Many Asset Classes.” Journal of Financial Economics, 126 (2017), 1–35.Google Scholar
He, Z., and Krishnamurthy, A.. “Intermediary Asset Pricing.” American Economic Review, 103 (2013), 732–770.Google Scholar
Huang, M.“Liquidity Shocks and Equilibrium Liquidity Premia.” Journal of Economic Theory, 109 (2003), 104–129.Google Scholar
Jagannathan, R., and Wang, Y.. “Lazy Investors, Discretionary Consumption, and the Cross-Section of Stock Returns.” Journal of Finance, 62 (2007), 1623–1661.Google Scholar
Kamara, A.; Korajczyk, R. A.; Lou, X.; and Sadka, R.. “Horizon Pricing.” Journal of Financial and Quantitative Analysis, 51 (2016), 1769–1793.Google Scholar
Kothari, S. P.; Shanken, J.; and Sloan, R. G.. “Another Look at the Cross-Section of Expected Stock Returns.” Journal of Finance, 50 (1995), 185–224.Google Scholar
Lee, C. F.“Investment Horizon and the Functional Form of the Capital Asset Pricing Model.” Review of Economics and Statistics, 58 (1976), 356–363.Google Scholar
Lee, C. F.; Wu, C.; and Wei, J.. “The Heterogeneous Investment Horizon and the Capital Asset Pricing Model: Theory and Implications.” Journal of Financial and Quantitative Analysis, 25 (1990), 361–376.Google Scholar
Levhari, D., and Levy, H.. “The Capital Asset Pricing Model and the Investment Horizon.” Review of Economics and Statistics, 59 (1977), 92–104.Google Scholar
Lewellen, J.; Nagel, S.; and Shanken, J.. “A Skeptical Appraisal of Asset Pricing Tests.” Journal of Financial Economics, 96 (2010), 175–194.Google Scholar
Lintner, J.“The Valuation of Risky Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets.” The Review of Economics and Statistics, 47 (1965), 13–37.Google Scholar
Lo, A., and MacKinlay, C.. “When are Contrarian Profits due to Stock Market Overreaction?” Review of Financial Studies, 3 (1990), 175–205.Google Scholar
Longstaff, F.“Temporal Aggregation and the Continuous-Time Capital Asset Pricing Model.” Journal of Finance, 44 (1989), 871–887.Google Scholar
Martellini, L., and Urosevic, B.. “Static Mean-Variance Analysis with Uncertain Time Horizon.” Management Science, 52 (2006), 955–964.Google Scholar
Merton, R. C.“An Intertemporal Capital Asset Pricing Model.” Econometrica, 41 (1973), 867–887.Google Scholar
Mossin, J.“Equilibrium in a Capital Asset Market.” Econometrica, 34 (1966), 768–783.Google Scholar
Richard, S. F.“Optimal Consumption, Portfolio, and Life Insurance Rules for an Uncertain Lived Individual in a Continuous Time Model.” Journal of Financial Economics, 2 (1975), 187–203.Google Scholar
Scholes, M. S., and Williams, J.. “Estimating Betas from Non-Synchronous Data.” Journal of Financial Economics, 5 (1977), 308–328.Google Scholar
Shanken, J.“On the Estimation of Beta-Pricing Models.” Review of Financial Studies, 5 (1992), 1–33.Google Scholar
Sharpe, W. F.“Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk.” Journal of Finance, 29 (1964), 425–442.Google Scholar
Wiggins, J. B.“Betas around Stock Splits Revisited.” Journal of Financial and Quantitative Analysis, 27 (1992), 631–640.Google Scholar