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Estimating Beta

Published online by Cambridge University Press:  01 November 2016

Fabian Hollstein  and
Marcel Prokopczuk
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Abstract

We conduct a comprehensive comparison of market beta estimation techniques. We study the performance of several historical, time-series model, and option-implied estimators for estimating realized market beta. Thereby, we find the hybrid methodology of Buss and Vilkov to consistently outperform all other approaches. In addition, all other approaches, including fully implied and dynamic conditional beta, based on generalized autoregressive conditional heteroskedasticity (GARCH) models, are dominated by a simple beta estimate based on historical (co-)variances and an approach based on the Kalman filter. Our conclusions remain unchanged after performing several robustness checks.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 51 , Issue 4 , August 2016 , pp. 1437 - 1466
Copyright
Copyright © Michael G. Foster School of Business, University of Washington 2016 

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References

Agnolucci, P.“Volatility in Crude Oil Futures: A Comparison of the Predictive Ability of GARCH and Implied Volatility Models.” Energy Economics, 31 (2009), 316–321.Google Scholar
Andersen, T. G.; Bollerslev, T.; Diebold, F. X.; and Wu, G.. “Realized Beta: Persistence and Predictability.” Advances in Econometrics, 20 (2006), 1–39.Google Scholar
Baker, M.; Bradley, B.; and Wurgler, J.. “Benchmarks as Limits to Arbitrage: Understanding the Low Volatility Anomaly.” Financial Analysts Journal, 67 (2010), 40–54.Google Scholar
Bakshi, G.; Kapadia, N.; and Madan, D.. “Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options.” Review of Financial Studies, 16 (2003), 101–143.Google Scholar
Bakshi, G., and Madan, D.. “Spanning and Derivative-Security Valuation.” Journal of Financial Economics, 55 (2000), 205–238.Google Scholar
Bali, T. G.; Engle, R. F.; and Tang, Y.. “Dynamic Conditional Beta Is Alive and Well in the Cross-Section of Daily Stock Returns.” Working Paper, Georgetown University (2015).Google Scholar
Baule, R.; Korn, O.; and Saßning, S.. “Which Beta Is Best? On the Information Content of Option-Implied Betas.” European Financial Management, 22 (2016), 450–483.Google Scholar
Black, A.; Fraser, P.; and Power, D.. “UK Unit Trust Performance 1980–1989: A Passive Time-Varying Approach.” Journal of Banking & Finance, 16 (1992), 1015–1033.CrossRefGoogle Scholar
Black, F.“Studies of Stock Price Volatility Changes.” Proceedings of the 1976 Meetings of the American Statistical Association, Business and Economical Statistics Section, 34 (1976), 177–181.Google Scholar
Black, F., and Scholes, M.. “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy, 81 (1973), 637–654.Google Scholar
Blume, M. E.“Betas and Their Regression Tendencies.” Journal of Finance, 30 (1975), 785–795.Google Scholar
Bollerslev, T.“Modelling the Coherence in Short-Run Nominal Exchange Rates: A Multivariate Generalized ARCH Model.” Review of Economics and Statistics, 72 (1990), 498–505.Google Scholar
Buss, A., and Vilkov, G.. “Measuring Equity Risk with Option-Implied Correlations.” Review of Financial Studies, 25 (2012), 3113–3140.Google Scholar
Canina, L., and Figlewski, S.. “The Informational Content of Implied Volatility.” Review of Financial Studies, 6 (1993), 659–681.CrossRefGoogle Scholar
Cappiello, L.; Engle, R. F.; and Sheppard, K.. “Asymmetric Dynamics in the Correlations of Global Equity and Bond Returns.” Journal of Financial Econometrics, 4 (2006), 537–572.Google Scholar
Carr, P., and Wu, L.. “Variance Risk Premiums.” Review of Financial Studies, 22 (2009), 1311–1341.CrossRefGoogle Scholar
Chakravarty, S.; Gulen, H.; and Mayhew, S.. “Informed Trading in Stock and Option Markets.” Journal of Finance, 59 (2004), 1235–1258.Google Scholar
Chang, B.-Y.; Christoffersen, P.; Jacobs, K.; and Vainberg, G.. “Option-Implied Measures of Equity Risk.” Review of Finance, 16 (2012), 385–428.Google Scholar
Charoenwong, C.; Jenwittayaroje, N.; and Low, B. S.. “Who Knows More about Future Currency Volatility?” Journal of Futures Markets, 29 (2009), 270–295.Google Scholar
Christensen, B. J., and Prabhala, N. R.. “The Relation between Implied and Realized Volatility.” Journal of Financial Economics, 50 (1998), 125–150.Google Scholar
Christie, A. A.“The Stochastic Behavior of Common Stock Variances: Value, Leverage and Interest Rate Effects.” Journal of Financial Economics, 10 (1982), 407–432.Google Scholar
Dennis, P., and Mayhew, S.. “Risk-Neutral Skewness: Evidence from Stock Options.” Journal of Financial and Quantitative Analysis, 37 (2002), 471–493.Google Scholar
Driessen, J.; Maenhout, P. J.; and Vilkov, G.. “The Price of Correlation Risk: Evidence from Equity Options.” Journal of Finance, 64 (2009), 1377–1406.Google Scholar
Engle, R. F.“Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models.” Journal of Business & Economic Statistics, 20 (2002), 339–350.Google Scholar
Engle, R. F.“Dynamic Conditional Beta.” Working Paper, New York University (2014).CrossRefGoogle Scholar
Faff, R. W.; Hillier, D.; and Hillier, J.. “Time Varying Beta Risk: An Analysis of Alternative Modelling Techniques.” Journal of Business Finance & Accounting, 27 (2000), 523–554.CrossRefGoogle Scholar
Fama, E. F., and MacBeth, J. D.. “Risk, Return, and Equilibrium: Empirical Tests.” Journal of Political Economy, 81 (1973), 607–636.Google Scholar
Ferson, W. E., and Harvey, C. R.. “The Variation of Economic Risk Premiums.” Journal of Political Economy, 99 (1991), 385–415.Google Scholar
Ferson, W. E., and Harvey, C. R.. “The Risk and Predictability of International Equity Returns.” Review of Financial Studies, 6 (1993), 527–566.CrossRefGoogle Scholar
Fleming, J.“The Quality of Market Volatility Forecasts Implied by S&P 100 Index Option Prices.” Journal of Empirical Finance, 5 (1998), 317–345.CrossRefGoogle Scholar
French, D. W.; Groth, J. C.; and Kolari, J. W.. “Current Investor Expectations and Better Betas.” Journal of Portfolio Management, 10 (1983), 12–17.Google Scholar
Frijns, B.; Tallau, C.; and Tourani-Rad, A.. “The Information Content of Implied Volatility: Evidence from Australia.” Journal of Futures Markets, 30 (2010), 134–155.Google Scholar
Ghysels, E.“On Stable Factor Structures in the Pricing of Risk: Do Time-Varying Betas Help or Hurt?” Journal of Finance, 53 (1998), 549–573.Google Scholar
Glosten, L. R.; Jagannathan, R.; and Runkle, D. E.. “On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks.” Journal of Finance, 48 (1993), 1779–1801.Google Scholar
Guo, D.“The Predictive Power of Implied Stochastic Variance from Currency Options.” Journal of Futures Markets, 16 (1996), 915–942.3.0.CO;2-P>CrossRefGoogle Scholar
Hansen, P. R., and Lunde, A.. “Consistent Ranking of Volatility Models.” Journal of Econometrics, 131 (2006), 97–121.CrossRefGoogle Scholar
Harvey, D.; Leybourne, S.; and Newbold, P.. “Testing the Equality of Prediction Mean Squared Errors.” International Journal of Forecasting, 13 (1997), 281–291.Google Scholar
Jiang, G. J., and Tian, Y. S.. “The Model-Free Implied Volatility and Its Information Content.” Review of Financial Studies, 18 (2005), 1305–1342.Google Scholar
Jorion, P.“Predicting Volatility in the Foreign Exchange Market.” Journal of Finance, 50 (1995), 507–528.CrossRefGoogle Scholar
Kempf, A.; Korn, O.; and Saßning, S.. “Portfolio Optimization Using Forward-Looking Information.” Review of Finance, 20 (2015), 467–490.Google Scholar
Lewellen, J., and Nagel, S.. “The Conditional CAPM Does Not Explain Asset-Pricing Anomalies.” Journal of Financial Economics, 82 (2006), 289–314.Google Scholar
Lintner, J.“The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets.” Review of Economics and Statistics, 47 (1965), 13–37.Google Scholar
Martens, M., and Zein, J.. “Predicting Financial Volatility: High-Frequency Time-Series Forecasts vis-à-vis Implied Volatility.” Journal of Futures Markets, 24 (2004), 1005–1028.Google Scholar
Mincer, J. A., and Zarnowitz, V.. “The Evaluation of Economic Forecasts.” In Economic Forecasts and Expectations: Analysis of Forecasting Behavior and Performance, NBER (1969), 1–46.Google Scholar
Mossin, J.“Equilibrium in a Capital Asset Market.” Econometrica, 34 (1966), 768–783.Google Scholar
Newey, W. K., and West, K. D.. “A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix.” Econometrica, 55 (1987), 703–708.Google Scholar
Pagan, A.“Some Identification and Estimation Results for Regression Models with Stochastically Varying Coefficients.” Journal of Econometrics, 13 (1980), 341–363.Google Scholar
Pagan, A. R., and Schwert, G. W.. “Alternative Models for Conditional Stock Volatility.” Journal of Econometrics, 45 (1990), 267–290.Google Scholar
Patton, A. J.“Volatility Forecast Comparison Using Imperfect Volatility Proxies.” Journal of Econometrics, 160 (2011), 246–256.Google Scholar
Poon, S.-H., and Granger, C. W.. “Forecasting Volatility in Financial Markets: A Review.” Journal of Economic Literature, 41 (2003), 478–539.CrossRefGoogle Scholar
Prokopczuk, M., and Wese Simen, C.. “The Importance of the Volatility Risk Premium for Volatility Forecasting.” Journal of Banking & Finance, 40 (2014), 303–320.Google Scholar
Ross, S. A.“The Arbitrage Theory of Capital Asset Pricing.” Journal of Economic Theory, 13 (1976), 341–360.Google Scholar
Sharpe, W. F.“Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk.” Journal of Finance, 19 (1964), 425–442.Google Scholar
Siegel, A. F.“Measuring Systematic Risk Using Implicit Beta.” Management Science, 41 (1995), 124–128.Google Scholar
Skintzi, V. D., and Refenes, A.-P. N.. “Implied Correlation Index: A New Measure of Diversification.” Journal of Futures Markets, 25 (2005), 171–197.Google Scholar
Szakmary, A.; Ors, E.; Kim, J. K.; and Davidson, W. N. III. “The Predictive Power of Implied Volatility: Evidence from 35 Futures Markets.” Journal of Banking & Finance, 27 (2003), 2151–2175.Google Scholar
Taylor, S. J.; Yadav, P. K.; and Zhang, Y.. “The Information Content of Implied Volatilities and Model-Free Volatility Expectations: Evidence from Options Written on Individual Stocks.” Journal of Banking & Finance, 34 (2010), 871–881.Google Scholar
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