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A unified framework jointly explaining business conditions, stock returns, volatility and “volatility feedback news” effects

Chang-Jin Kim and Yunmi Kim

Abstract

One of central questions to macroeconomics and finance has been whether macroeconomic factors are useful predictors for expected stock returns. The general consensus is somewhat surprising in that financial factors, rather than macroeconomic factors, have predictive power on stock returns. Such predictability of financial factors is justified on the ground that those factors can act as a proxy for future business conditions and undiversifiable risk. Hence, they should be priced in terms of expected returns. However, as suggested by Campbell, S., and F. Diebold. 2009. “Stock Returns and Expected Business Conditions: Half a Century of Direct Evidence.” Journal of Business & Economic Statistics 27 (2): 266–278, such a justification can be puzzling because macroeconomic factors are likely to have a closer and more direct link to future business conditions than financial factors. In this paper, we will attempt to solve this puzzling problem by accounting for market volatility when measuring the relationship between stock returns and macroeconomic factors. As a result, we propose a unified framework in which the three components of macroeconomic factors, market volatility, and stock returns are jointly embedded.

JEL Classification: C32; C51; G12

Acknowledgments

We would like to thank Bruce Mizrach (the Editor), an Associate Editor, and two anonymous referees for their insightful comments and suggestions on an earlier draft of this article. This work was supported by the 2015 Research Fund of the University of Seoul for Yunmi Kim.

Appendix

For maximum likelihood estimation of our proposed model in (17)–(22), we derive the following (log) likelihood function:

(23)lnL(θ1,θ2)=tlnf(rt,zt|It1;θ1,θ2)=tlnf(rt|zt,It1;θ1)+tlnf(zt|It1;θ2),

where θ1(β,σ02,σ12,γ0,γ1),θ2 ≡ (vec(ϕ1)′, … vec(ϕp)′, vechu)′)′, and f(•) is the conditional density. Note that vec(ϕi) is the standard vectorizing function and vechu) is the vector (of size [n(n + 1)/2] × 1) obtained by vectorizing only the lower triangular part of the symmetric matrix Σu. Based on equation (23), we sequentially estimate θ2 by maximizing the second term in (23), which is equivalent to estimating θ2 from equation (22) by OLS. Then, we estimate θ1 by maximizing the first term in (23). To maximize the first term, it is convenient to express the likelihood function f(rt|zt, It−1; θ1) appearing inside the summation as follows:

(24)f(rt|zt,It1;θ1)=St=0,1f(rt|St,zt,It1;θ1)Pr(St|zt;θ1)

where Pr[St=0|zt]=Φ(γ0γ1zt);Pr[St=1|zt]=1Φ(γ0γ1zt);

f(rt|St=0,It1,zt)=12πσ02exp(et22σ02); f(rt|St=1,It1,zt)=12πσ12exp(et22σ12); and where et=rt[β0+β1h{FZt1}][β1h{(In×pρF)1ρF(ZtFZt1)}].

References

Beaudry, P., and F. Portier. 2004. “An Exploration into Pigou’s Theory of Cycles.” Journal of Monetary Economics 51 (6): 1183–1216.10.1016/j.jmoneco.2003.10.003Search in Google Scholar

Beaudry, P., and B. Lucke. 2010. “Letting Different Views about Business Cycles Compete.” NBER Macroeconomics Annual 24 (1): 413–456.10.1086/648305Search in Google Scholar

Beaudry, P., and F. Portier. 2014. “News-Driven Business Cycles: Insights and Challenges.” Journal of Economic Literature 52 (4): 993–1074.10.1257/jel.52.4.993Search in Google Scholar

Bollerslev, T., and H. Zhou. 2006. “Volatility Puzzles: A Simple Framework for Gauging Return-Volatility Regressions.” Journal of Econometrics 131 (1): 123–150.10.1016/j.jeconom.2005.01.006Search in Google Scholar

Campbell, J. 1999. “Asset Prices, Consumption, and the Business Cycle.” In Handbook of Macroeconomics, Volume 1, edited by J. B. Taylor and M. Woodford, 1231–1303. North-Holland: Amsterdam.Search in Google Scholar

Campbell, J., and R. Shiller. 1988. “The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors.” Review of Financial Studies 1: 195–228.10.1093/rfs/1.3.195Search in Google Scholar

Campbell, J., and L. Hentschel. 1992. “No News is Good News: An Asymmetric Model of Changing Volatility in Stock Returns.” Journal of Financial Economics 31: 281–331.10.1016/0304-405X(92)90037-XSearch in Google Scholar

Campbell, S., and F. Diebold. 2009. “Stock Returns and Expected Business Conditions: Half a Century of Direct Evidence.” Journal of Business & Economic Statistics 27 (2): 266–278.10.1198/jbes.2009.0025Search in Google Scholar

Chen, N. F., R. Roll, and S. Ross. 1986. “Economic Forces and the Stock Market.” Journal of Business 59: 383–403.10.1086/296344Search in Google Scholar

Diebold, F. X., J. H. Lee, and G. C. Weinbach. 1994. “Regime Switching with Time-Varying Transition Probabilities.” In Non-stationary Time Series Analysis and Cointegration, 283–302. Oxford: Oxford University Press.Search in Google Scholar

Fama, E., and K. French. 1989. “Business Conditions and Expected Returns on Stocks and Bonds.” Journal of Financial Economics 25: 23–49.10.1016/0304-405X(89)90095-0Search in Google Scholar

Filardo, A. J. 1994. “Business-Cycle Phases and Their Transitional Dynamics.” Journal of Business & Economic Statistics 12 (3): 299–308.Search in Google Scholar

Flannery, M. J., and A. A. Protopapadakis. 2002. “Macroeconomic Factors Do Influence Aggregate Stock Returns.” Review of Financial Studies 15 (3): 751–782.10.1093/rfs/15.3.751Search in Google Scholar

French, K., W. Schwert, and R. Stambaugh. 1987. “Expected Stock Returns and Volatility.” Journal of Financial Economics 19: 3–30.10.1016/0304-405X(87)90026-2Search in Google Scholar

Glosten, L., R. Jagannathan, and D. Runkle. 1993. “On the Relation Between the Expected Value and the Volatility of the Nominal Excess Return on Stocks.” Journal of Finance 48: 1779–1801.10.1111/j.1540-6261.1993.tb05128.xSearch in Google Scholar

Hamilton, J. D., and G. Lin. 1996. “Stock Market Volatility and the Business Cycle.” Journal of Applied Econometrics 11: 573–593.10.1002/(SICI)1099-1255(199609)11:5<573::AID-JAE413>3.0.CO;2-TSearch in Google Scholar

Kim, Y., and C. R. Nelson. 2014. “Pricing Stock Market Volatility: Does it Matter whether the Volatility is Related to the Business Cycle?” Journal of Financial Econometrics 12 (2): 307–328.10.1093/jjfinec/nbt014Search in Google Scholar

Kim, C.-J., J. Morley, and C. R. Nelson. 2004. “Is There a Positive Relationship between Stock Market Volatility and the Equity Premium?” Journal of Money, Credit, and Banking 36: 339–360.10.1353/mcb.2004.0055Search in Google Scholar

Lettau, M., and S. Ludvigson. 2001. “Consumption, Aggregate Wealth, and Expected Stock Returns.” Journal of Finance 56: 815–849.10.1111/0022-1082.00347Search in Google Scholar

Lewellen, J. 1999. “The Time-Series Relations among Expected Return, Risk, and Book-to-Market.” Journal of Financial Economics 54: 5–43.10.1016/S0304-405X(99)00030-6Search in Google Scholar

McQueen, G., and V. Roley. 1993. “Stock Prices, News, and Business Conditions.” Review of Financial Studies 6: 683–707.10.1093/rfs/5.3.683Search in Google Scholar

Pearce, D. K., and V. V. Roley. 1985. “Stock Prices and Economic News.” Journal of Business 58: 49–67.10.1086/296282Search in Google Scholar

Ross, S. A. 1976. “The Arbitrage Theory and Capital Asset Pricing.” Journal of Economic Theory 13: 341–360.10.1016/0022-0531(76)90046-6Search in Google Scholar

Schwert, G. W. 1981. “The Adjustment of Stock Prices to Information About Inflation.” Journal of Finance 36 (1): 15–29.10.1111/j.1540-6261.1981.tb03531.xSearch in Google Scholar

Sims, C. A. 1980. “Macroeconomics and Reality.” Econometrica 48 (1): 1–48.10.2307/1912017Search in Google Scholar

Stock, J., and M. W. Watson. 2001. “Vector Autoregressions.” Journal of Economic Perspectives 15 (4): 101–115.10.1257/jep.15.4.101Search in Google Scholar

Turner, C., R. Startz, and C. R. Nelson. 1989. “A Markov Model of Heteroscedasticity, Risk, and Learning in the Stock Market.” Journal of Financial Economics 25: 3–22.10.1016/0304-405X(89)90094-9Search in Google Scholar

Yu, J. 2005. “On Leverage in a Stochastic Volatility Model.” Journal of Econometrics 127: 165–178.10.1016/j.jeconom.2004.08.002Search in Google Scholar

Supplementary Material

The online version of this article offers supplementary material (DOI: https://doi.org/10.1515/snde-2016-0151).

Published Online: 2018-08-14

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