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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 EMAIL logo


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


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.


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


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:


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)}].


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Supplementary Material

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Published Online: 2018-08-14

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