Four types of tail dependence structures between U.S. dollar index and S&P 500 stock returns:1990-2019

ABSTRACT

This research investigates four tail relationships between the U.S. dollar and S&P 500 returns by a dynamic mixture copula model with a link between the dependence structure and dependence intensity. The empirical results find that four tail relationships are evident and time-varying. Regarding the negative dependence, the tail relationship is prominently stronger in the situation where the U.S. dollar depreciates and the stock index increases than in the situation where the U.S. dollar appreciates and the stock index declines. Regarding the positive dependence, the situation of two returns increase occurs slightly more frequently than the situation of two returns decrease.

KEYWORDS:

• U.S. dollar index
• S&P 500
• tail dependence
• mixture mechanism

JEL CLASSIFICATION:

• C32
• F31
• G10

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

¹ The dynamic structure and dynamic intensity refers to the time-varying weights of copula functions and time-varying copula parameters, respectively.

² A similar approach has been employed by Naeem et al. (2021) to analyse energy markets and green bonds

³ The S&P 500 index covers the largest ratio of U.S. stock market capitalization, as compared to the Nasdaq Composite index and the Dow Jones Industrial Average index.

⁴ The time-series process of $r_{it}$ is described as follows:

$r_{it}=a_{io}+a_{i1}{r}_{i,t-1}+\sqrt{h_{it}}{v}_{it},v_{it}\sim st\left(d{f}_i\right)$

$h_{it}=w_i+{\alpha }_i{\left(\sqrt{h_{i,t-1}}{v}_{i,t-1}\right)}^2+{\beta }_i{h}_{i,t-1}$

⁵ The parameter $w_{pt}$ is defined as follows: $w_{pt}=\left(\mathrm{l}n\left(C_{G,t}\right)+ln\left(C_{RG,t}\right)\right)/\left(ln\left(C_{G,t}\right)+ln\left(C_{RG,t}\right)+ln\left(C_{CRG,t}\right)+ln\left(C_{CCRG,t}\right)\right)$.

⁶ Results are available upon request.

⁷ Results for marginal specifications are available upon request.

Additional information

Funding

This work was supported by the Ministry of Science and Techonology of Taiwan.