Does the CBOE Volatility Index Predict Downside Risk at the Tokyo Stock Exchange ?

This study investigates the predictability of the preceding day’s US volatility index (VIX) from the Chicago Board Options Exchange (CBOE) for sharp price drops of the Tokyo Stock Price Index (TOPIX) by employing several versions of probit models. All our results indicate that the preceding day’s US S&P 500 VIX movement has predictive power for sharp price declines of the TOPIX in Japan. As we repeatedly examined several left tail risks in TOPIX price changes and we also tested by applying some different versions of probit models, our evidence of the forecast power of the S&P 500 VIX for downside risk of the TOPIX shall be very robust.


Introduction
In a globalizing economy, much more academics and practitioners are paying attention to the research of international stock market connections.However, we note that many past investigations have been performed for overall stock market evolution, which contains all conditions or state of bull, bear, and ordinary markets (see, e.g., Diebold and Yilmaz, 2012;Wang, 2014).In light of this point, this study newly examines the international equity market linkages with a particular focus on the downward stock market condition.
More concretely, from the above new viewpoint, this study empirically tests the predictive power of the preceding day's US S&P 500 volatility index (VIX) from the Chicago Board Options Exchange (CBOE) for sharp price drops of the Tokyo Stock Price Index (TOPIX) by applying several versions of probit models.Our investigations employing US and Japanese financial market data reveal the following new findings.(1) First, the estimation results from our simple univariate probit model suggest that the dynamic evolution of the preceding day's US VIX has statistically significant predictive power for large TOPIX price drops in Japan.(2) Second, the estimation results from our autoregressive (AR)(3)-probit model also indicate that the preceding day's US VIX has statistically significant forecast power for large declines in TOPIX.(3) Finally, the estimation results from our probit model with different control variables again suggest that the preceding day's US VIX has statistically significant predictive power for the next day's sharp TOPIX price declines in Japan.The above new robust evidence from our examinations with new analyzing viewpoint is the contribution of this work.
Regarding the organization of the rest of this paper, Section 2 reviews previous studies; Section 3 explains our data and variables for our research; Section 4 documents our analyzing methodology; Section 5 supplies our empirical results; and Section 6 documents our interpretations and conclusions.

Literature Review
In this section, we concisely review existing literature focusing only on recent studies.Wang (2014) recently investigated the integration and causality relationships among six major East Asian stock markets, and this study also examined their interactions with the US market before and during the financial crisis from 2007 to 2009.Ülkü and Baker (2014) examined the connection between macroeconomic linkages and stock market linkages by inspecting the relations between macroeconomic betas and stock market betas.Mensi et al. (2016) examined the spillover effects between the US stock market and those of the BRICs (Brazil, Russia, India, China) and South Africa.Laopodis (2016) studied the linkages of US seventeen industry returns, the US stock market, and several economic fundamental variables.As for the study in the context of downward stock markets, by focusing on the US stock market, Tsuji (2016) rigorously evidenced the superior forecast power of volatility forecasts derived from several kinds of generalized autoregressive conditional heteroskedasticity (GARCH) models (This paper can be downloaded from the journal's web site.).However, there seems to be little previous study that examined the forecast power of the US VIX for sharp drops of the Japanese stock market.

Data and Variables
In this section, we describe our data and variables used in this study.First, DTPX means the first difference as to the price of the TOPIX in Japan, TPX.Next, DSPX denotes the first difference as to the level of the S&P 500 VIX in the US, SPX.Further, as control variables, we employ DTERM and DEX.More concretely, DTERM means the first difference series of the interest rate spread between the benchmark 10-year Japanese government bond yield and the Japanese three-month interbank offered rate.In addition, DEX denotes the first difference of the time-series as to the exchange rate of the Japanese yen to the US dollar.
All our data are daily time-series and the sample period examined in this work is from January 2, 2004 to September 5, 2016.The data source of all our data is Thomson Reuters.In Figure 1, we exhibit the daily time-series evolution of SPX and TPX for our sample period.This figure suggests that when the US VIX largely increases, the TOPIX sharply drops.

Testing Methodology
In this section, we document our testing methodology.In this study, we employ three kinds of probit models to test the forecast power of the US S&P 500 VIX for sharp price drops in the TOPIX.It is emphasized that our repeated examinations with below different three probit models should be effective for robustness checks as to the predictability of the US VIX.
Our first model is the following simple univariate probit model: In the above model ( 1), DTPX denotes the first diferrence of the TOPIX, DSPX denotes the first diferrence of the S&P 500 VIX, k% VaR means the k% Value at Risk, and k takes one of the values of 94, 95, 96, 97, 98, and 99 in our analyses (the same hereinafter).Hence, all our investigations test the predictive power of the US S&P 500 VIX for the downside tail risk in the price changes of the TOPIX in Japan.
Table 3. Predictive power of the volatility index of the S&P 500 for large drops in the TOPIX: Results of AR( 3 The second model used in our tests is the following AR(3)-probit model (2): Further, our third model is the following multiple probit model: We note that in this third model (3), the first lags of DTPX, DTERM, and DEX are included as control variables.

Figure 1 .
Figure 1.Dynamic daily evolution of the S&P 500 VIX and the TOPIX Note: DSPX(−1) means the first lag of the first difference as to the S&P 500 VIX in the US.DTPX(−k) means the kth lag of the first difference as to the TOPIX price in Japan.McFadden R 2 denotes the McFadden's R-squared value.***, **, and * indicate the statistical significance at the 1%, 5%, and 10% levels, respectively.

DSPX
Note: DSPX(−1) means the first lag of the first difference as to the S&P 500 VIX in the US.DTPX(−k) means the kth lag of the first difference as to the TOPIX price in Japan.DTERM(−1) means the first lag of the first difference as to the Japanese term spread and DEX(−1) denotes the first lag of the first difference as to the exchange rate of the Japanese yen to the US dollar.McFadden R 2 denotes the McFadden's R-squared value.***, **, and * indicate the statistical significance at the 1%, 5%, and 10% levels, respectively.

Table 1 .
Descriptive statistics of US and Japanese financial market variables DSPX means the first difference as to the US S&P 500 VIX, SPX.DTPX means the first difference as to the TOPIX in Japan, TPX.DTERM means the first difference as to the Japanese term spread and DEX denotes the first difference as to the exchange rate of the Japanese yen to the US dollar.

Table 2 .
Predictive power of the volatility index of the S&P 500 for large drops in the TOPIX: Results of univariate probit models Note: DSPX(−1) means the first lag of the first difference as to the S&P 500 VIX in the US.McFadden R 2 denotes the McFadden's R-squared value.*** indicates the statistical significance at the 1% level.

Table 4 .
Predictive power of the volatility index of the S&P 500 for large drops in the TOPIX: Results of probit models with control variables