**4. Data**

The data in this study cover the US aggregate stock market index (TTMK-US\$*RI*) for the monthly observations spanning from January 1990 through June 2019. To measure the risks in the stock and bond markets, I use the implied stock market volatility (VIX*t*) obtained from the S&P 500 index options and *MOVEt*, the one-month Merrill Lynch Option Volatility Estimate of bond volatility. To conduct robustness tests, the US aggregate stock market indices also include the Dow-Jones Industrial Average (DJIA), the NASDAQ Composite Index (NASDAQ), the RUSSELL 2000 (RUSSELL), and the S&P 500 Value stock index (VALUE). For bond markets, the data cover the bond price indices of maturities for 30 years, 10 years, seven years, five years, and two years. The data for the total stock market, VIX, MOVE, and bond markets indices are obtained from Thomson Reuters' Datastream. Returns are constructed by taking the log-di fference of the price indices times 100.

The data for the categorical uncertainty indices are equivalent to the economic policy uncertainty (EPU) data used by Baker et al. (2016). The construction of the EPU index is based on the following components: newspaper coverage of policy-related economic uncertainty, which is based on 10 large

<sup>3</sup> This section follows closely to Engle (2009, pp. 45–49).

newspapers; the number of federal tax code provisions set to expire in future years; and disagreements among economic forecasters, which are used as a proxy for uncertainty. Based on a similar procedure, Baker, Bloom, and Davis (BBD) construct categorical indices, including the MPU and FPU indices. Of these indices, the MPU and FPU are based on several dimensions of information: (i) the Access World News database of over 2000 newspapers; (ii) a balanced panel of 10 major national and regional US papers, including a broader set of terms designed to capture domestic and foreign sources of monetary policy and fiscal policy uncertainties; and (iii) data scaled by the total number of articles. The term sets for economic policy, monetary policy, and fiscal policy uncertainty indices are given in the Appendix A. These data can be downloaded from the link given below: http: //www.policyuncertainty.com/categorical\_terms.html.

Note that the choice of the US data is based on the rationale that these data can be used to construct a dynamic correlation between stocks and bonds with combinations of di fferent stock indices and maturities of bonds. More importantly, our goal is to use policy uncertainty, including economic policy uncertainty, fiscal policy uncertainty and monetary policy uncertainty to explain the dynamic correlations. These data are more consistently available in the US market and not as accessible in other markets. The data constraint limits our research scope.

#### **5. Empirical Estimations**

#### *5.1. Estimated Stock–Bond Dynamic Correlations*

Table 1 provides di fferent correlation matrices of stock returns, bond returns, risk and uncertainty. Panel A. reports the correlations of total stock market (TTMK) return and bond returns with di fferent maturities. The statistics show negative correlation coe fficients ranging from −0.12 to −0.15. The corresponding t-ratios are statistically significant, the only exception is the coe fficient of a two-year bond. The other elements in this table are the correlations of bond returns, which range between 0.59 and 0.98. Panel B presents the correlations among di fferent measures of stock returns and range from 0.74 to 0.95 (VALUE and DJIA). Due to the high correlation in both types of assets, most researchers tend to use only one type of stock measure, i.e., total market return, and one type of bond return, i.e., 10-year bond, to engage empirical analysis. Panel C provides a correlation matrix that illustrates the correlation of VIX and di fferent categorical policy uncertainties. It shows that FPU and MPU are highly correlated with EPU, and VIX has the highest correlation with MOVE. To visually demonstrate, Figure 1 presents time varying correlations for VIX, MOVE, EPU, FPU, and MPU in the US market. Panel D reports the summary of statistics for VIX and uncertainty variables. Among them, the FPU surprisingly has the highest standard deviation, while the VIX has the lowest. The information is not usually observable by the public.


**Table 1.** Correlation matrices of stock returns, bond returns, risk, and uncertainty.

**Panel A.** Correlations of bond index returns.


**Table 1.** *Cont*.

**Panel D.** Summary of statistics of risk and uncertainty.

**Figure 1.** Time-varying VIX, MOVE, EPU, FPU, and MPU in the US market.

#### *5.2. Estimated Stock–Bond Correlation Coe*ffi*cients*

Table 2 contains parametric estimates of the covariance between stock and various bond returns using the ADCC-GARCH model as represented by the system of Equations (1)–(5). Estimates in Table 2 are pairwise covariances between TTMK stock returns and one of the bond returns from 30 year to two year bonds, *hij*(*RmR*<sup>30</sup>*<sup>y</sup> b* ), *hij*(*RmR*<sup>10</sup>*<sup>y</sup> b* ), *hij*(*RmR*<sup>7</sup>*yb* ), *hij*(*RmR*<sup>5</sup>*yb* ), and *hij*(*RmR*<sup>2</sup>*yb* ). The reported statistics for conditional variances indicate that the lagged conditional variance, β*ij*, and the lagged shock squared, <sup>α</sup>*ij*, are largely statistically significant except for α11. This result indicates that the GARCH-type model is relevant. Turning to the asymmetric impact of shocks on conditional variance, we find that most of the estimated coefficients in the stock and bond markets γ*ij* are highly significant. The exception is γ11, which is not consistent with the expected sign. Judging from the estimated coefficient and the associated t-statistics, the variance equation is apparently dominated by the predictive power from the lagged variance term.<sup>4</sup> Having estimated *hij*(*Rm*,*Rb*), it can derive: ρ<sup>ˆ</sup>*ij*,*<sup>t</sup>* = *hij*,*<sup>t</sup>* √*hii*,*<sup>t</sup>*√*hjj*,*<sup>t</sup>*.

**Table 2.** Estimates of the asymmetric dynamic correlation (ADCC) models parameters for stock–bond return correlations.

.


Note: This table estimate the parameters for conditional variance and covariance between total stock returns and various bond returns. For an *ADCC*(*RmR*<sup>10</sup>*<sup>y</sup> b* ) model, the model is given by: ⎡⎢⎢⎢⎢⎢⎢⎣ *h*11,*t h*12,*t h*22,*t* ⎤⎥⎥⎥⎥⎥⎥⎦ = ⎡⎢⎢⎢⎢⎢⎢⎣ ω11 ω12 ω22 ⎤⎥⎥⎥⎥⎥⎥⎦ + ⎡⎢⎢⎢⎢⎢⎢⎣ α11 0 0 0 α12 0 0 0 α22 ⎤⎥⎥⎥⎥⎥⎥⎦⎡⎢⎢⎢⎢⎢⎢⎢⎣ <sup>ε</sup>21,*<sup>t</sup>*−<sup>1</sup> <sup>ε</sup>1,*t*−1ε2,*t*−<sup>1</sup> <sup>ε</sup>22,*<sup>t</sup>*−<sup>1</sup> ⎤⎥⎥⎥⎥⎥⎥⎥⎦ + ⎡⎢⎢⎢⎢⎢⎢⎣ γ11 0 0 0 γ12 0 0 0 γ22 ⎤⎥⎥⎥⎥⎥⎥⎦⎡⎢⎢⎢⎢⎢⎢⎢⎣ <sup>η</sup>21,*<sup>t</sup>*−<sup>1</sup> η1,*t*−<sup>1</sup>η2,*t*−<sup>1</sup> <sup>η</sup>22,*<sup>t</sup>*−<sup>1</sup> ⎤⎥⎥⎥⎥⎥⎥⎥⎦for (η1,*t*−<sup>1</sup> < 0, η2,*t*−<sup>1</sup> < 0) + ⎡⎢⎢⎢⎢⎢⎢⎣ β11 0 0 0 β12 0 0 0 β22 ⎤⎥⎥⎥⎥⎥⎥⎦⎡⎢⎢⎢⎢⎢⎢⎣ *h*11,*t*−<sup>1</sup> *h*12,*t*−<sup>1</sup> *h*22,*t*−<sup>1</sup> ⎤⎥⎥⎥⎥⎥⎥⎦

The estimated result for *ADCC*(*RmR*<sup>10</sup>*<sup>y</sup> b*) model is given by:

$$
\begin{aligned}
\begin{bmatrix} h\_{11J} \\ h\_{12J} \\ h\_{22J} \end{bmatrix} &= \begin{bmatrix} 1.280 \\ 0.002 \\ 0.325 \end{bmatrix} + \begin{bmatrix} 0.094 & 0 & 0 \\ 0 & 0.138 & 0 \\ 0 & 0 & 0.096 \end{bmatrix} \begin{bmatrix} \varepsilon\_{1J-1}^{2} \\ \varepsilon\_{1J-1}\varepsilon\_{2J-1}^{2} \\ \varepsilon\_{2J-1}^{2} \end{bmatrix} + \begin{bmatrix} 0.175 & 0 & 0 \\ 0 & -0.057 & 0 \\ 0 & 0 & -0.149 \end{bmatrix} \begin{bmatrix} \eta\_{1J-1}^{2} \\ \eta\_{1J-1}\eta\_{2J-1} \\ \eta\_{2J-1}^{2} \end{bmatrix} \\ &+ \begin{bmatrix} 0.743 & 0 & 0 \\ 0 & 0.823 & 0 \\ 0 & 0 & 0.897 \end{bmatrix} \begin{bmatrix} h\_{1J-1} \\ h\_{12J-1} \\ h\_{22J-1} \end{bmatrix} \end{aligned}
$$

<sup>4</sup> To illustrate the model, in the footnote of Table 2, one can plug the estimated parameters into the model using *hij*(*RmR*<sup>10</sup>*<sup>y</sup> b*).

The parameter *hij*,*<sup>t</sup>* is the variance and covariance of asset *i* and *j* in the estimated equation (subscripts *i* = (*Rm*) and *j* = (*Rb*), which stand for stock and bond returns, respectively); ω, α, and β are the parameters for the conditional variance equation; and γ is an asymmetric parameter. The first column is the estimated parameters and the second column is the t-statistics. The critical values at the 1%, 5%, and 10% are 2.60, 1.97, and 1.65, respectively. LLF denotes the log-likelihood function.

Figure 2 shows time series plots of dynamic conditional correlations for the monthly data between TTMK return and bond returns with different maturities based on Equation (6). Correlations between the returns of the two assets display noticeable variations throughout the sample period. In general, the plots clearly show a downward slope up to the time of 2004. During the beginning of the 2000s when the US market suffered from the dotcom collapse, the stock market dropped dramatically, and there was less of a decline in bond returns, causing the correlation to move downward as shown in the Figure 2 in this period. These results are consistent with the findings of Connolly et al. (2005), Chiang et al. (2015), and Li et al. (2015). However, during the global financial crisis period in 2008–2010, the stock market plummeted again, and the correlation coefficient also deepened in this period. After this crisis time the relationships become stationary and fluctuate around a very mild negative regime. A special feature derived from this study is that despite of their common movement around turning points, the dynamic paths show that the stock–bond return correlations vary with different bond maturities, which reflect different market conditions and preferences for bond maturities with different bondholders. These results sugges<sup>t</sup> that the path of ρ*SB*,*<sup>t</sup>* is based on only one stock return and one bond return, as is the case in conventional studies, which could produce a misleading and biased estimator.

**Figure 2.** Dynamic correlations between stock (TTMK) and various bond returns in the US.

#### *5.3. The Role of Uncertainty*

Early studies by Connolly et al. (2005), Andersson et al. (2008), and Chiang et al. (2015) stress the notion of using volatility measure as a proxy for uncertainty. Connolly et al. (2005) find that the correlation between stock and bond returns declines during periods with substantial increases in VIX. Andersson et al. (2008), Chiang et al. (2015), and Dimic et al. (2016) report that periods of elevated stock market uncertainty cause a decoupling between the relation of stock and bond returns, which is consistent with the "flight-to-quality" phenomenon. Antonakakis et al. (2013) and Li et al. (2015) employ the economic policy uncertainty in modeling the dynamic correlations. The current study extends this approach by adding monetary policy uncertainty and fiscal policy uncertainty in the test equation to explain the dynamic correlations between stock and bond returns. This notion is summarized in the regression model as follows:

$$\rho\_{Sb,t}^{\*} = q\_0 + q\_1 V I X\_{t-1} + q\_2 M OVE\_{t-1} + q\_3 EPL\_{t-1} + q\_4 M PLI\_{t-1} + q\_5 FPL\_{t-1} + q\_6 Trend + \varepsilon\_t \tag{7}$$

where <sup>ρ</sup><sup>ˆ</sup><sup>∗</sup>*Sb*,*<sup>t</sup>* is a Fisher transformation of stock–bond correlation coefficient, ρ<sup>ˆ</sup>*SB*,*t*, that is, <sup>ρ</sup><sup>ˆ</sup><sup>∗</sup>*Sb*,*<sup>t</sup>* = 1 2 *ln*[ <sup>1</sup>+ρ<sup>ˆ</sup>*SB*,*<sup>t</sup>* <sup>1</sup>−ρ<sup>ˆ</sup>*SB*,*<sup>t</sup>* ] and is bound to interval [−1,+1]. *VIXt*−<sup>1</sup> and *MOVEt*−<sup>1</sup> are the 1-month implied volatility in stock and bond markets, respectively. The *EPUt*−<sup>1</sup> is the economic policy uncertainty at time *t* − 1, while *MPUt*−<sup>1</sup> and *FPUt*−<sup>1</sup> are the monetary policy and fiscal policy uncertainties at time *t* − 1. Two special features are included in Equation (7). First, the financial risk and uncertainty are treated as independent factors to explain the stock–bond return correlations; second, in addition to the *EPUt*−1, the categorical policy impacts, such as the *MPUt*−<sup>1</sup> and *FPUt*−1, are included to highlight their distinctive effects. In the last term, the trend factor is added to capture of the presence of non-stationarity.

Table 3 presents consistent estimates (Newey and West 1987) of Equation (7) without including *EPUt*−1, *MPUt*−<sup>1</sup> and *FPUt*−1, while Table 4 shows results for this equation where the restriction of ϕ3 = ϕ4 = ϕ5 = 0 has been relaxed. Both models perform very well, the adjusted *R*-squares for the unrestricted model, which range from 0.48 to 0.81, are notably higher than those of the restricted model, indicating that the inclusion of the uncertainty variables helps to increase their explanatory power.Since the results in Table 3 are nested in Table 4, our interpretations focus on Table 4. Several points are noteworthy.

**Table 3.** Estimates of aggregate and categorical EPU, FPU, and MPU and on stock (TTMK)–bond return correlations.


Note: This table presents evidence of VIX and MOVE on ρ<sup>ˆ</sup><sup>∗</sup>*t*, the Fisher transformation of ρˆ*t*, which is the dynamic correlations between value stock–bond returns. That is, <sup>ρ</sup><sup>ˆ</sup><sup>∗</sup>*Sb*,*<sup>t</sup>*(···) = 12 ln[ 1+ρ<sup>ˆ</sup>*t* 1−ρ<sup>ˆ</sup>*<sup>t</sup>* ]). The subscript "sb" is suppressed to save space in table. For each model, the first column reports the estimated coefficients, the second column contains the estimated t-statistics. The critical values of t-distribution at the 1%, 5%, and 10% levels of significance are 2.60, 1.98, and 1.66, respectively. The numbers in the brackets are the *p*-values. *R*2 is the adjusted R-squared.



Note: This table presents evidence of financial risk and policy uncertainty on <sup>ρ</sup><sup>ˆ</sup><sup>∗</sup>*Sb*,*t*, the Fisher transformation of ρˆ*t*, which is the dynamic correlations between TTMK stock–bond returns. That is, <sup>ρ</sup><sup>ˆ</sup><sup>∗</sup>*Sb*,*<sup>t</sup>*(···) = 12 ln[ 1+ρ<sup>ˆ</sup>*t* 1−ρ<sup>ˆ</sup>*<sup>t</sup>* ]. The subscript "sb" is suppressed to save space in the table. For each model, the first column reports the estimated coefficients, the second column contains the estimated t-statistics. The critical values of t-distribution at the 1%, 5%, and 10% levels of significance are 2.60, 1.98, and 1.66, respectively. The numbers in the brackets are the *p*-values. *R*2 is the adjusted R-squared.

First, the coefficients of the trend factor are negative, indicating that in general the correlations between stock and bond returns slope downward, although feathering in the stochastic process is present. This result is consistent with the findings reported by Connolly et al. (2005) and Chiang et al. (2015).

Second, the risk variables of *VIXt*−<sup>1</sup> and *MOVEt*−<sup>1</sup> are negative, revealing that investors are actively switching between stock and bond depending on the level of risk in the market. This movement resembles a flight-to-quality as risk increases and flight-from-quality as risk declines. This finding is consistent with the results in the literature (Gulko 2002; Connolly et al. 2005; Andersson et al. 2008; Chiang et al. 2015).

Third, the estimated coe fficients of *EPUt*−<sup>1</sup> are positive and highly significant. This conforms with a market phenomenon in which a sudden rise in uncertainty impedes prospects for economic activities, thereby dampening output production and future cash flows. Facing weakening liquidity, investors tend to sell o ff stocks and bonds. The dominance of this income e ffect will lead to a positive movement between stock and bond prices, a reaction that is consistent with a study by Hong et al. (2014), which emphasizes the response to market volatile.

Fourth, the estimated coe fficients for *FPUt*−<sup>1</sup> and *MPUt*−<sup>1</sup> are negative and significant at the one percent level. This should not be surprising, since a rise in MPU tends to increase uncertainty in interest rate, which is more likely to create a strong substitution e ffect that causes a shift from high uncertainty asset-stocks to relatively low uncertainty asset-bonds and leads to a decoupling of stock and bond returns. A similar shift also holds true for an upward shift in FPU, especially in the case of bond financing of governmen<sup>t</sup> deficits. It is recognized that an increase in *FPUt*−<sup>1</sup> and *MPUt*−<sup>1</sup> could create an income e ffect; however, the negative coe fficients imply that the substitution e ffect dominates the income e ffect.

Fifth, the estimated results favor the inclusion of uncertainty variables as incremental variables. This can be seen in the reported χ<sup>2</sup>(3) statitic, which tests the joint significance of the coefficients with ϕ3 = ϕ4 = ϕ5 = 0. The *p*-values of the Chi-squared test, which are in brackets, indicate the rejection of the null, suggesting that the inclusion of the uncertainty variables helps to improve the explanation of the dynamic correlations between stock and bond returns. Evidence thus indicates that the exclusion of uncertainty variables in the literature (Connolly et al. 2005; Andersson et al. 2008; Chiang et al. 2015) is subject to an omitted variable problem. In addition, the χ<sup>2</sup>(2) statistic for testing equality of coe fficients for ϕ4 = ϕ5 = 0 against alternatives is also significant in all of cases, this test indicates the exclusion of categorical uncertainty even in the case of *EPU* (Antonakakis et al. 2013; Li et al. 2015) su ffers from a missing variable problem.

In summary, this study contributes to the literature in two ways. First, the e ffect of risk is separated from the uncertainty e ffect, showing both types of variables contribute to the variations of stock–bond correlations. Second, unlike the EPU, evidence shows the coe fficients of FPU and MPT are negative, which provides an incremental contribution in the ability to predict time-varying correlations of stock and bond returns, <sup>ρ</sup><sup>ˆ</sup><sup>∗</sup>*Sb*,*t*. These categorical uncertainty variables have not been explored in the literature.

#### **6. Robustness Tests**

#### *6.1. Di*ff*erence of Stock Indices*

Despite of successful outcomes of the time-varying behavior of <sup>ρ</sup><sup>ˆ</sup><sup>∗</sup>*Sb*,*<sup>t</sup>* in relation to the risk/uncertainty, it is important to examine the robustness of the parametric relations, which can be done by using alternative measures of stock indices. In this section, the test equations apply to stock indices including the DJIA, NASDAQ, RUSSELL, and VALUE. Pairings of stock returns with bond returns of maturities of 30 years, 10 years, seven years, five years, and two years are used to derive <sup>ρ</sup><sup>ˆ</sup><sup>∗</sup>*Sb*,*<sup>t</sup>* (·). The estimated equations are reported in Tables 5–8, and the test results are summarized as follows.


**Table 5.** Estimates of aggregate and categorical EPU, FPU, and MPU and on stock (DJIA)–bond return correlations.

Note: This table presents evidence of financial risk and policy uncertainty on <sup>ρ</sup><sup>ˆ</sup><sup>∗</sup>*Sb*,*t*, the Fisher transformation of ρˆ*t*, which is the dynamic correlations between DJIA stock–bond returns. That is, <sup>ρ</sup><sup>ˆ</sup><sup>∗</sup>*Sb*,*<sup>t</sup>* (···) = 1 2 ln[ 1+ρ<sup>ˆ</sup>*t* 1−ρ<sup>ˆ</sup>*<sup>t</sup>* ]. The subscript "sb" is suppressed to save space in the table. For each model, the first column reports the estimated coe fficients, the second column contains the estimated t-statistics. The critical values of t-distribution at the 1%, 5%, and 10% levels of significance are 2.60, 1.98, and 1.66, respectively. The numbers in the brackets are the *p*-values. *R* 2 is the adjusted R-squared.

**Table 6.** Estimates of aggregate and categorical EPU, FPU and MPU and on stock (NASDAQ)–bond return correlations.


Note: This table presents evidence of financial risk and policy uncertainty on <sup>ρ</sup><sup>ˆ</sup><sup>∗</sup>*Sb*,*t*, the Fisher transformation of ρˆ*t*, which is the dynamic correlations between NASDAQ stock–bond returns. That is, <sup>ρ</sup><sup>ˆ</sup><sup>∗</sup>*Sb*,*<sup>t</sup>* (···) = 1 2 ln[ 1+ρ<sup>ˆ</sup>*t* 1−ρ<sup>ˆ</sup>*<sup>t</sup>* ]). The subscript "sb" is suppressed to save space in the table. For each model, the first column reports the estimated coe fficients, the second column contains the estimated t-statistics. The critical values of t-distribution at the 1%, 5%, and 10% levels of significance are 2.60, 1.98, and 1.66, respectively. The numbers in the brackets are the *p*-values. *R* 2 is the adjusted R-squared.

First, the evidence clearly indicates that the coe fficients of stock–bond return correlations slope downward as indicated by the negative sign and are statistically significant. However, the coe fficients of *VIXt*−<sup>1</sup> have mixed signs. Although most of them are negative, yet, the coe fficients of *VIXt*−<sup>1</sup> in the NASDAQ and RUSSELL stock returns are positive, reflecting the possibility that investors with di fferent stocks holding have di fferent degrees of sensitivity to financial shock and react di fferently. From an econometric point of view, this may also result from a spurious correlation. Another financial risk variable, *MOVEt*−1, however, presents consistent results. Except ρˆ∗ *t* (*RmR*<sup>7</sup>*<sup>y</sup> b* ) (in Tables 7 and 8), the coe fficients show negative signs and are statistically significant.


**Table 7.** Estimates of aggregate and categorical EPU, FPU, and MPU and on stock (RUSSELL)–bond return correlations.

Note: This table presents evidence of financial risk and policy uncertainty on <sup>ρ</sup><sup>ˆ</sup><sup>∗</sup>*Sb*,*t*, the Fisher transformation of ρˆ*t*, which is the dynamic correlations between Russell stock–bond returns. That is, <sup>ρ</sup><sup>ˆ</sup><sup>∗</sup>*Sb*,*<sup>t</sup>* (···) = 1 2 ln[ 1+ρ<sup>ˆ</sup>*t* 1−ρ<sup>ˆ</sup>*<sup>t</sup>* ]). The subscript "sb" is suppressed to save space in the table. For each model, the first column reports the estimated coe fficients, the second column contains the estimated t-statistics. The critical values of t-distribution at the 1%, 5%, and 10% levels of significance are 2.60, 1.98, and 1.66, respectively. The numbers in the brackets are the *p*-values. *R* 2 is the adjusted R-squared.

**Table 8.** Estimates of aggregate and categorical EPU, FPU, and MPU and on stock (VALUE)–bond return correlations.


Note: This table presents evidence of financial risk and policy uncertainty on ρˆ∗ *t*, the Fisher transformation of ρˆ*t*, which is the dynamic correlations between Value stock–bond returns. That is, ρˆ∗ *t*(···) = 1 2 ln[ 1+ρ<sup>ˆ</sup>*t* 1−ρ<sup>ˆ</sup>*<sup>t</sup>* ]). The subscript "sb" is suppressed to save space in the table. For each model, the first column reports the estimated coe fficients, the second column contains the estimated t-statistics. The critical values of t-distribution at the 1%, 5%, and 10% levels of significance are 2.60, 1.98, and 1.66, respectively. The numbers in the brackets are the *p*-values. *R* 2 is the adjusted R-squared.

Turning to the performance of the coe fficients of *EPUt*−1, *FPUt*−1, and *MPUt*−1, the signs are consistent with the results in Table 4. That is, the coe fficients of *EPUt*−<sup>1</sup> continue to present positive signs, showing the impact of a positive income e ffect on the stock–bond return correlation, while the coe fficients of *FPUt*−<sup>1</sup> and *MPUt*−<sup>1</sup> display negative signs, revealing that stock and bond returns are dominated by a substitution e ffect and move in diverse directions. The testing results sugges<sup>t</sup> that a portfolio combination of stocks and bonds are a better hedge against uncertainty if it originates from monetary policy or fiscal policy uncertainty. However, the benefits of stock and bond diversification are less apparent if the uncertainty is the result of a general economic policy uncertainty, since its impact on economic activity is pervasive.<sup>5</sup>

<sup>5</sup> Instead of stressing the sources of policy uncertainty, Baele et al. (2010) analyze monetary policy impact on the direction of equity-bond correlation by focusing on the effects of inflation. In periods with a contractionary monetary policy, which is usually associated with low inflation rate, the correlation displays a positive relation; nonetheless, during periods of high inflation, the stock–bond correlation presents a negative relation. Thus, it is hard to justify whether inflation plays a role in uncertainty or a real income effect. However, Pericoli (2018) shows that inflation rate is a significant factor. Further, instead

#### *6.2. Total Policy Uncertainty*

The above tests sugges<sup>t</sup> that the *EPUt*−<sup>1</sup> has a positive effect, while *FPUt*−<sup>1</sup> and *MPUt*−1have a negative effect on the <sup>ρ</sup><sup>ˆ</sup><sup>∗</sup>*Sb*,*<sup>t</sup>*(·). It is natural to pool all the uncertainty information together regardless of the sources of uncertainty. To this end, I define *TPUt* = *EPUt* + *FPUt* + *MPUt* as total policy uncertainty (*TPUt*). Table 9 reports the estimates of the test equation, which uses *TPUt* as a measure of uncertainty. Consistent with previous findings, the coefficients of *VIXt*−<sup>1</sup> have mixed signs. However, the signs for *MOVEt*−<sup>1</sup> consistently present negative signs and most of them are statistically significant.

**Table 9.** Estimates of correlations of total stock market returns and 10-year bond returns in response to financial risk and total policy uncertainty.


Notes: This table presents evidence of financial risk and policy uncertainty on <sup>ρ</sup><sup>ˆ</sup><sup>∗</sup>*Sb*,*t*, the Fisher transformation of ρˆ*t*, which is the dynamic correlations between Value stock–bond returns. That is, <sup>ρ</sup><sup>ˆ</sup><sup>∗</sup>*Sb*,*<sup>t</sup>*(···) = 12 ln[ 1+ρ<sup>ˆ</sup>*t* 1−ρ<sup>ˆ</sup>*<sup>t</sup>* ]). The subscript "sb" is suppressed to save space in the table. For each model, the first column reports the estimated coefficients, the second column contains the estimated t-statistics. The critical values of t-distribution at the 1%, 5%, and 10% levels of significance are 2.60, 1.98, and 1.66, respectively. *R*2 is the adjusted R-squared.

With respect to the sign of *TPUt*−1, evidence shows that the coefficients on TTMK, NASDAQ, and RUSSELL exhibit negative signs and are statistically significant. This result is consistent with market behavior of investors who during a rise in *TPUt*−<sup>1</sup> tend to sell off more uncertain stock and move their funds to bonds, effectively exhibiting the substitution effect. However, the coefficients of *TPUt*−<sup>1</sup> for the DJIA and VALUE stocks are positive and statistically significant, indicating a dominance of the income effect. A review of the S&P 500 Value index, which has a style-concentrated index designed to track the performance of stocks that exhibit the strongest value, shows that the value of these stocks is very much in line with that of the DJIA. In sum, estimates of correlations between total stock market returns and 10-year bond returns show different signs in response to total policy uncertainty is essentially executed under different degrees of force from income effect and substitution effect.
