# Risk and Policy Uncertainty on Stock–Bond Return Correlations: Evidence from the US Markets

## Abstract

**:**

## 1. Introduction

## 2. The Relationship between Stock Returns and Bond Returns

## 3. A Dynamic Conditional Correlation Model

**R**} represents a bivariate return series, expressed as

_{t}**R**

_{t}= [${R}_{1,t}{R}_{2,t}{]}^{\prime}$ is a 2 × 1 vector for stock market returns, ${\mu}_{t}$ is the mean value of asset 1 or 2, which has the conditional expectation of multivariate time series properties2,

**u**$|$${F}_{t-1}=[{u}_{1,t}{u}_{2,t}{]}^{\prime}~N\left(0,{H}_{t}\right),{F}_{t-1}$ is the information set up for (and including) time t − 1. In the context of this study, it is convenient to treat ${R}_{1,t}$ as the return on stocks and ${R}_{2,t}$ as the bond return for one of the bond instruments. In the multivariate DCC-GARCH structure, the conditional variance-covariance matrix H

_{t}_{t}is assumed to be

_{t}is the time-varying conditional correlation matrix, which satisfies the following conditions:

## 4. Data

_{t}) obtained from the S&P 500 index options and MOVE

_{t}, 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-difference of the price indices times 100.

## 5. Empirical Estimations

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

#### 5.2. Estimated Stock–Bond Correlation Coefficients

#### 5.3. The Role of Uncertainty

## 6. Robustness Tests

#### 6.1. Difference of Stock Indices

_{t}

_{−1}, FPU

_{t}

_{−1}, and MPU

_{t}

_{−1}, the signs are consistent with the results in Table 4. That is, the coefficients of EPU

_{t}

_{−1}continue to present positive signs, showing the impact of a positive income effect on the stock–bond return correlation, while the coefficients of FPU

_{t}

_{−1}and MPU

_{t}

_{−1}display negative signs, revealing that stock and bond returns are dominated by a substitution effect and move in diverse directions. The testing results suggest 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.5

#### 6.2. Total Policy Uncertainty

_{t}

_{−1}has a positive effect, while FPU

_{t}

_{−1}and MPU

_{t}

_{−1}have a negative effect on the ${\widehat{\rho}}_{Sb,t}^{\ast}(\xb7)$. It is natural to pool all the uncertainty information together regardless of the sources of uncertainty. To this end, I define TPU

_{t}= EPU

_{t}+ FPU

_{t}+ MPU

_{t}as total policy uncertainty (TPU

_{t}). Table 9 reports the estimates of the test equation, which uses TPU

_{t}as a measure of uncertainty. Consistent with previous findings, the coefficients of $VI{X}_{t-1}$ have mixed signs. However, the signs for $MOV{E}_{t-1}$ consistently present negative signs and most of them are statistically significant.

## 7. Conclusions

_{t}

_{−1}), this study arrives at more consistent results. In this case, the coefficients tend to have negative signs with a couple of exceptions. For this reason, we can reach a more concrete conclusion that a rise in MOVE

_{t}

_{−1}leads to a decoupling of stock and bond returns. Thus, MOVE

_{t}

_{−1}to some extent reflects different market information and complementarily contributes to explaining movements in stock and bond return correlations.

_{t}

_{−1}has a positive and significant effect on the stock–bond return correlation. This result is consistent with a dominant income effect resulting from a rise in economic policy uncertainty that impedes economic activities and leads to a decline in income. This decline brings about a decrease in liquidity and in turn weakens demand for both stocks and bonds. Therefore, both stock and bond prices move in the same direction.

_{t}

_{−1}and MPU

_{t}

_{−1}are negative and highly significant. The negative sign of this policy uncertainty is mainly due to the dominance of the substitution effect, which prompts investors to replace higher uncertainty assets with lower uncertainty assets due to an upward shift in policy uncertainty. This occurs because of a policy stance that causes a sudden rise in MPU

_{t}

_{−1}(or FPU

_{t}

_{−1}in bond financing) and increases uncertainty in interest rates, prompting a selloff in stocks and a flight-to-quality phenomenon. Note that this market action essentially stems from a heightened fear from policy uncertainty rather than something of inherent in the asset’s return. It is possible that a rise in MPU

_{t}

_{−1}(or FPU

_{t}

_{−1}) could threaten the future cash flow and reduce the demand for both stocks and bonds. However, the evidence of a negative coefficient indicates the dominant force of the substitution effect. An implication of a negative coefficient suggests that a portfolio can benefit from a combination of stocks and bonds as a way of diversification and hedging against monetary policy or fiscal policy uncertainty.

_{t}

_{−1}and FPU

_{t}

_{−1}on stock–bond correlations. In addition to the VIX

_{t}

_{−1}, MOVE

_{t}

_{−1}and EPU

_{t}

_{−1}, our Chi-squared statistics consistently suggest the rejection of the null, MPU

_{t}

_{−1}= FPU

_{t}

_{−1}= 0, and support the incremental significance of MPU

_{t}

_{−1}and FPU

_{t}

_{−1}in the test equation. This evidence has not previously been shown in the literature to explain the stock–bond return correlation.

## Funding

## Conflicts of Interest

## Appendix A

Variable | Description | Source |
---|---|---|

EPU_{t} | Economic policy uncertainty index involves: ‘‘economic’’ or ‘‘economy’’; ‘‘uncertain’’ or ‘‘uncertainty’’; and one or more of ‘‘Congress,’’ ‘‘deficit,’’ ‘‘Federal Reserve,’’ ‘‘legislation,’’ ‘‘regulation,’’ or ‘‘White House’’ in 10 major newspapers. | Baker et al. (2016) * |

$FP{U}_{t}$ | Fiscal policy uncertainty index involves terms of “government budget” or discretionary fiscal policy”, “government revenue”, “tax” or “Taxation”, “government deficit”, “government spending” or “government expenditure”, “social security expenditures”, “defense spending”, “Legislation”, “public debt” or “government debt”, “National bonds”, among others. | Davis (2016) ** |

$MP{U}_{t}$ | Monetary policy uncertainty index involves terms of “monetary policy”, monetary easing”, quantitative easing”, “negative interest rate”, “official discount rate”, “monetary operation(s)”, “inflation target”, among others. | Davis (2016) ** |

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1 | Li et al. (2015) argue that when EPU declines, a flight from quality could also occur, resulting in a reduction in the correlations. However, the reduction in EPU can signify an improvement in the market environment, which would raise investors’ demand for both stocks and bonds, thereby pushing up their correlations. This could produce an asymmetric effect. |

2 | Some researchers use domestic macroeconomic factors, such as inflation rate, business cycle patterns, and policy stance, on the stock–bond correlation (Ilmanen 2003; Yang et al. 2009; Dimic et al. 2016; Pericoli 2018). |

3 | This section follows closely to Engle (2009, pp. 45–49). |

4 | To illustrate the model, in the footnote of Table 2, one can plug the estimated parameters into the model using ${h}_{ij}({R}_{m}{R}_{b}^{10y})$. |

5 | 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 of using government bonds, one might use junk bonds to trace the dynamic correlations (Glassman 2018), which will be the subject of future research. |

Correlation (t-Statistic) | Rm_TTMK | Rb_30Y | Rb_10Y | Rb_7Y | Rb_5Y | Rb_2Y |
---|---|---|---|---|---|---|

Rm_TTMK | 1 | |||||

----- | ||||||

Rb_30Y | −0.1209 | 1 | ||||

−2.28 | ----- | |||||

Rb_10Y | −0.1191 | 0.9215 | 1 | |||

−2.24 | 44.39 | ----- | ||||

Rb_7Y | −0.1191 | 0.8638 | 0.9809 | 1 | ||

−2.24 | 32.08 | 94.42 | ----- | |||

Rb_5Y | −0.1456 | 0.7798 | 0.9407 | 0.9701 | 1 | |

−2.75 | 23.31 | 51.87 | 74.76 | ----- | ||

Rb_2Y | −0.1544 | 0.5934 | 0.7764 | 0.8278 | 0.9073 | 1 |

−0.15 | 13.79 | 23.05 | 27.60 | 40.37 | ----- |

Correlation (t-Statistic) | Rm_TTMK | R_DJIA | R_Nasdaq | R_Russell | R_Value |
---|---|---|---|---|---|

Rm_TTMK | 1 | ||||

----- | |||||

R_DJIA | 0.9333 | 1 | |||

48.70 | ----- | ||||

R_Nasdaq | 0.8752 | 0.7391 | 1 | ||

33.90 | 20.56 | ----- | |||

R_Russell | 0.8466 | 0.7543 | 0.8552 | 1 | |

29.80 | 21.52 | 30.92 | ----- | ||

R_Value | 0.9447 | 0.9451 | 0.7350 | 0.8101 | 1 |

53.96 | 54.19 | 20.31 | 25.89 | ----- |

Correlation (t-Statistic) | VIX | MOVE | EPU | FPU | MPU |
---|---|---|---|---|---|

VIX | 1 | ||||

----- | |||||

MOVE | 0.5969 | 1 | |||

13.84 | ----- | ||||

EPU | 0.4099 | 0.2997 | 1 | ||

8.36 | 5.84 | ----- | |||

FPU | 0.2945 | 0.1490 | 0.8974 | 1 | |

5.73 | 2.80 | 37.84 | ----- | ||

MPU | 0.3803 | 0.3020 | 0.7659 | 0.5515 | 1 |

7.65 | 5.89 | 22.16 | 12.30 | ----- |

Statistics | VIX | MOVE | EPU | FPU | MPU |
---|---|---|---|---|---|

Mean | 19.32 | 93.84 | 96.74 | 101.71 | 87.58 |

Median | 17.40 | 91.30 | 85.92 | 81.96 | 71.37 |

Maximum | 59.89 | 213.90 | 271.83 | 374.31 | 407.94 |

Minimum | 9.51 | 46.20 | 37.27 | 23.05 | 16.57 |

Std. Dev. | 7.44 | 27.16 | 41.05 | 63.54 | 56.14 |

Skewness | 1.72 | 0.95 | 1.18 | 1.59 | 1.80 |

Kurtosis | 7.60 | 5.24 | 4.26 | 5.68 | 8.06 |

Observations | 348.00 | 348.00 | 348.00 | 348.00 | 348.00 |

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

Parameters | ${\mathit{h}}_{\mathit{i}\mathit{j}}({\mathit{R}}_{\mathit{m}}{\mathit{R}}_{\mathit{b}}^{30\mathit{y}})$ | ${\mathit{h}}_{\mathit{i}\mathit{j}}({\mathit{R}}_{\mathit{m}}{\mathit{R}}_{\mathit{b}}^{10\mathit{y}})$ | ${\mathit{h}}_{\mathit{i}\mathit{j}}({\mathit{R}}_{\mathit{m}}{\mathit{R}}_{\mathit{b}}^{7\mathit{y}})$ | ${\mathit{h}}_{\mathit{i}\mathit{j}}({\mathit{R}}_{\mathit{m}}{\mathit{R}}_{\mathit{b}}^{5\mathit{y}})$ | ${\mathit{h}}_{\mathit{i}\mathit{j}}({\mathit{R}}_{\mathit{m}}{\mathit{R}}_{\mathit{b}}^{2\mathit{y}})$ | |||||
---|---|---|---|---|---|---|---|---|---|---|

${\omega}_{11}$ | 0.708 | 2.21 | 1.281 | 2.70 | 1.357 | 2.62 | 1.169 | 2.35 | 1.280 | 2.68 |

${\omega}_{12}$ | 0.030 | 0.80 | 0.002 | 0.02 | −0.066 | −1.05 | −0.088 | −2.09 | 0.002 | 0.02 |

${\omega}_{22}$ | 0.865 | 2.44 | 0.325 | 1.81 | 0.121 | 1.41 | 0.050 | 1.30 | 0.325 | 1.79 |

${\alpha}_{11}$ | 0.082 | 1.57 | 0.094 | 1.42 | 0.099 | 1.29 | 0.120 | 1.54 | 0.094 | 1.39 |

${\alpha}_{12}$ | 0.022 | 4.03 | 0.138 | 4.83 | 0.094 | 2.79 | 0.067 | 2.46 | 0.138 | 4.21 |

${\alpha}_{22}$ | 0.136 | 3.03 | 0.096 | 2.79 | 0.106 | 2.41 | 0.103 | 2.29 | 0.096 | 2.70 |

${\gamma}_{11}$ | 0.070 | 1.40 | 0.175 | 2.33 | 0.192 | 2.31 | 0.133 | 1.67 | 0.175 | 2.30 |

${\gamma}_{12}$ | −0.052 | −3.71 | −0.057 | −1.50 | 0.033 | 0.52 | 0.073 | 1.36 | −0.058 | −0.92 |

${\gamma}_{22}$ | −0.206 | −3.71 | −0.149 | −3.55 | −0.150 | −2.88 | −0.118 | −2.40 | −0.149 | −3.39 |

${\beta}_{11}$ | 0.844 | 19.49 | 0.743 | 12.38 | 0.728 | 11.35 | 0.746 | 11.49 | 0.743 | 12.38 |

${\beta}_{12}$ | 0.998 | 17.63 | 0.823 | 23.69 | 0.843 | 21.83 | 0.859 | 24.09 | 0.823 | 23.68 |

${\beta}_{22}$ | 0.898 | 21.75 | 0.897 | 17.83 | 0.918 | 19.57 | 0.914 | 18.19 | 0.897 | 17.62 |

LLF | −1844 | −1672 | −1594 | −1488 | −1673 |

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

PI = TTMK | ${\widehat{\mathit{\rho}}}_{\mathit{t}}^{\ast}({\mathit{R}}_{\mathit{m}}{\mathit{R}}_{\mathit{b}}^{30\mathit{y}})$ | ${\widehat{\mathit{\rho}}}_{\mathit{t}}^{\ast}({\mathit{R}}_{\mathit{m}}{\mathit{R}}_{\mathit{b}}^{10\mathit{y}})$ | ${\widehat{\mathit{\rho}}}_{\mathit{t}}^{\ast}({\mathit{R}}_{\mathit{m}}{\mathit{R}}_{\mathit{b}}^{7\mathit{y}})$ | ${\widehat{\mathit{\rho}}}_{\mathit{t}}^{\ast}({\mathit{R}}_{\mathit{m}}{\mathit{R}}_{\mathit{b}}^{5\mathit{y}})$ | ${\widehat{\mathit{\rho}}}_{\mathit{t}}^{\ast}({\mathit{R}}_{\mathit{m}}{\mathit{R}}_{\mathit{b}}^{2\mathit{y}})$ | |||||
---|---|---|---|---|---|---|---|---|---|---|

$C$ | 0.945 | 14.34 | 0.668 | 8.80 | 0.642 | 5.26 | 0.673 | 13.27 | 0.781 | 12.79 |

$VI{X}_{t-1}$ | −0.006 | −2.52 | −0.005 | −1.73 | 0.001 | 0.25 | 0.001 | 0.56 | −0.005 | −2.33 |

$MOV{E}_{t-1}$ | −0.002 | −2.15 | −0.003 | −3.10 | −0.001 | −1.33 | −0.002 | −3.74 | −0.003 | −5.30 |

Trend | −0.004 | −24.65 | −0.003 | −14.28 | −0.003 | −10.93 | −0.003 | −27.75 | −0.002 | −15.42 |

${\overline{R}}^{2}$ | 0.68 | 0.41 | 0.71 | 0.72 | 0.48 |

**Table 4.**Estimates of aggregate and categorical EPU, FPU, and MPU, and on stock (TTMK)–bond return correlations.

PI = TTMK | ${\widehat{\mathit{\rho}}}_{\mathit{t}}^{\ast}({\mathit{R}}_{\mathit{m}}{\mathit{R}}_{\mathit{b}}^{30\mathit{y}})$ | ${\widehat{\mathit{\rho}}}_{\mathit{t}}^{\ast}({\mathit{R}}_{\mathit{m}}{\mathit{R}}_{\mathit{b}}^{10\mathit{y}})$ | ${\widehat{\mathit{\rho}}}_{\mathit{t}}^{\ast}({\mathit{R}}_{\mathit{m}}{\mathit{R}}_{\mathit{b}}^{7\mathit{y}})$ | ${\widehat{\mathit{\rho}}}_{\mathit{t}}^{\ast}({\mathit{R}}_{\mathit{m}}{\mathit{R}}_{\mathit{b}}^{5\mathit{y}})$ | ${\widehat{\mathit{\rho}}}_{\mathit{t}}^{\ast}({\mathit{R}}_{\mathit{m}}{\mathit{R}}_{\mathit{b}}^{2\mathit{y}})$ | |||||
---|---|---|---|---|---|---|---|---|---|---|

$C$ | 0.000 | 0.00 | 0.370 | 1.91 | −0.680 | −5.91 | −0.444 | −3.66 | 0.513 | 3.13 |

$VI{X}_{t-1}$ | −0.007 | −2.00 | −0.003 | −1.00 | −0.002 | −1.73 | −0.001 | −0.99 | −0.005 | −2.12 |

$MOV{E}_{t-1}$ | −0.001 | −1.40 | −0.002 | −2.97 | −0.001 | −3.82 | −0.002 | −5.27 | −0.003 | −5.54 |

$EP{U}_{t-1}$ | 0.857 | 6.15 | 0.674 | 5.43 | 0.766 | 10.79 | 0.715 | 9.34 | 0.406 | 3.96 |

$FP{U}_{t-1}$ | −0.409 | −4.59 | −0.415 | −6.11 | −0.231 | −5.67 | −0.250 | −5.79 | −0.203 | −3.57 |

$MP{U}_{t-1}$ | −0.254 | −4.55 | −0.222 | −5.01 | −0.236 | −9.25 | −0.217 | −8.18 | −0.157 | −4.60 |

Trend | −0.004 | −11.98 | −0.002 | −11.93 | −0.003 | −28.00 | −0.003 | −27.70 | −0.002 | −14.60 |

${\chi}^{2}\left(3\right)$ | 38.12 | [0.00] | 18.30 | [0.00] | 197.92 | [0.00] | 127.64 | [0.00] | 21.86 | [0.00] |

${\chi}^{2}\left(2\right)$ | 29.81 | [0.00] | 17.60 | [0.00] | 91.81 | [0.00] | 74.36 | [0.00] | 21.85 | [0.00] |

${\overline{R}}^{2}$ | 0.73 | 0.48 | 0.81 | 0.79 | 0.51 |

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

PI = DJIA | ${\widehat{\mathit{\rho}}}_{\mathit{t}}^{\ast}({\mathit{R}}_{\mathit{m}}{\mathit{R}}_{\mathit{b}}^{30\mathit{y}})$ | ${\widehat{\mathit{\rho}}}_{\mathit{t}}^{\ast}({\mathit{R}}_{\mathit{m}}{\mathit{R}}_{\mathit{b}}^{10\mathit{y}})$ | ${\widehat{\mathit{\rho}}}_{\mathit{t}}^{\ast}({\mathit{R}}_{\mathit{m}}({\mathit{R}}_{\mathit{m}}{\mathit{R}}_{\mathit{b}}^{7\mathit{y}})$ | ${\widehat{\mathit{\rho}}}_{\mathit{t}}^{\ast}({\mathit{R}}_{\mathit{m}}{\mathit{R}}_{\mathit{b}}^{5\mathit{y}})$ | ${\widehat{\mathit{\rho}}}_{\mathit{t}}^{\ast}({\mathit{R}}_{\mathit{m}}{\mathit{R}}_{\mathit{b}}^{2\mathit{y}})$ | |||||
---|---|---|---|---|---|---|---|---|---|---|

$C$ | −1.148 | −4.66 | −1.116 | −9.04 | −1.019 | −9.09 | −0.834 | −7.19 | 0.100 | 0.93 |

$VI{X}_{t-1}$ | −0.016 | −4.62 | 0.000 | −0.04 | −0.004 | −3.08 | 0.003 | 2.59 | 0.000 | 0.11 |

$MOV{E}_{t-1}$ | −0.001 | −0.69 | −0.002 | −3.62 | −0.000 | −0.63 | −0.002 | −4.87 | −0.002 | −3.90 |

$EP{U}_{t-1}$ | 1.003 | 7.35 | 0.874 | 9.94 | 0.725 | 9.04 | 0.706 | 8.43 | 0.279 | 3.56 |

$FP{U}_{t-1}$ | −0.252 | −3.20 | −0.229 | −4.79 | −0.172 | −3.96 | −0.203 | −4.56 | −0.127 | −3.09 |

$MP{U}_{t-1}$ | −0.308 | −5.16 | −0.274 | −8.63 | −0.215 | −7.30 | −0.233 | −7.86 | −0.104 | −3.83 |

Trend | −0.004 | −10.01 | −0.004 | −23.49 | −0.003 | −24.63 | −0.003 | −21.82 | −0.002 | −16.65 |

${\chi}^{2}\left(3\right)$ | 76.80 | [0.00] | 216.77 | [0.00] | 232.68 | [0.00] | 130.12 | [0.00] | 15.60 | [0.00] |

${\chi}^{2}\left(2\right)$ | 28.91 | [0.00] | 74.98 | [0.00] | 53.30 | [0.00] | 62.22 | [0.00] | 15.52 | [0.00] |

${\overline{R}}^{2}$ | 0.73 | 0.82 | 0.84 | 0.77 | 0.61 |

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

PI = NASD | ${\widehat{\mathit{\rho}}}_{\mathit{t}}^{\ast}({\mathit{R}}_{\mathit{m}}{\mathit{R}}_{\mathit{b}}^{7\mathit{y}})$ | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

$C$ | −0.641 | −4.21 | 0.100 | 0.76 | 0.056 | 0.46 | 0.182 | 1.51 | 0.307 | 2.76 |

$VI{X}_{t-1}$ | 0.003 | 1.29 | 0.003 | 1.27 | 0.003 | 1.71 | 0.002 | 1.20 | 0.001 | 0.76 |

$MOV{E}_{t-1}$ | −0.002 | −1.89 | −0.002 | −4.50 | −0.003 | −5.20 | −0.003 | −6.12 | −0.003 | −6.07 |

$EP{U}_{t-1}$ | 0.670 | 4.08 | 0.467 | 5.31 | 0.438 | 5.17 | 0.357 | 4.20 | 0.285 | 3.52 |

$FP{U}_{t-1}$ | −0.258 | −3.33 | −0.293 | −6.18 | −0.265 | −5.87 | −0.211 | −4.63 | −0.188 | −4.34 |

$MP{U}_{t-1}$ | −0.186 | −2.83 | −0.145 | −4.76 | −0.139 | −4.76 | −0.124 | −4.28 | −0.093 | −3.37 |

Trend | −0.003 | −7.14 | −0.002 | −11.36 | −0.001 | −9.84 | −0.001 | −11.66 | −0.002 | −13.7 |

${\chi}^{2}\left(3\right)$ | 20.07 | [0.00] | 50.21 | [0.00] | 44.47 | [0.00] | 30.44 | [0.00] | 29.01 | [0.00] |

${\chi}^{2}\left(2\right)$ | 11.36 | [0.00] | 40.53 | [0.00] | 36.68 | [0.00] | 24.90 | [0.00] | 19.78 | [0.00] |

${\overline{R}}^{2}$ | 0.67 | 0.48 | 0.41 | 0.46 | 0.52 |

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

PI = RUSS | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|

$C$ | −0.258 | −1.37 | −0.160 | −1.46 | −1.440 | −5.56 | −0.037 | −0.38 | 0.231 | 2.35 |

$VI{X}_{t-1}$ | 0.005 | 1.84 | 0.004 | 2.76 | −0.023 | −7.96 | 0.003 | 2.41 | 0.003 | 1.84 |

$MOV{E}_{t-1}$ | −0.001 | −0.92 | −0.002 | −4.31 | 0.001 | 0.94 | −0.002 | −4.70 | −0.002 | −4.16 |

$EP{U}_{t-1}$ | 0.555 | 3.26 | 0.465 | 4.83 | 1.063 | 7.83 | 0.269 | 3.49 | 0.181 | 2.53 |

$FP{U}_{t-1}$ | −0.321 | −3.47 | −0.273 | −5.81 | −0.215 | −2.77 | −0.157 | −4.05 | −0.143 | −3.76 |

$MP{U}_{t-1}$ | −0.152 | −2.17 | −0.138 | −3.62 | −0.400 | −9.01 | −0.094 | −3.16 | −0.065 | −2.40 |

Trend | −0.002 | −5.23 | −0.001 | −8.38 | −0.002 | −11.31 | −0.001 | −9.62 | −0.001 | −12.26 |

${\chi}^{2}\left(3\right)$ | 14.87 | [0.00] | 37.73 | [0.00] | 190.74 | [0.00] | 19.85 | [0.00] | 29.16 | [0.00] |

${\chi}^{2}\left(2\right)$ | 12.08 | [0.00] | 34.93 | [0.00] | 81.31 | [0.00] | 16.67 | [0.00] | 14.17 | [0.00] |

${\overline{R}}^{2}$ | 0.49 | 0.39 | 0.47 | 0.37 | 0.45 |

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

PI = VALUE | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|

$C$ | −1.259 | −3.62 | −1.241 | −9.10 | −1.910 | −8.44 | −0.871 | −7.28 | 0.249 | 1.95 |

$VI{X}_{t-1}$ | −0.022 | −4.90 | −0.003 | −2.07 | −0.027 | −8.63 | 0.003 | 2.06 | −0.002 | −1.23 |

$MOV{E}_{t-1}$ | −0.000 | −0.38 | −0.001 | −1.78 | 0.002 | 3.11 | −0.002 | −3.71 | −0.002 | −3.33 |

$EP{U}_{t-1}$ | 1.209 | 7.61 | 0.947 | 9.32 | 1.235 | 8.24 | 0.763 | 9.04 | 0.326 | 3.82 |

$FP{U}_{t-1}$ | −0.315 | −3.03 | −0.227 | −4.29 | −0.263 | −3.08 | −0.225 | −4.98 | −0.150 | −3.23 |

$MP{U}_{t-1}$ | −0.381 | −5.43 | −0.294 | −7.55 | −0.399 | −7.79 | −0.246 | −8.05 | −0.136 | −4.60 |

Trend | −0.004 | −9.37 | −0.004 | −23.90 | −0.003 | −15.83 | −0.003 | −23.56 | −0.002 | −17.94 |

${\chi}^{2}\left(3\right)$ | 70.86 | [0.00] | 233.42 | [0.00] | 219.45 | [0.00] | 140.30 | [0.00] | 21.86 | [0.00] |

${\chi}^{2}\left(2\right)$ | 33.35 | [0.00] | 57.04 | [0.00] | 61.84 | [0.00] | 66.15 | [0.00] | 21.85 | [0.00] |

${\overline{R}}^{2}$ | 0.67 | 0.83 | 0.65 | 0.80 | 0.60 |

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

Indpt. Variable | TTMK | DJIA | NASDAQ | RUSSELL | VALUE | |||||
---|---|---|---|---|---|---|---|---|---|---|

$C$ | 1.239 | 7.59 | −0.207 | −1.77 | 0.704 | 6.87 | 0.427 | 3.96 | −0.270 | −2.06 |

$VI{X}_{t-1}$ | −0.001 | −0.47 | 0.000 | 0.04 | 0.004 | 1.78 | 0.005 | 3.34 | −0.003 | −1.68 |

$MOV{E}_{t-1}$ | −0.002 | −2.80 | −0.002 | −2.89 | −0.002 | −4.23 | −0.002 | −4.10 | −0.001 | −1.37 |

$TP{U}_{t-1}$ | −0.048 | −4.23 | 0.060 | 7.28 | −0.032 | −4.49 | −0.023 | −3.18 | 0.074 | 8.18 |

Trend | −0.003 | −13.08 | −0.003 | −19.94 | −0.002 | −12.61 | −0.001 | −9.15 | −0.004 | −20.60 |

${\overline{R}}^{2}$ | 0.43 | 0.73 | 0.42 | 0.33 | 0.75 |

© 2020 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Chiang, T.C.
Risk and Policy Uncertainty on Stock–Bond Return Correlations: Evidence from the US Markets. *Risks* **2020**, *8*, 58.
https://doi.org/10.3390/risks8020058

**AMA Style**

Chiang TC.
Risk and Policy Uncertainty on Stock–Bond Return Correlations: Evidence from the US Markets. *Risks*. 2020; 8(2):58.
https://doi.org/10.3390/risks8020058

**Chicago/Turabian Style**

Chiang, Thomas C.
2020. "Risk and Policy Uncertainty on Stock–Bond Return Correlations: Evidence from the US Markets" *Risks* 8, no. 2: 58.
https://doi.org/10.3390/risks8020058