**1. Introduction**

The investigation on correlations of stock and bond returns has long been a key concern of portfolio managers and financial market strategists (Connolly et al. 2005; Panchenko and Wu 2009; Baur and Lucey 2009; Li et al. 2019, among others). This is because the derived parametric relations could provide useful guidance in portfolio selection, dynamic asset allocation, and risk management. For most of this time, two questions have dominated the literature. First, are stock returns and bond returns positively or negatively correlated? Second, what are the factors that cause correlations to vary over time? The theoretical claim of the first issue contends that both required rates of return for stock and bond yields are viewed as part of a discount factor to calculate the future cash flows of investments. This argumen<sup>t</sup> is based on the valuation model that has been adopted and used in the "Fed model" (Kwan 1996; Yardeni 1997). It is observed that any economic shocks, such as income, inflation rate, policy innovation, or external shock that disturb an existing equilibrium, will cause investors to reallocate their funds between assets with lower returns to ones with higher returns. An e fficient arbitrage will eliminate the return di fferentials and establish return parity conditions after executing full adjustment (Tobin 1969). This view focuses on economic fundamentals analyzed over a long-run perspective.

However, evidence of the decoupling phenomenon observed by Gulko (2002) finds a negative sign for the correlation that obviously occurred in the crisis period; this finding reflects a short run "flight-to-quality" process (Baur and Lucey 2009). To advance the study, Connolly et al. (2005) examine the US market and discover that the implied stock volatility (VIX) spikes during periods of market turmoil leads to decline in stock prices (Whaley 2009). It is argued that the VIX variable has a power in predicting stock returns (Connolly et al. 2005) and find that VIX displays a negative e ffect on the

stock–bond correlation. Further study by Chiang et al. (2015) documents that both implied volatility of stock and conditional volatility of bond returns have significantly negative e ffects on variations in stock–bond returns.

To distinguish their work from previous models, some researchers identify economic policy uncertainty (EPU) as a key factor that dictates the time-varying correlations between stock and bond returns (Antonakakis et al. 2013; Jones and Olson 2013; Li et al. 2015). Antonakakis et al. (2013) show that the dynamic correlation between EPU and S&P500 returns is consistently negative over time, with exception of a financial crisis period. Li et al. (2015) report that innovations in EPU have a negative and asymmetrical impact on subsequent stock–bond correlations, since a rise in EPU will likely prompt risk averse investors to sell off risky stocks and purchase lower risk bonds, leading to a negative correlation.<sup>1</sup>

Considering the above evidence of risk/uncertainty on stock returns, this paper attempts to contribute to the study of the e ffects of policy uncertainty on stock–bond relations. This study di ffers from existing models in the following ways. First, this study focus on broad information in developing measures of financial risks such as VIX, Merrill Lynch Option Volatility Estimate (MOVE) and uncertainty (EMU) to explain the time-varying correlations between stock and bond returns. Second, in addition to EPU, this study investigates the impact of categorical policy uncertainties, including both fiscal policy uncertainty (FPU) and monetary policy uncertainty (MPU). The testing result suggests that the FPU and MPU give rise to di fferent e ffects vis-à-vis that of EPU. Third, instead of testing a correlation coe fficient derived from a single measure of aggregate stock returns that covaries with a specific bond yield, this study conducts tests on the return correlations involving di fferent measures of aggregate stock returns and a spectrum of bond yields for di fferent maturities. Thus, the estimated results will provide broad coverage of dynamic correlation behavior. Fourth, the net e ffect of various policy uncertainty is summarized in total policy uncertainty (TPU). Evidence demonstrates that the results are mixed due to the di fferent impact, which the income and substitution e ffects have on stock–bond return correlations.

The remainder of the paper is structured as follows. Section 2 describes a dynamic correlation model and derives the time-varying correlations. Section 3 provides rationales for using risk and uncertainty variables to explain the time-varying behavior of stock–bond return correlation. Section 4 describes the sample data. Section 5 reports the estimates developed from the use of policy uncertainty to explain the dynamic stock–bond correlations. Section 6 provides robustness tests. Section 7 concludes the paper.

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

As mentioned earlier, stock and bond returns are positively correlated since both stock and bond markets commonly react to economic news, such as changes in inflation rate, economic growth, the real interest rate, and business cycle, in similar ways. When investors perceive that economic prospects are good, demand for bonds increase, as does demand for stocks, leading to a positive correlation. Experience from the late 1990s suggests that an upward shift in the wealth e ffect encourages investors to hold both types of assets simultaneously. Campbell and Ammer (1993), Kwan (1996), and d'Addona and Kind (2006) document this phenomenon.

Historical experience also reveals a negative correlation between stock–bond returns, which is especially noticeably in the stock market during a downturn period or a financial crisis. When the stock market plummets, risk averse investors may move funds from the stock market to safer assets and increase the demand for bond market, forming a "flight-to-quality" phenomenon (Baur and Lucey 2009; Hakkio and Keeton 2009). On the contrary, when the economy recovers and stock prices start to rally, investors become less risk averse and opt to switch back to stock market, leading to a "flight-from-quality"

<sup>1</sup> 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.

phenomenon. Thus, the correlation between stock and bond returns displays a negative relation. Evidence by Gulko (2002), Connolly et al. (2005), Baur and Lucey (2009), and Chiang et al. (2015) support this hypothesis.

Despite their contributions, which use VIX as a measure to explain the time-varying correlation of stock–bond returns, their work appears to inadequately capture all the necessary information associated with uncertainty. For instance, President Trump revealed in the first week of October that high-level trade negotiations between the US and China had concluded in a "very substantial phase one deal" and that phase two would start almost immediately after phase one was signed. This statement, a sure sign of reduced uncertainty, would be expected to improve investors' sentiment, and indeed, Wall Street stocks closed higher on 11 October 2019 as the S&P 500 gained 32.14 points (or 1.09%), DJIA moved ahead 319.92 points (or 1.21%) and Nasdaq 106.26 advanced points (1.34%). This episode motivates this study to investigate the role of economic policy uncertainty on asset prices. In addition, the impacts of monetary policy uncertainty (MPU) and fiscal policy uncertainty (FPU) are also included to the test equation as a way of differentiating the impact of dynamic correlation behavior of stock–bond returns.

It is generally recognized that a sudden rise in EPU is likely to impede the smoothness of operations in economic activities and hence cause income uncertainty, which tamps down liquidity (Brunnermeier and Pedersen 2009) and leads to a decline in demand for assets (Bloom 2009, 2014; Chiang 2019). This phenomenon may be called the income uncertainty e ffect. Conversely, as EPU lessens, investors feel less uncertain about the future and more encouraged to increase their demand for assets, driving a positive correlation between stock and bond returns (Hong et al. 2014).

On the other hand, the substitution effect describes a phenomenon in which stock and bond returns move in opposite directions as uncertainty about economic activity changes in the market. This occurs as uncertainty heightens; investors then sell off their riskier assets (stock) and move their funds into safer assets (bond). This shift results in a negative relation between stock and bond returns. Further, as uncertainty declines, investors then switch from lower return assets (bond) to higher return assets (stocks), causing a negative relation between stock and bond returns (Li et al. 2015). Thus, the substitution effect tends to produce a negative relation between stock and bond returns. In fact, the concept of income effect is essentially derived from Tobin (1969) and then applied by Barsky (1989), Hong et al. (2014), and Li et al. (2015) to analyze the impact of economic uncertainty, triggered by economic policy uncertainty, on asset returns. The analysis can be extended to examine the impacts of monetary policy uncertainty (MPU) and fiscal policy uncertainty (FPU). As stated above, the impacts of MPU and FPU on stock return and bond return could also be attributed to the income effect and substitution effect; the ultimate impact on the returns of these two asset classes depends on the relative influence of these two forces.

#### **3. A Dynamic Conditional Correlation Model**

To derive the dynamic correlation series, the literature follows a seminal study by Engle (2002) who proposes a dynamic conditional correlation model, which is designed to estimate asset market returns (de Goeij and Marquering 2004; Chiang et al. 2007; Yu et al. 2010; Antonakakis et al. 2013; Jones and Olson 2013; Li et al. 2015; Ehtesham and Siddiqui 2019; Allard et al. 2019). This model is frequently used because of its ability to capture a vector of return correlations and describe the volatility clustering phenomenon. Moreover, it could alleviate the heteroscedasticity problem (Forbes and Rigobon 2002). In this study, { *Rt*} represents a bivariate return series, expressed as

$$\mathcal{R}\_t = \mu\_t + \mathfrak{u}\_t \tag{1}$$

where *Rt* = [*R*1,*t <sup>R</sup>*2,*t*] is a 2 × 1 vector for stock market returns, μ*t* is the mean value of asset 1 or 2, which has the conditional expectation of multivariate time series properties2, *ut*|*Ft*−<sup>1</sup> = [*<sup>u</sup>*1,*tu*2,*t*] ∼

<sup>2</sup> 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).

*N*(0, *Ht*), *Ft*−<sup>1</sup> 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 *Ht* is assumed to be

$$H\_t = D\_t P\_t D\_t \tag{2}$$

where *Dt* = *diag*{*Ht*} −1/2 is the 2 × 2 diagonal matrix of time-varying standard deviations from univariate models, and *Pt* is the time-varying conditional correlation matrix, which satisfies the following conditions:

$$P\_t = \text{diag}\{\mathbf{Q}\_t\}^{-1/2} \mathbf{Q}\_t \text{diag}\{\mathbf{Q}\_t\}^{-1/2} \tag{3}$$

Now *Pt* in Equation (3) is a correlation matrix with ones on the diagonal and o ff-diagonal elements that have an absolute value less than one. Use of an asymmetric DCC model recognizes a shock dynamic adjustment of correlation for negative shock may be di fferent than it is for a positive outcome (Cappiello et al. 2006; Engle 2009).<sup>3</sup> In this expression, it can be written as:

$$Q\_t = \Omega + a \left. \varepsilon\_{t-1} \varepsilon\_{t-1}' + \gamma \eta\_{t-1} \eta\_{t-1}' + \beta Q\_{t-1} \tag{4}$$

where the *Qt* is positive definite and η*<sup>t</sup>*−1 = min[<sup>ε</sup>*t* , 0].

The product of η*i*,*<sup>t</sup>*η*j*,*<sup>t</sup>* will be nonzero; only these two variables are negative. Thus, a positive value of γ indicates that correlations increase more in response to market falls than they do to market rises. The equation is written as

$$
\hat{\Omega} = (1 - \alpha - \beta)\overline{Q} - \gamma \overline{N} \tag{5}
$$

where *Qt* = -*Qij*,*<sup>t</sup>* is the 2 × 2 time-varying covariance matrix of ε*t*, *Q* = *E*[<sup>ε</sup>*t*<sup>ε</sup> *t* ] is the 2 × 2 unconditional variance matrix of ε*t* (where <sup>ε</sup>*i*,*<sup>t</sup>* = *ui*,*<sup>t</sup>*/ ! *hii*,*t*, *i* = 1 and 2), *N* = *E* "γη*t*<sup>η</sup> *t* # is the 2 × 2 unconditional variance matrix of η*t*; *a*, β, and γ are non-negative scalar parameters satisfying (1 − α − β − γ) > 0. The substitution of Equation (5) for four yields

$$\rho\_{ij,t} = \frac{Q\_{ij,t}}{\sqrt{Q\_{ii,t}}\sqrt{Q\_{jj,t}}} \tag{6}$$

which can be used to calculate the correlations for the two assets. As proposed by Engle (2002, 2009) and Cappiello et al. (2006), the asymmetric dynamic correlation (ADCC) model can be estimated by using a two-stage approach to maximize the log-likelihood function.
