# Do Sustainable Stocks Offer Diversification Benefits for Conventional Portfolios? An Empirical Analysis of Risk Spillovers and Dynamic Correlations

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## Abstract

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## 1. Introduction

## 2. Literature Review

## 3. Methodology

## 4. Empirical Findings

#### 4.1. Data

#### 4.2. Model Identification

#### 4.3. Volatility Spillover Tests

_{ij}(i ≠ j) estimates for all regional indexes. On the other hand, significant and positive volatility spillovers are observed from conventional to sustainable indices, implied by highly significant b

_{12}estimates consistently for each region. This finding suggests that uncertainty regarding global equity markets spills over to the market for sustainable stocks, driving return volatility in this market segment. Risk transmissions, however, are found to be unidirectional, implied by insignificant spillover effects from sustainable to conventional indexes. It can thus be argued that sustainable stocks do not necessarily exhibit segmentation from their conventional counterparts and are driven by the common fundamental uncertainties affecting equity markets globally. The findings also suggest that the criteria applied in the identification of socially responsible investments do not necessarily shield these stocks from equity market shocks.

_{ii}+ b

_{ii}), we generally observe moderate to weak volatility persistence, relatively weaker in the case of sustainable indexes. The volatility persistence coefficients for the conventional (sustainable) indices are estimated as 0.433 (0.162), 0.413 (0.165), 0.509 (0.237), and 0.463 (0.172) for the World, Americas, Europe, and Asia-Pacific regions, respectively. Considering positive own volatility shocks observed in the case of sustainable indexes, implied by highly significant b

_{11}estimates, it can be argued that historical information on return and volatility in sustainable equity markets could be utilized in forecasting future volatility despite the evidence of weak volatility persistence in these markets.

#### 4.4. Dynamic Correlations

## 5. Portfolio Analysis

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Time-series plots of conventional and sustainability indexes.

**Note:**This figure provides the plots of the daily levels of the conventional and sustainability indices for the period 1 January 2004 to 2 September 2015. SIWORLD (GLOBAL), SINAMR (AMRCS), SIEUROPE (EUROPE), and SIASPCF (ASPCF) denote Dow Jones Sustainability (Conventional Global) Indices for the World, North America, Europe, and Asia-Pacific, respectively.

**Figure 2.**Smoothed probability estimates of regime 1.

**Note:**The figure plots the smoothed probability estimates of the low volatility regime (regime 1). The shaded regions in the figures correspond to the periods where the smoothed probability of regime 1 is the maximum.

**Figure 3.**Dynamic correlation estimates from the MS-DCC-GARCH.

**Note:**Figure plots the dynamic correlation estimates from the MS-DCC-GARCH model given in Equations (1)–(3). The correlations are obtained as the correlation coefficients are regime dependent and directly obtained from Equations (1)–(4) using the ML estimation. Since the correlations are regime-dependent and the two sets of correlations ${\rho}_{ij,1,t}$ and ${\rho}_{ij,2,t}$ are estimated for regimes 1 and 2, we obtain ${\rho}_{ij,t}={p}_{1,t}{\rho}_{ij,1,t}+\left(1-{p}_{1,t}\right){\rho}_{ij,2,t}$, where ${p}_{1,t}=P({s}_{t}=1|{\psi}_{t-1})$ is the predictive probability of being in regime 1 at time $t$ given the information set ${\psi}_{t-1}$ available through time $t-1$. See Note to Table 3 for model details.

SIWOLRD | SINAMRC | SIEUROPE | SIASPCF | GLOBAL | AMRCS | EUROPE | ASPCF | |

Mean | 0.01 | 0.01 | 0.01 | 0.01 | 0.02 | 0.02 | 0.01 | 0.01 |

S.D. | 1.14 | 1.14 | 1.45 | 1.32 | 1.10 | 1.22 | 1.42 | 1.16 |

Min | −7.77 | −8.99 | −9.93 | −10.33 | −7.89 | −9.74 | −10.13 | −9.11 |

Max | 8.84 | 9.45 | 10.46 | 10.84 | 9.88 | 10.51 | 10.51 | 9.01 |

Skewness | −0.30 | −0.42 | −0.09 | −0.34 | −0.44 | −0.48 | −0.12 | −0.47 |

Kurtosis | 8.95 | 11.30 | 7.59 | 6.35 | 9.89 | 11.40 | 7.58 | 6.72 |

JB | 10,227.42 *** | 16,313.24 *** | 7318.62 *** | 5190.91 *** | 12,516.18 *** | 16,620.02 *** | 7301.17 *** | 5855.89 *** |

Q(1) | 34.07 *** | 16.53 *** | 1.14 | 0.96 | 85.75 *** | 9.92 *** | 0.10 | 1.32 |

Q(5) | 57.59 *** | 31.22 *** | 29.83 *** | 7.18 | 98.61 *** | 19.57 *** | 26.79 *** | 4.34 |

ARCH(1) | 120.66 *** | 202.02 *** | 113.33 *** | 94.02 *** | 152.65 *** | 140.80 *** | 100.00 *** | 82.70 *** |

ARCH(5) | 798.47 *** | 797.38 *** | 593.67 *** | 899.63 *** | 915.00 *** | 789.89 *** | 611.35 *** | 837.62 *** |

n | 3044 | 3044 | 3044 | 3044 | 3044 | 3044 | 3044 | 3044 |

Pearson Correlation Coefficient Estimates | ||||||||

World | Americas | Europe | Asia-Pacific | |||||

Full sample | 0.966 | 0.987 | 0.995 | 0.976 | ||||

Subprime Crises Period | 0.967 | 0.992 | 0.996 | 0.985 |

**Note:**This table gives the descriptive statistics for logarithmic returns. SIWORLD, SINAMR, SIEUROPE, and SIASPCF denote Dow Jones Sustainability Indices (DJSI) for the World, North America, Europe, and Asia-Pacific, respectively, while GLOBAL, AMRCS, EUROPE, and ASPCF denote Dow Jones conventional Global Indices (DJGI) for the World, Americas, Europe and Asia-Pacific. The daily data covers the period 1 January 2004 to 2 September 2015 with n = 3044 observations. In addition to the mean, the standard deviation (S.D.), minimum (min), maximum (max), skewness, and kurtosis statistics, the table reports the Jarque–Bera normality test (JB), the Ljung–Box first (Q(1)), the fourth (Q(5)) autocorrelation tests, and the first (ARCH(1)) and the fourth (ARCH(5)) order Lagrange multiplier (LM) tests for the autoregressive conditional heteroscedasticity (ARCH), and Pearson correlations coefficient estimates. Full sample and subprime mortgage crises period (December 2007–June 2009) Pearson correlation coefficients are reported for World, Americas, Europe, and ASIA-Pacific, which represented the sustainability and conventional index pairs, (SIWORLD GLOBAL), (SINAMRC AMRCS), (SIEUROPE UROPE), and (SIASPCF ASPCF), respectively. The asterisks ***, ** and * represent significance at the 1%, 5%, and 10% levels, respectively.

ARCH-LM(1) | JB | Q(10) | Q(20) | p | |
---|---|---|---|---|---|

SIWOLRD | 2.724 | 197.383 *** | 5.454 | 19.214 | 4 |

(0.010) | (<0.001) | (0.793) | (0.443) | ||

SINAMRC | 5.277 ** | 427.863*** | 6.409 | 17.684 | 2 |

(0.022) | (<0.001) | (0.698) | (0.544) | ||

SIEUROPE | 0.122 | 230.330 *** | 4.802 | 16.135 | 0 |

(0.727) | (<0.001) | (0.851) | (0.648) | ||

SIASPCF | 0.001 | 92.166 *** | 4.638 | 11.789 | 4 |

(0.980) | (<0.001) | (0.865) | (0.895) | ||

GLOBAL | 2.160 | 244.572 *** | 4.439 | 19.661 | 4 |

(0.142) | (<0.001) | (0.880) | (0.415) | ||

AMRCS | 5.790 | 436.193 *** | 7.645 | 18.204 | 2 |

(0.016) | (<0.001) | (0.570) | (0.509) | ||

EUROPE | 0.294 | 220.475 *** | 4.543 | 16.985 | 0 |

(0.588) | (<0.001) | (0.872) | (0.591) | ||

ASPCF | 0.311 | 160.252 *** | 7.192 | 16.732 | 4 |

(0.577) | (<0.001) | (0.617) | (0.608) |

**Note**: The table reports diagnostic tests for univariate autoregressive GARCH model fits. An AR(p)-GARCH(1,1) model was fitted to each series. The AR order p was selected by the Akaike information criterion (AIC). Table reports the Jarque–Bera normality test (JB), the Ljung-Box 10th (Q(10)) and the 20th (Q(20)) autocorrelation tests, and the first (ARCH(1)) order Lagrange multiplier (LM) tests for the autoregressive conditional heteroscedasticity (ARCH). The p-values of the tests are given in parentheses. The asterisks ***, ** and * represent significance at the 1%, 5%, and 10% levels, respectively. The symbol “>” signifies “less than” the number it precedes.

Parameters | Models | |||
---|---|---|---|---|

World | Americas | Europe | Asia-Pasiific | |

Panel A: Spillover parameters | ||||

${c}_{s}$ | 0.0033 (0.0139) | 0.0159 (0.0099) | 0.0052 (0.0371) | 0.0319 (0.0289) |

${c}_{c}$ | 0.0159 (0.0305) | 0.0176 (0.0378) | 0.0202 (0.0672) | 0.0168 (0.0317) |

${a}_{s,s}$ | 0.0358 (0.0304) | 0.0162 (0.0303) | 0.0189 (0.0821) | 0.0173 (0.0562) |

${a}_{s,c}$ | 0.0633 (0.7564) | 0.0249 (1.9827) | 0.0082 (2.8751) | 0.0110 (2.8601) |

${a}_{c,s}$ | 0.0252 (0.8179) | 0.0582 (1.7571) | 0.0593 (2.9988) | 0.1014 (3.7029) |

${a}_{c,c}$ | 0.0337 *** (0.0106) | 0.0786 *** (0.0092) | 0.0772 ** (0.0365) | 0.0945 *** (0.0192) |

${b}_{s,s}$ | 0.1266 *** (0.0265) | 0.1496 *** (0.0388) | 0.2183 *** (0.0590) | 0.1549 *** (0.0229) |

${b}_{s,c}$ | 0.4627 *** (0.0253) | 0.6228 *** (0.0306) | 0.4593 *** (0.0721) | 0.3965 *** (0.0526) |

${b}_{c,s}$ | 0.8503 (0.6626) | 0.6612 (2.3041) | 0.7239 (2.9214) | 0.9425 (2.1682) |

${b}_{c,c}$ | 0.4003 (0.7189) | 0.3353 (2.0511) | 0.4324 (3.0450) | 0.3686 (2.8084) |

Panel B: DCC parameters | ||||

$\alpha \left({s}_{t}=1\right)$ | 0.0181 *** (0.0036) | 0.0427 *** (0.0040) | 0.0880 *** (0.0054) | 0.0361 *** (0.0060) |

$\beta \left({s}_{t}=1\right)$ | 0.9750 *** (0.0063) | 0.9430 *** (0.0058) | 0.8528 *** (0.0102) | 0.9553 *** (0.0147) |

$\alpha \left({s}_{t}=2\right)$ | 0.0677 *** (0.0250) | 0.0839 *** (0.0108) | 0.1073 *** (0.0301) | 0.0778 * (0.0444) |

$\beta \left({s}_{t}=2\right)$ | 0.7769 *** (0.0999) | 0.8730 *** (0.0172) | 0.8095 *** (0.0602) | 0.8314 *** (0.1668) |

Panel C: Regime Inference | ||||

log L of MS-DCC | −4029.247 | −3084.625 | −2785.198 | −4495.000 |

log L of DCC | −5103.762 | −4034.694 | −3898.901 | −5275.907 |

AIC of MS-DCC | 2.661 | 2.041 | 1.844 | 2.968 |

AIC of DCC | 3.360 | 2.658 | 2.569 | 3.474 |

LR linearity Test | 2149.030 *** | 1900.138 *** | 2227.405 *** | 1561.813 *** |

${p}_{11}$ | 0.982 | 0.984 | 0.969 | 0.979 |

${p}_{22}$ | 0.935 | 0.930 | 0.889 | 0.930 |

${n}_{1}$ | 2387.100 | 2478.600 | 2377.700 | 2352.100 |

${n}_{2}$ | 655.900 | 564.400 | 665.300 | 690.900 |

Prob(Regime 1) | 0.781 | 0.812 | 0.781 | 0.770 |

Prob(Regime 2) | 0.219 | 0.188 | 0.219 | 0.230 |

Duration of Regime 1 | 55.140 | 61.670 | 32.080 | 47.740 |

Duration of Regime 2 | 15.420 | 14.320 | 8.980 | 14.220 |

**Note:**This table reports the estimates of the MS-DCC-GARCH model given in Equations (1)–(3). The matrix R for the World, Americas, Europe, and Asia-Pacific models are formed as R = (SIWORLD GLOBAL), R = (SINAMRC AMRCS), R = (SIEUROPE UROPE), and R = (SIASPCF ASPCF), respectively. The GARCH part of the model is specified as a GARCH(1,1). The subscript $s$ denotes the SRI return series while subscript $c$ denotes conventional return series. The models are estimates over the full sample period 1 January 2004–2 September 2015 with n = 3044 observations. The lag order for the Vector Autoregressive VAR part of the model was selected by the AIC and is one for all four models. The MS-DCC-GARCH model was estimated using the maximum likelihood (ML) method. The likelihood ratio (LR) linearity test is reported with p-value of the [67]. Standard errors of the estimates are given in parentheses. log L stands for the log likelihood, ${p}_{ii}$ for the regime transition probabilities, Prob (Regime i) for the ergodic (limit) probability of regime i, and ${n}_{i}$ for the number of observations falling in regime i according to the ergodic probability. ***, ** and * represent significance at the 1%, 5%, and 10% levels, respectively.

Test Type | Wald | NT-R | NT-NR | HH |
---|---|---|---|---|

Panel A: Unidirectional volatility spillovers from conventional to sustainable | ||||

${H}_{0}:$ GLOBAL $\Rightarrow $ SIWORLD | 26.0335 *** | 33.5088 *** | 9.9801 *** | 7.9773 ** |

${H}_{0}:$ AMRCS $\Rightarrow $ SINMARC | 3.9563 | 1.7234 | 5.2534 | 2.3548 |

${H}_{0}:$ EUROPE $\Rightarrow $ SIEUROPE | 6.9236 | 3.9381 | 5.1069 | 9.6125 ** |

${H}_{0}:$ ASPCF $\Rightarrow $ SIASPCF | 7.2269 | 5.2085 | 4.9439 | 7.6233 |

Panel B: Unidirectional volatility spillovers from sustainable to conventional | ||||

${H}_{0}:$ SIWORLD $\Rightarrow $ GLOBAL | 5.7180 * | 9.9768 *** | 13.6846 *** | 3.0029 |

${H}_{0}:$ SINMARC $\Rightarrow $ AMRCS | 1.8908 | 1.1614 | 5.285 | 2.1588 |

${H}_{0}:$ SIEUROPE $\Rightarrow $ EUROPE | 4.4583 | 2.2569 | 3.0597 | 0.338 |

${H}_{0}:$ SIASPCF $\Rightarrow $ ASPCF | 4.7144 | 3.1005 | 2.1225 | 0.3585 |

Panel C: Bi-directional volatility spillovers between sustainable and conventional | ||||

${H}_{0}:$ GLOBAL $\iff $ SIWORLD | 19.4387 *** | 0.2948 | 32.5822 *** | 42.6304 *** |

${H}_{0}:$ AMRCS $\iff $ SINMARC | 5.847 | 2.8848 | 10.5384 ** | 4.5136 |

${H}_{0}:$ EUROPE $\iff $ SIEUROPE | 11.3819 ** | 6.195 | 8.1666 * | 9.9505 ** |

${H}_{0}:$ ASPCF $\iff $ SIASPCF | 11.9413 ** | 8.3090 * | 7.0664 | 7.9818 * |

**Note:**The table reports causality tests for testing the null hypothesis of no one unidirectional volatility spillover from variable X to variable Y, demoted, X $\Rightarrow $ Y as well as the bidirectional volatility spillover, denoted X $\iff $ Y. The Wald tests for testing the no volatility spillover restrictions were imposed on Equation (1). The tests report that the tests are distributed as Chi-square with 2 and 4 degrees of freedom, respectively, for unidirectional and bidirectional tests. The HH test is the [69] LM test of causality on conditional variance. NT-R is the [68] robust test of the causality in conditional variance, while the NT-NR is the non-robust version of the [68] test. HH, NT-R, and NT-NR tests are LM tests and the univariate specification for conditional variances is a GARCH(1,1) model. We compute HH, NT-R, and NT-NR tests to tests only causality in conditional variance from X variable (Japan or US) to Y variable. ***, ** and * represent significance at the 1%, 5%, and 10% levels, respectively.

Mean | S.D. | Min | Max | HE | Sharpe Ratio | |
---|---|---|---|---|---|---|

Panel A: World Market | ||||||

Undiversified Portfolio Return | 0.028 | 1.154 | −7.886 | 9.883 | -- | 0.024 |

MS-DCC-GARCH Hedged Portfolio Return | 0.018 | 0.295 | −1.928 | 1.961 | 93.567 | 0.061 |

DCC-GARCH Hedged Portfolio Return | 0.017 | 0.293 | −1.931 | 2.026 | 93.478 | 0.058 |

MS-DCC-GARCH Optimal Portfolio Return | 0.034 | 1.012 | −8.413 | 7.775 | 23.082 | 0.034 |

DCC-GARCH Optimal Portfolio Return | 0.024 | 0.940 | −6.590 | 9.883 | 33.664 | 0.026 |

MS-DCC-GARCH Optimal Hedge Ratio | 0.929 | 0.070 | 0.780 | 1.209 | -- | -- |

DCC-GARCH Optimal Hedge Ratio | 0.935 | 0.059 | 0.814 | 1.122 | -- | -- |

MS-DCC-GARCH Optimal Portfolio Weight | 0.618 | 0.417 | 0.000 | 1.000 | -- | -- |

DCC-GARCH Optimal Portfolio Weight | 0.635 | 0.407 | 0.000 | 1.000 | -- | -- |

Panel B: Americas Market | ||||||

Undiversified Portfolio Return | 0.022 | 1.268 | −9.736 | 10.515 | -- | 0.017 |

MS-DCC-GARCH Hedged Portfolio Return | 0.010 | 0.199 | −1.177 | 0.959 | 97.533 | 0.050 |

DCC-GARCH Hedged Portfolio Return | 0.009 | 0.201 | −1.177 | 1.068 | 97.478 | 0.045 |

MS-DCC-GARCH Optimal Portfolio Return | 0.009 | 0.458 | −9.453 | 8.993 | 16.666 | 0.020 |

DCC-GARCH Optimal Portfolio Return | 0.009 | 0.472 | −9.453 | 8.993 | 14.638 | 0.019 |

MS-DCC-GARCH Optimal Hedge Ratio | 1.047 | 0.053 | 0.828 | 1.221 | -- | -- |

DCC-GARCH Optimal Hedge Ratio | 1.042 | 0.015 | 0.960 | 1.080 | -- | -- |

MS-DCC-GARCH Optimal Portfolio Weight | 0.078 | 0.216 | 0.000 | 1.000 | -- | -- |

DCC-GARCH Optimal Portfolio Weight | 0.002 | 0.027 | 0.000 | 1.000 | -- | -- |

Panel C: European Market | ||||||

Undiversified Portfolio Return | 0.019 | 1.476 | −10.130 | 10.512 | -- | 0.013 |

MS-DCC-GARCH Hedged Portfolio Return | 0.006 | 0.149 | −1.804 | 1.601 | 98.987 | 0.040 |

DCC-GARCH Hedged Portfolio Return | 0.005 | 0.149 | −1.804 | 1.601 | 98.979 | 0.034 |

MS-DCC-GARCH Optimal Portfolio Return | 0.038 | 1.429 | −10.130 | 10.512 | 6.342 | 0.027 |

DCC-GARCH Optimal Portfolio Return | 0.015 | 1.466 | −10.130 | 10.512 | 1.354 | 0.010 |

MS-DCC-GARCH Optimal Hedge Ratio | 0.977 | 0.028 | 0.865 | 1.088 | -- | -- |

DCC-GARCH Optimal Hedge Ratio | 0.977 | 0.006 | 0.956 | 0.996 | -- | -- |

MS-DCC-GARCH Optimal Portfolio Weight | 0.744 | 0.409 | 0.000 | 1.000 | -- | -- |

DCC-GARCH Optimal Portfolio Weight | 0.980 | 0.073 | 0.295 | 1.000 | -- | -- |

Panel D: Asia-Pacific Market | ||||||

Undiversified Portfolio Return | 0.017 | 1.218 | −9.114 | 9.008 | -- | 0.014 |

MS-DCC-GARCH Hedged Portfolio Return | 0.005 | 0.239 | −1.431 | 1.434 | 96.135 | 0.021 |

DCC-GARCH Hedged Portfolio Return | 0.003 | 0.240 | −1.340 | 1.295 | 96.104 | 0.013 |

MS-DCC-GARCH Optimal Portfolio Return | 0.016 | 1.094 | −9.114 | 9.008 | 3.775 | 0.015 |

DCC-GARCH Optimal Portfolio Return | 0.017 | 1.192 | −9.114 | 9.008 | 0.000 | 0.014 |

MS-DCC-GARCH Optimal Hedge Ratio | 0.854 | 0.052 | 0.700 | 1.052 | -- | -- |

DCC-GARCH Optimal Hedge Ratio | 0.851 | 0.005 | 0.837 | 0.868 | -- | -- |

MS-DCC-GARCH Optimal Portfolio Weight | 0.977 | 0.130 | 0.000 | 1.000 | -- | -- |

DCC-GARCH Optimal Portfolio Weight | 1.000 | 0.000 | 1.000 | 1.000 | -- | -- |

**Note:**The in-sample period covers 2 January 2004–19 February 2014 with 2644 observations. HE stands for the hedge effectiveness index.

Mean | S.D. | Min | Max | HE | Sharpe Ratio | |
---|---|---|---|---|---|---|

Panel A: World Market | ||||||

Undiversified Portfolio Return | −0.015 | 0.686 | −3.986 | 2.119 | -- | -0.022 |

MS-DCC-GARCH Hedged Portfolio Return | 0.008 | 0.219 | −1.154 | 1.369 | 89.818 | 0.037 |

DCC-GARCH Hedged Portfolio Return | 0.008 | 0.220 | −1.206 | 1.375 | 89.712 | 0.036 |

MS-DCC-GARCH Optimal Portfolio Return | 0.018 | 0.525 | −2.284 | 3.038 | 41.380 | 0.034 |

DCC-GARCH Optimal Portfolio Return | 0.010 | 0.566 | −2.284 | 2.488 | 32.011 | 0.018 |

MS-DCC-GARCH Optimal Hedge Ratio | 0.916 | 0.069 | 0.760 | 1.071 | -- | -- |

DCC-GARCH Optimal Hedge Ratio | 0.927 | 0.041 | 0.844 | 1.025 | -- | -- |

MS-DCC-GARCH Optimal Portfolio Weight | 0.648 | 0.390 | 0.000 | 1.000 | -- | -- |

DCC-GARCH Optimal Portfolio Weight | 0.734 | 0.299 | 0.000 | 1.000 | -- | -- |

Panel B: Americas Market | ||||||

Undiversified Portfolio Return | 0.002 | 0.792 | −3.988 | 3.438 | -- | 0.003 |

MS-DCC-GARCH Hedged Portfolio Return | 0.006 | 0.141 | −0.661 | 0.458 | 96.830 | 0.043 |

DCC-GARCH Hedged Portfolio Return | 0.006 | 0.152 | −0.649 | 0.500 | 96.287 | 0.039 |

MS-DCC-GARCH Optimal Portfolio Return | 0.005 | 0.700 | −2.903 | 3.438 | 21.883 | 0.007 |

DCC-GARCH Optimal Portfolio Return | 0.003 | 0.800 | −3.552 | 3.853 | −2.088 | 0.004 |

MS-DCC-GARCH Optimal Hedge Ratio | 0.995 | 0.050 | 0.864 | 1.161 | -- | -- |

DCC-GARCH Optimal Hedge Ratio | 1.037 | 0.011 | 0.994 | 1.073 | -- | -- |

MS-DCC-GARCH Optimal Portfolio Weight | 0.370 | 0.421 | 0.000 | 1.000 | -- | -- |

DCC-GARCH Optimal Portfolio Weight | 0.001 | 0.011 | 0.000 | 0.153 | -- | -- |

Panel C: European Market | ||||||

Undiversified Portfolio Return | −0.040 | 0.917 | −3.182 | 3.122 | -- | −0.044 |

MS-DCC-GARCH Hedged Portfolio Return | −0.001 | 0.132 | −1.067 | 1.181 | 97.930 | −0.008 |

DCC-GARCH Hedged Portfolio Return | −0.002 | 0.132 | −1.095 | 1.181 | 97.928 | −0.015 |

MS-DCC-GARCH Optimal Portfolio Return | −0.032 | 0.827 | −2.911 | 3.122 | 18.625 | −0.039 |

DCC-GARCH Optimal Portfolio Return | −0.039 | 0.891 | −3.182 | 3.122 | 5.500 | −0.044 |

MS-DCC-GARCH Optimal Hedge Ratio | 0.975 | 0.029 | 0.840 | 1.060 | -- | -- |

DCC-GARCH Optimal Hedge Ratio | 0.981 | 0.006 | 0.967 | 0.997 | -- | -- |

MS-DCC-GARCH Optimal Portfolio Weight | 0.734 | 0.393 | 0.000 | 1.000 | -- | -- |

DCC-GARCH Optimal Portfolio Weight | 0.933 | 0.165 | 0.200 | 1.000 | -- | -- |

Panel D: Asia-Pacific Market | ||||||

Undiversified Portfolio Return | −0.019 | 0.708 | −4.425 | 2.146 | -- | −0.027 |

MS-DCC-GARCH Hedged Portfolio Return | 0.003 | 0.328 | −4.267 | 0.851 | 78.579 | 0.009 |

DCC-GARCH Hedged Portfolio Return | 0.002 | 0.332 | −4.370 | 0.886 | 78.034 | 0.006 |

MS-DCC-GARCH Optimal Portfolio Return | −0.007 | 0.639 | −2.305 | 2.146 | 18.430 | −0.011 |

DCC-GARCH Optimal Portfolio Return | −0.019 | 0.708 | −4.425 | 2.146 | 0.000 | −0.027 |

MS-DCC-GARCH Optimal Hedge Ratio | 0.824 | 0.063 | 0.686 | 1.080 | -- | -- |

DCC-GARCH Optimal Hedge Ratio | 0.845 | 0.005 | 0.835 | 0.861 | -- | -- |

MS-DCC-GARCH Optimal Portfolio Weight | 0.928 | 0.222 | 0.000 | 1.000 | -- | -- |

DCC-GARCH Optimal Portfolio Weight | 1.000 | 0.000 | 1.000 | 1.000 | -- | -- |

**Note:**The out-of-sample period covers 20 February 2014–2 September 2014 with 400 observations. HE stands for the hedge effectiveness index.

© 2017 by the authors. 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**

Balcilar, M.; Demirer, R.; Gupta, R. Do Sustainable Stocks Offer Diversification Benefits for Conventional Portfolios? An Empirical Analysis of Risk Spillovers and Dynamic Correlations. *Sustainability* **2017**, *9*, 1799.
https://doi.org/10.3390/su9101799

**AMA Style**

Balcilar M, Demirer R, Gupta R. Do Sustainable Stocks Offer Diversification Benefits for Conventional Portfolios? An Empirical Analysis of Risk Spillovers and Dynamic Correlations. *Sustainability*. 2017; 9(10):1799.
https://doi.org/10.3390/su9101799

**Chicago/Turabian Style**

Balcilar, Mehmet, Riza Demirer, and Rangan Gupta. 2017. "Do Sustainable Stocks Offer Diversification Benefits for Conventional Portfolios? An Empirical Analysis of Risk Spillovers and Dynamic Correlations" *Sustainability* 9, no. 10: 1799.
https://doi.org/10.3390/su9101799