Diversification and hedging strategies of green bonds in financial asset portfolios during the COVID-19 pandemic

Figures & data

Table 1. Descriptive Statistics of the returns.

	GREEN	WORLD	PIMCO	COMM	CLEAN
Mean	0.009	0.024	0.008	−0.026	0.047
Median	0.007	0.052	0.009	0.001	0.072
SD	0.318	0.983	0.434	0.840	1.370
Minimum	−2.410	−10.441	−5.083	−4.268	−12.498
Maximum	2.013	8.406	6.818	3.390	11.035
Skewness	−0.579	−1.510	−0.010	−0.357	−1.049
Kurtosis-3	6.326	23.809	74.710	2.4642	15.546
JB	2697.3**	37560**	363970**	429.17**	16046**
Q(20)	20.390	194.776**	21.227	18.1201	30.795*
Q^2(20)	580.030**	1923.74**	1424.340**	485.628**	1723.22**
ADF	−15.990**	−17.508**	−13.7965**	−16.466**	−16.374**
KPSS	0.048	0.026	0.089	0.192	0.499
ARCH(10)	34.247**	89.292**	83.978**	19.707**	70.772
Corr. with Green	1.000	0.127	0.378	0.180	0.159

The reported statistics are for daily returns of green bond and conventional financial assets (MSCI world, Pimco bonds, Commodity, and Clean energy) indices for the period from 6 November 2014 to 5 November 2020. SD is the standard deviation. JB denotes the Jarque- Bera test for normality. Q(20) and Q² (20) are Box-Pierce statistics for serial correlation in return and square returns up to 20 lags. ADF is the augmented Dicky-Fuller unit root test, while KPSS is the Kwiatkowski-Phillips-Schmidt-shin test for stationarity. ARCH (10) is the heteroscedasticity test of Engle (1982) up to 20 lags. Corre. With Green is the constant correlation between green bond and each of conventional financial assets. **, * indicate statistical significance at 1% and 5% levels, respectively.

Table 2. Parameter estimates for cDCC model based on multivariate Student distribution.

	GREEN	WORLD	PIMCO	COMM	CLEAN
Panel A: Mean equation
μ	0.013** (0.007)	0.069** (0.017)	0.012 (0.006)	−0.011 (0.018)	0.0508 (0.028)
δ	0.017 (0.027)	0.073* (0.031)	−0.037 (0.028)	−0.033 (0.027)	0.164** (0.028)
Panel B: Variance equation
ω	0.002 (0.001)	0.024** (0.007)	0.007** (0.002)	0.0135* (0.006)	0.031* (0.013)
α	0.071** (0.023)	0.240** (0.049)	0.138** (0.031)	0.051** (0.011)	0.127** (0.032)
b	0.914** (0.026)	0.751** (0.038)	0.781** (0.048)	0.929** (0.016)	0.858** (0.033)
Panel C: DCC equation
θ1	0.021** (0004)
θ2	0.942** (0.013)
v	7.235** (0.501)
Panel D: Diagnostic tests
BP Q(20)	30.1925 [0.067}	23.0515 [0.286]	26.291 [0.156]	15.376 [0.754]	11.345 [0.936]
BP Q^2(20)	25.014 [0.201]	16.610 [0.678]	30.772 [0.0582]	12.411 [0.901]	16.479 [0.686]

Panels A B, and C show the estimated coefficients of the conditional mean, conditional variance and conditional correlation for all full-period from 6 November 2014 to 5 November 2020. Panel D presents the diagnostic tests. ρ_ig is the expected value of the dynamic conditional correlations between financial assets and green bond, while θ₁ and θ₂ examine the influences of last period’s residuals and covariance on the current level of the covariance. v is student’s t distribution shape parameter. The Panel D reports diagnostic test statistics for the univariate and multivariate standardized residuals for the cDCC- GARCH(1,1) model. BP-Q (20) and BP²-Q (20) stand for the Box – Pierce-Q statistics for standardized and standardized squared residuals, respectively, for up to 20 lags. Robust standard errors of the estimated coefficients are given in parenthesis and the p-values of the diagnostic tests are given in square brackets. ** and * denote statistical significance at the 1% and 5% significance levels, respectively.

Figure 1. Dynamic conditional correlations.

Table 3. DCC, Hedge ratios and optimal portfolio weights summary statistics.

	Full sample					Pre-COVID-19				During COVID-19
	Mean	SD	Min	Max		Mean	SD	Min	Max	Mean	SD	Min	Max
Panel A: DCC
WORLD/GREEN	0.088	0.099	−0.281	0.410		0.086	0.099	−0.224	0.410	0.103	0.099	−0.281	0.235
PIMCO/GREEN	0.367	0.066	0.140	0.581		0.368	0.064	0.140	0.539	0.364	0.076	0.197	0.581
COMM/GREEN	0.177	0.080	0.156	0.409		0.172	0.078	−0.121	0.409	0.208	0.087	−0.156	0.361
CLEAN/GREEN	0.117	0.089	−0.238	0.415		0.115	0.088	−0.238	0.415	0.131	0.095	−0.200	0.253
Panel B: HR
WORLD/GREEN	0.205	0.354	−2.397		2.864	0.193	0.310	−1.143	2.864	0.292	0.576	−2.397	1.389
PIMCO/GREEN	0.369	0.156	0.142		1.964	0.355	0.107	0.142	0.815	0.474	0.330	0.178	1.963
COMM/GREEN	0.485	0.231	−0.221		1.228	0.476	0.225	−0.316	1.228	0.551	0.263	−0.521	1.132
CLEAN/GREEN	0.436	0.431	−2.104		2.341	0.398	0.365	−1.006	2.341	0.724	0.693	−2.105	2.127
Panel C: Portfolio weights
WORLD/GREEN	0.843	0.111	0.428		1.000	0.830	0.110	0.428	1.000	0.938	0.053	0.732	1.000
PIMCO/GREEN	0.472	0.164	0.060		1.000	0.456	0.153	0.060	0.898	0.584	0.194	0.238	1.000
COMM/GREEN	0.923	0.047	0.725		1.000	0.922	0.048	0.725	1.000	0.932	0.041	0.815	1.000
CLEAN/GREEN	0.945	0.048	0.712		1.000	0.939	0.047	0.712	1.000	0.990	0.011	0.878	1.000

The table shows summary statistics of dynamic conditional correlations, hedge ratios, and optimal weights for the portfolios between each conventional asset and green bond. We report the results for the full period and each sub-sample period (pre- and during COVID-19).

Figure 2. Optimal hedge ratios.

Figure 3. Optimal green bond weights.

Table 4. Portfolios’ average risk/downside risk reduction and utility gain improvement.

Portfolio	Portf. I	Portf. II	Portf. III	Portf IV	Portf. II	Portf. III		Portf. IV
Panel A	Variance				Hedging Effectiveness
Full period
WORLD/GREEN	1.037	1.018	0.088	0.296	0.018	0.915	0.714
PIMCO/GREEN	0.152	0.121	0.066	0.086	0.204	0.566	0.434
COMM/GREEN	0.695	0.668	0.096	0.222	0.039	0.862	0.681
CLEAN/GREEN	1.892	1.850	0.098	0.521	0.022	0.948	0.724
Pre-Covid-19
WORLD/GREEN	0.563	0.550	0.073	0.170	0.023	0.870	0.696
PIMCO/GREEN	0.075	0.064	0.052	0.056	0.147	0.307	0.253
COMM/GREEN	0.644	0.610	0.084	0.201	0.053	0.870	0.688
CLEAN/GREEN	1.121	1.096	0.085	0.318	0.022	0.924	0.716
During Covid-19
WORLD/GREEN	4.550	4.485	0.190	1.223	0.014	0.958	0.973
PIMCO/GREEN	0.723	0.542	0.165	0.309	0.250	0.772	0.573
COMM/GREEN	1.149	1.100	0.184	0.381	0.043	0.840	0.654
CLEAN/GREEN	7.603	7.440	0.195	2.024	0.021	0.974	0.973
Panel B	Value-at-risk (VaR)				VaR reduction
Full period
WORLD/GREEN	1.292	1.286	0.417	0.742	0.005	0.677	0.426
PIMCO/GREEN	0.509	0.457	0.394	0.404	0.102	0.226	0.206
COMM/GREEN	1.375	1.354	0.476	0.777	0.015	0.654	0.435
CLEAN/GREEN	1.899	1.818	0.464	0.954	0.043	0.745	0.498
Pre-Covid-19
WORLD/GREEN	1.090	1.078	0.393	0.638	0.011	0.639	0.415
PIMCO/GREEN	0.449	0.402	0.372	0.371	0.105	0.171	0.174
COMM/GREEN	1.325	1.308	0.454	0.746	0.013	0.657	0.437
CLEAN/GREEN	1.640	1.563	0.442	0.831	0.047	0.730	0.493
During Covid-19
WORLD/GREEN	2.790	2.828	0.594	1.514	−0.014	0.787	0.457
PIMCO/GREEN	0.955	0.867	0.549	0.647	0.092	0.425	0.322
COMM/GREEN	1.741	1.699	0.637	1.007	0.024	0.634	0.421
CLEAN/GREEN	3.823	3.709	0.627	1.871	0.030	0.836	0.511
Portfolio	Portf. I	Portf. II	Portf. III	Portf IV	Portf. II	Portf. III	Portf IV
Panel C	Expected Shortfall (ES)				ES reduction
Full period
WORLD/GREEN	1.594	1.581	0.564	0.887	0.008	0.646	0.444
PIMCO/GREEN	0.610	0.568	0.479	0.507	0.069	0.215	0.169
COMM/GREEN	1.669	1.641	0.597	0.941	0.017	0.642	0.436
CLEAN/GREEN	2.365	2.344	0.598	1.258	0.001	0.747	0.468
Pre-Covid-19
WORLD/GREEN	1.354	1.344	0.533	0.767	0.007	0.606	0.434
PIMCO/GREEN	0.536	0.502	0.449	0.463	0.063	0.162	0.136
COMM/GREEN	1.611	1.586	0.571	0.907	0.016	0.646	0.437
CLEAN/GREEN	2.031	2.013	0.570	1.090	0.009	0.719	0.463
During Covid-19
WORLD/GREEN	3.372	3.345	0.789	1.779	0.008	0.766	0.472
PIMCO/GREEN	1.162	1.050	0.703	0.836	0.096	0.395	0.281
COMM/GREEN	2.095	2.049	0.789	1.198	0.022	0.623	0.428
CLEAN/GREEN	4.844	4.497	0.804	2.505	0.072	0.834	0.483
Panel D	Utility				Utility improvement
Full period
WORLD/GREEN	−4.125	−4.074	−0.342	−1.169	0.012	0.917	0.717
PIMCO/GREEN	−0.600	−0.488	−0.255	−0.336	0.187	0.477	0.440
COMM/GREEN	−2.806	−2.708	−0.378	−0.898	0.035	0.865	0.680
CLEAN/GREEN	−7.519	−7.360	−0.383	−2.057	0.021	0.949	0.726
Pre-Covid-19
WORLD/GREEN	−2.228	−2.178	−0.291	−0.670	0.022	0.869	0.699
PIMCO/GREEN	−0.293	−0.252	−0.204	−0.218	0.140	0.304	0.256
COMM/GREEN	−2.562	−2.472	−0.334	−0.815	0.035	0.869	0.682
CLEAN/GREEN	−4.460	−4.361	−0.334	−0.971	0.022	0.925	0.782
During Covid-19
WORLD/GREEN	−18.192	−17.958	−0.721	−4.867	0.013	0.960	0.732
PIMCO/GREEN	−2.276	−2.1469	−0.640	−1.208	0.057	0.281	0.469
COMM/GREEN	−4.619	−4.4598	−0.704	−1.514	0.034	0.848	0.672
CLEAN/GREEN	−30.197	−29.596	−0.742	−7.969	0.020	0.975	0.736

The table reports portfolios’ average risk/downside risk reduction and utility gain improvement for the full period and the two sub-sample periods (pre- and during COVID-19).

Engle, R. F. 1982. “Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of UK Inflation.” Econometrica 50: 987–1008.

 Web of Science ®Google Scholar