Returns and volatility of water investments

Figures & data

Table 1. Descriptive statistics

	WOWAX	S-Net	S&P	MSCI ACWI	Asia	Europe	Latin America	US	Pictet	KBC Eco
Full period: January 2004–October 2014
Mean	0.03	0.03	0.03	0.03	0.04	0.01	0.00	0.03	−0.00	0.03
Median	0.02	0.07	0.08	0.04	0.00	0.01	0.07	0.00	0.00	0.06
Maximum	0.72	9.27	10.90	15.86	13.27	13.96	10.54	12.14	4.61	10.92
Minimum	0.00	−7.55	−8.07	−8.52	−9.23	−10.09	−12.25	−7.56	−3.84	−8.42
Std. Dev.	0.05	1.04	1.11	1.21	1.55	1.41	1.71	1.35	0.61	1.14
Skewness	4.60	−0.43	−0.33	0.41	0.40	−0.04	−0.53	0.35	0.13	−0.31
Kurtosis	36.24	10.84	11.86	17.67	8.19	10.91	7.89	10.10	6.37	12.60
Jarque-Bera	140,135.3	7333.34	9,317.92	25,460.85	3,259.47	7,382.23	2,952.22	5,998.03	1,349.24	10,905.00
Probability	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
Observations	2,827	2,827	2,827	2,827	2,827	2,827	2,827	2,827	2,827	2,827
Pre-GFC period: January 2004–December 2007
Mean	−0.0	0.07	0.08	0.07	0.09	0.09	0.06	0.05	0.01	0.07
Median	−0.02	0.11	0.116	0.07	0.00	0.09	0.10	0.00	0.01	0.08
Maximum	0.000	2.50	2.92	6.08	13.27	3.71	10.54	6.44	1.95	2.75
Minimum	−0.72	−3.17	−3.51	−5.06	−6.63	−3.25	−8.16	−7.39	−1.73	−3.35
Std. dev.	0.06	0.73	0.76	1.00	1.92	0.91	1.65	1.35	0.52	0.77
Skewness	−4.06	−0.42	−0.29	0.09	0.77	−0.07	−0.13	−0.29	0.01	−0.33
Kurtosis	26.99	4.10	4.14	4.96	6.73	3.88	6.18	5.84	3.79	4.57
Jarque-Bera	27,903.69	84.14	72.56	170.02	711.34	35.07	445.35	366.6973	27.62	128.35
Probability	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
Observations	1,043	1,043	1,043	1,043	1,043	1,043	1,043	1,043	1,043	1,043
GFC period: January 2008–December 2010
Mean	0.02	−0.01	−0.01	−0.02	−0.01	−0.08	−0.01	−0.00	−0.01	−0.01
Median	0.01	0.05	0.07	0.02	0.00	−0.05	0.10	0.00	−0.00	0.06
Maximum	0.10	9.27	10.90	15.86	5.83	13.96	8.65	12.14	4.61	10.92
Minimum	0.00	−7.55	−8.07	−8.52	−9.23	−10.09	−12.25	−6.45	−3.84	−8.42
Std. Dev.	0.02	1.49	1.60	1.68	1.48	2.00	2.03	1.66	0.79	1.65
Skewness	1.60	−0.28	−0.17	0.63	−0.58	0.18	−0.92	0.81	0.27	−0.14
Kurtosis	5.77	8.07	8.79	15.91	7.72	8.50	8.93	10.08	6.21	9.16
Jarque-Bera	586.69	853.15	1,100.60	5498.51	774.98	994.49	1263.38	1728.09	347.98	1,244.69
Probability	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
Observations	784	784	784	784	784	784	784	784	784	784
Post-GFC period: January 2011–October 2014
Mean	0.0	0.02	0.02	0.04	0.02	−0.00	−0.03	0.05	−0.00	0.04
Median	0.01	0.03	0.04	0.03	0.00	0.00	0.02	0.02	0.00	0.06
Maximum	0.48	3.58	3.61	5.06	6.56	4.12	6.49	9.05	2.31	4.08
Minimum	0.00	−5.50	−5.51	−4.07	−6.07	−7.21	−7.89	−7.56	−2.10	−5.70
Std. Dev.	0.05	0.88	0.94	0.94	1.11	1.27	1.48	1.04	0.55	0.95
Skewness	3.51	−0.40	−0.41	−0.11	−0.15	−0.34	−0.26	0.39	−0.07	−0.39
Kurtosis	21.74	6.53	6.27	4.72	5.57	5.108	4.96	12.70	4.57	6.22
Jarque-Bera	16,703.68	548.06	476.57	126.52	280.13	205.0	172.54	3,954.23	104.48	458.75
Probability	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
Observations	1,000	1,000	1,000	1,000	1,000	1,000	1,000	1,000	1,000	1,000

Notes: This table reports the descriptive statistics for four water indices-World Water Index (WOWAX), S-Net Global Water Index (S-Net), S&P Global Water Index (S&P) and MSCI ACWI Water Utilities Index (MSCI ACWI) and four water markets-Asia, Europe, Latin America and US water markets, and two water funds-Pictet Global Water Fund (Pictet) and KBC ECO Water Fund (KBC Eco). Descriptive statistics include daily mean, maximum, minimum, standard deviation (std.dev.), and performance-related statistics in different (full, pre-GFC, GFC, and post-GFC) periods.

Data are collected from the Thomson Reuters DataStream database. Daily data are transformed to the form of R_t = ln(Price_t/Price_t−1) × 100 and the prices are in US dollars.

Notes: This figure presents the four water indices, four water markets and two water funds share prices movements during the full, pre-GFC, GFC, and post-GFC periods. Source: Thomson Reuters DataStream database.

Figure 2. Movements of mean, maximum, minimum, and standard deviation during full, pre-GFC, GFC, and post-GFC periods.

Notes: Mean Maximum, Minimum and Std. Dev results are summarized as graphs here for different (full, pre-GFC, GFC and post-GFC) periods in Table 2. Source: Thomson Reuters DataStream database.

Table 2. Correlation matrix among water indices, water markets and water funds

	WOWAX	S-Net	S&P	MSCI ACWI	Asia	Europe	Latin America	US	Pictet	KBC Eco
Full period: January 2004–October 2014
WOWAX	1
S-Net	0.01	1
S&P	0.01	0.94	1
MSCI ACWI	0.01	0.67	0.71	1
Asia	0.01	0.29	0.26	0.14	1
Europe	0.02	0.71	0.79	0.72	0.18	1
Latin America	0.02	0.58	0.56	0.40	0.21	0.42	1
US	0.01	0.54	0.49	0.48	0.07	0.27	0.28	1
Pictet	0.02	0.42	0.47	0.35	0.13	0.54	0.27	0.09	1
KBC ECO	0.01	0.93	0.91	0.64	0.24	0.68	0.53	0.52	0.41	1
Pre-GFC period: January 2004–December 2007
WOWAX	1
S-Net	−0.036	1
S&P	−0.02	0.88	1
MSCI ACWI	−0.03	0.61	0.62	1
Asia	−0.00	0.30	0.27	0.10	1
Europe	−0.03	0.68	0.76	0.82	0.14	1
Latin America	−0.03	0.56	0.50	0.32	0.17	0.37	1
US	−0.05	0.48	0.39	0.24	0.03	0.19	0.23	1
Pictet	−0.02	0.34	0.40	0.40	0.05	0.49	0.17	0.06	1
KBC ECO	−0.04	0.88	0.85	0.58	0.22	0.68	0.49	0.46	0.39	1
GFC period: January 2008–Dec ember 2010
WOWAX	1
S-Net	−0.03	1
S&P	−0.02	0.96	1
MSCI ACWI	0.01	0.71	0.76	1
Asia	−0.00	0.36	0.34	0.21	1
Europe	0.01	0.71	0.79	0.69	0.29	1
Latin America	−0.00	0.65	0.66	0.50	0.27	0.50	1
US	−0.03	0.56	0.51	0.61	0.14	0.28	0.31	1
Pictet	0.00	0.42	0.48	0.32	0.24	0.57	0.34	0.06	1
KBC ECO	−0.04	0.95	0.94	0.68	0.33	0.69	0.60	0.55	0.41	1
Post-GFC period: January 2011–October 2014
WOWAX	1
S-Net	0.01	1
S&P	0.01	0.95	1
MSCI ACWI	−0.04	0.63	0.72	1
Asia	0.01	0.25	0.22	0.09	1
Europe	0.01	0.73	0.81	0.75	0.12	1
Latin America	0.00	0.51	0.51	0.36	0.20	0.37	1
US	−0.04	0.61	0.61	0.59	0.04	0.36	0.33	1
Pictet	0.02	0.49	0.54	0.36	0.12	0.56	0.26	0.19	1
KBC ECO	0.01	0.92	0.90	0.59	0.21	0.68	0.49	0.57	0.46	1

Notes: This table reports the correlation results among four water indices, four water markets and two water funds during full, pre-GFC, GFC, and post-GFC periods. This table shows that S-Net is highly and significantly correlated with S&P, and MSCI ACWI is also highly and positively correlated with Europe in different (full, pre-GFC, GFC, and post-GFC) periods.

Table 3. ARMA (1, 1) model

	WOWAX	S-Net	S&P	MSCI ACWI	Asia	Europe	Latin America	US	Pictet	KBC Eco
Full period: January 2004–October 2014
Constant	0.03	−0.00	0.03	0.01	0.03	−0.01	−0.02	0.00	−0.00	0.00
	(0.00)	(0.72)	(0.40)	(0.24)	(0.19)	(0.15)	(0.22)	(0.99)	(0.61)	(0.62)
AR(1)	0.98	0.22	−0.07	0.67	0.18	−0.91	0.52	0.67	0.97	0.30
	(0.00)***	(0.09)*	(0.06)*	(0.09)*	(0.21)	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***
MA (1)	0.91	0.35	−0.22	0.69	0.30	−0.86	0.59	0.74	0.98	0.54
	(0.00)***	(0.00)***	(0.05)**	(0.08)*	(0.03)**	(0.00)***	(0.00)***	(0.00)***	(0.00)****	(0.00)***
R-Squared	0.16	0.93	0.93	0.63	0.12	0.75	0.35	0.41	0.33	0.89
Pre-GFC period: January 2004–December 2007
Constant	−0.05	0.00	0.08	0.01	0.09	0.01	−0.05	0.05	0.01	−0.00
	(0.00)	(0.27)	(0.00)	(0.40)	(0.07)	(0.28)	(0.20)	0.10	(0.33)	(0.52)
AR(1)	0.99	0.24	0.23	0.87	0.01	−0.96	0.89	0.87	0.75	0.18
	(0.00)***	(0.14)	(0.25)	(0.00)***	(0.97)	(0.00)***	(0.00)***	(0.00)***	(0.02)**	(0.06)*
MA (1)	0.94	0.41	0.08	0.90	0.09	−0.98	0.91	0.90	0.78	0.46
	(0.00)***	(0.01)***	(0.68)	(0.00)***	(0.80)	(0.00)***	(0.00)***	(0.00)***	(0.01)**	(0.00)***
R-Squared	0.11	0.88	0.85	0.70	0.15	0.81	0.33	0.32	0.26	0.83
GFC period: January 2008–December 2010
Constant	0.02	−0.00	−0.01	−0.03	−0.01	−0.07	−.00	.017	0.00	0.01
	(0.00)	(0.49)	(0.77)	(0.46)	(0.81)	(0.16)	(0.57)	(0.76)	(0.92)	(0.47)
AR(1)	0.01	0.94	−0.18	0.73	−0.99	−0.85	0.01	0.74	−0.57	0.98
	(0.00)***	(0.00)***	(0.24)	(0.00)***	(0.00)***	(0.00)***	(0.93)	(0.07)*	(0.42)	(0.00)***
MA(1)	0.02	0.98	−0.38	0.77	−1.00	−0.76	0.19	0.77	−0.60	1.00
	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.33)	(0.05)**	(0.38)	(0.00)***
R-Squared	0.01	0.96	0.96	0.70	0.17	0.75	0.47	0.52	0.36	0.92
Post-GFC period: January 2011–October 2014
Constant	0.03	−0.00	0.00	0.05	0.02	−0.04	−0.07	0.02	−0.00	0.01
	(0.00)	(0.46)	0.79	(0.01)	0.39	(0.08)	0.11	(0.40)	(0.76)	0.16
AR(1)	0.97	−0.05	0.05	−0.98	0.71	0.93	0.43	−0.72	−0.76	0.08
	(0.00)***	(0.80)	(0.86)	(0.00)***	(0.00)***	(0.00)***	(0.42)	(0.00)***	(0.00)***	(0.52)
MA (1)	0.86	0.07	0.15	−0.97	0.77	0.92	0.47	−0.60	−0.79	0.31
	(0.00)***	(0.74)	(0.64)	(0.00)***	(0.00)***	(0.00)***	(0.36)	(0.00)***	(0.00)***	(0.01)**

Notes: The estimation results from this table denotes the forecast for four water indices, four water markets and two water funds in different (full, pre-GFC, GFC, and post-GFC) periods which is derived from the ARMA(1, 1) model. p-values are given in brackets.

*Represent significance at the 10% level.

**Represent significance at the 5% level.

***Represent significance at the 1% level.

At the end of each day, we run the following model using daily stock returns in different (full, pre-GFC, GFC, and post-GFC) periods:

AR model: $y_t={\phi }_i{y}_{t-1}+{\phi }_i{y}_{t-2}+\dots +{\phi }_i{y}_{t-p}+{\mathrm{\xi }}_t=\sum _{i=1}^p{\phi }_i{y}_{t-i}$,

MA model: $y_t={\lambda }_j{\mathrm{\xi }}_{t-1}+{\lambda }_j{\mathrm{\xi }}_{t-2}+\dots +{\lambda }_j{\mathrm{\xi }}_{t-p}+{\mathrm{\xi }}_t=\sum _{j=1}^q{\lambda }_j{\mathrm{\xi }}_{t-j}$,

ARMA model: $y_t=\mu +\sum _{i=1}^p{\phi }_i{y}_{t-i}+\sum _{j=1}^q{\lambda }_j{\mathrm{\xi }}_{t-j}+{\mathrm{\xi }}_t$

Table 4. ARMA-GARCH (1, 1) model

	WOWAX	S-Net	S&P	MSCI ACWI	Asia	Europe	Latin America	US	PICTET	KBC EcO
Full period: January 2004–October 2014
µ	0.99	0.04	−0.16	−0.80	0.47	−0.84	0.60	0.41	0.50	0.17
	(0.00)***	(0.75)	(0.43)	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.02)**	(0.75)	(0.00)***
φ	−0.77	−0.181	0.07	0.78	−0.55	0.83	−0.64	−0.49	−0.51	−0.37
	(0.00)***	(0.17)	(0.72)	(0.00)****	(0.00)****	(0.00)***	(0.00)***	(0.00)***	(0.05)**	(0.00)***
α	1.99	0.05	0.05	0.02	0.07	0.04	0.09	0.04	0.02	0.28
	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)
β	0.31	0.92	0.93	0.96	0.92	0.95	0.72	0.95	0.96	0.46
	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)****	(0.00)***	(0.00)****
ω	0.00	0.00	0.00	0.00	0.01	0.00	0.35	0.00	0.00	0.03
	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)
Pre-GFC period: January 2004–December 2007
µ	0.99	0.38	0.94	0.87	0.31	−0.96	0.90	0.25	0.61	0.07
	(0.00)***	(0.01)**	(0.00)***	(0.00)***	(0.11)	(0.00)***	(0.00)***	(0.47)	(0.34)	(0.52)
φ	−0.94	−0.53	−0.96	−0.90	−0.45	0.97	−0.92	−0.33	−0.63	−0.34
	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.01)**	(0.00)***	(0.00)***	(0.329)	(0.30)	(0.00)
α	0.34	0.05	0.12	0.12	0.04	0.16	0.08	0.16	0.01	0.23
	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)
β	0.72	0.84	0.19	0.48	0.93	0.40	0.62	0.19	0.97	0.34
	(0.00)***	(0.00)***	(0.08)*	(0.00)***	(0.00)	(0.00)***	(0.00)***	(0.09)*	(0.00)**	(0.00)**
ω	0.00	0.00	0.05	0.12	0.08	0.06	0.54	0.81	0.00	0.04
	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.23)	(0.00)
GFC period: January 2008–December 2010
µ	0.98	−.002	−0.45	0.70	0.31	−0.78	0.33	−0.57	0.98	0.32
	(0.00)***	(0.94)	(0.09)*	(0.00)***	(0.40)	(0.00)***	(0.21)	(0.14)	(0.00)***	(0.01)**
φ	−0.97	−0.09	0.34	−0.76	−0.40	0.69	−0.46	0.62	−0.97	−0.54
	(0.00)***	(0.76)	(0.22)	(0.00)***	(0.27)	(0.00)***	(0.05)**	(0.09)*	(0.00)***	(0.00)***
α	0.05	0.03	0.07	0.03	0.15	0.04	0.08	0.09	0.05	0.34
	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)
β	0.80	0.96	0.92	0.96	0.82	0.94	0.82	0.88	0.80	0.55
	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***
ω	0.00	0.00	0.00	0.00	0.04	0.00	0.19	0.03	0.00	0.02
	(0.02)	(0.50)	(0.02)	(0.64)	(0.00)	(0.20)	(0.00)	(0.00)	(0.01)	(0.00)
Post-GFC period: January 2011–October 2014
µ	0.98	−0.15	0.07	−0.97	0.75	0.94	0.37	−0.70	0.54	−0.08
	(0.00)***	(0.56)	(0.80)	(0.00)***	(0.00)***	(0.00)***	(0.62)	(0.00)***	(0.63)	(0.73)
φ	−0.92	0.03	−0.17	0.96	−0.83	−0.94	−0.41	0.64	−0.52	−0.04
	(0.00)***	(0.90)	(0.54)	(0.00)***	(0.00)***	(0.00)***	(0.58)	(0.00)***	(0.65)	(0.87)
α	0.11	0.06	0.12	0.10	0.09	0.05	0.07	0.14	0.03	0.33
	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.04)	(0.00)	(0.00)	(0.00)	(0.00)
β	0.89	0.88	−0.00	0.66	0.87	−0.11	0.82	0.56	0.94	0.10
	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.76)	(0.00)***	(0.00)***	(0.00)***	(0.11)
ω	0.00	0.00	0.03	0.06	0.03	0.36	0.16	0.13	0.00	0.06
	(0.00)	(0.021)	(0.00)	(0.00)	(0.01)	(0.00)	(0.00)	(0.00)	(0.06)	(0.00)

Notes: This table presents the estimation results of an ARMA-GARCH (1, 1) model for four water indices, four water markets and two water funds returns and volatility in different (full, pre-GFC, GFC, and post-GFC) periods. p-values are given in brackets.

*Represent significance at the 10% level.

**Represent significance at the 5% level.

***Represent significance at the 1% level.

Model: At the end of each day, we run the following model using daily stock returns in different (full, pre-GFC, GFC, and post-GFC) periods:

$\sigma (L)(y_t-\mu )=\sigma (L){\mathrm{\xi }}_t$

${\sigma }_t^2=\omega +\sum _{i=1}^p{\alpha }_i{\sigma }_{t-1}^2+\sum _{j=1}^q{\beta }_j{\rho }_{t-j}^2+{\mathrm{\xi }}_t$

where $\sigma (L)$ is lag polynomials, and ${\mathrm{\xi }}_t=Z_t{\rho }_t$. Importantly, ${\alpha }_i,\dots ,{\alpha }_p,{\beta }_i,\dots ,{\beta }_p$ are constant coefficients. A fact that should be mindful when modeling conditional variances is that $\omega$, ${\alpha }_i$ and ${\beta }_j$ are non-negative.

Table 5. EGARCH (1, 1) model

	WOWAX	S-Net	S&P	MSCI ACWI	Asia	Europe	Latin America	US	Pictet	KBC Eco
Full period: January 2004–October 2014
	0.07	−0.12	−0.16	−0.00	−0.12	−0.07	0.04	−0.10	−0.00	−0.49
w	(0.00)	(0.00)	(0.00)	(0.08)	(0.00)	(0.00)	(0.00)	(0.00)	(0.01)	(0.00)
β	1.00	0.98	0.98	0.99	0.17	0.99	0.94	0.99	0.99	0.74
	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***
γ	0.27	−0.01	−0.00	0.07	−0.01	0.00	0.10	−0.00	0.06	0.52
	(0.00)***	(0.07)*	(0.00)***	(0.35)	(0.07)*	(0.74)	(0.00)***	(0.73)	(0.00)***	(0.00)***
	0.11	0.11	0.15	0.00	0.17	0.10	−0.05	0.13	0.00	−0.03
α	(0.00)***	(0.00)***	(0.00)***	(0.94)	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.18)	(0.00)***
Pre-GFC period: January 2004–December 2007
w	−0.11	−0.04	−1.05	−0.47	0.03	−3.79	0.16	0.11	−2.78	−1.16
	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)
β	1.00	0.03	0.25	0.60	0.97	−0.98	0.74	0.55	−0.72	0.49
	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***
γ	1.50	−0.02	−0.07	0.31	0.08	0.02	0.21	0.32	−0.04	0.60
	(0.00) ***	(0.02)**	(0.02)**	(0.00)***	(0.00)***	(0.00)***	(0.001)***	(0.00)*	(0.33)	(0.00)***
α	1.68	0.99	0.65	−0.00	0.04	−0.02	−0.04	0.08	−0.03	−0.06
	(0.00)***	(0.01)***	(0.00)***	(0.98)	(0.00)***	(0.00)***	(0.18)	(0.00)***	(0.21)	(0.05)**
GFC period: January 2008–December 2010
w	−14.44	0.00	−0.00	0.00	0.02	0.00	0.00	0.01	−0.95	−0.16
	(0.00)	(0.46)	(0.47)	(0.18)	(0.00)	(0.38)	(0.03)	(0.00)	(0.00)	(0.00)
β	−0.84	1.00	0.98	1.00	0.96	0.99	0.98	0.98	−094	0.57
	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***
γ	−0.07	0.07	0.12	0.06	0.30	0.06	0.03	0.18	−0.00	0.83
	(0.09)*	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.44)	(0.00) ***
α	−0.00	−0.00	−0.09	0.03	−0.01	−0.06	−0.07	−0.07	−0.06	−0.25
	(0.91)	(0.91)	(0.00)***	(0.00)***	(0.50)	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***
Post-GFC period: January 2008–October 2014
w	−0.11	−5.94	−3.10	−0.26	−0.04	−1.96	0.02	−0.16	−3.22	−1.58
	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)
β	1.00	−0.93	0.02	0.79	0.09	−0.83	0.94	0.79	−0.97	0.58
	(0.00)***	(0.00)***	(0.93)	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***
γ	−0.89	0.05	0.25	0.19	0.03	0.04	0.03	0.28	−0.01	−0.08
	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.01)***	(0.16)	(0.00)***	(0.00)***	(0.38)	(0.00)***
α	1.05	−0.04	0.03	0.03	0.97	0.01	−0.09	−0.01	0.00	0.49
	(0.00)***	(0.00)***	(0.43)	(0.17)	(0.00)***	(0.64)	(0.00)***	(0.70)	(0.57)	(0.00)***

Notes: This table presents the estimation results of an asymmetric EGARCH (1, 1) model for four water indices, four water markets, and two water funds leverage in different (full, pre-GFC, GFC, and post-GFC) periods.

*Represent significance at the 10% level.

**Represent significance at the 5% level.

***Represent significance at the 1% level.

Model: At the end of each day, we run the following model using daily stock returns in different (full, pre-GFC, GFC, and post-GFC) periods:

$log({\sigma }_t^2)=w+\beta log({\sigma }_{t-1}^2)+\gamma \frac{{\epsilon }_{t-1}}{\sqrt{{\sigma }_{t-1}^2}}+\alpha \left(\frac{\left|{\epsilon }_{t-1}\right|}{\sqrt{{\sigma }_{t-1}^2}}-\sqrt{\frac{2}{\pi }}\right)$

where the asymmetric positive and negative shocks ${(\epsilon }_{t-1})$on conditional variance and $\frac{{\epsilon }_{t-1}}{\sqrt{{\sigma }_t^2-1}}\sim N,(0,1)$ are captured in the parameter$\gamma$. The negative coefficient of γ indicates that volatility rises more than the positive coefficient $\gamma$. The parameter $\gamma$ (a negative sign) ensures that bad news generates more volatility than good news. The coefficient of α captures the assembling effects of the volatility.

Figure 3. Estimated volatility of EGARCH (1, 1) model during GFC period.

Notes: This figure presents the estimated volatility of daily returns of the four water indices, four water markets, and two water funds which reveals more information regarding the volatility during GFC periods. Source: Thomson Reuters DataStream database.

Table

Manager	Fund	Launch date	Description
Pictet AM	Pictet Water Fund	2000	Luxembourg-based global managed fund
	Nomura Water Fund	2004	Mirror of Pictet Luxembourg fund
	Criterion Water Inf. Fund	2007	Mirror of Pictet Luxembourg fund
SAM	Sustainable Water Fund	2001	Global managed fund
	Nikko Global Water Fund	2007	Mirror of SAM Sustainable Water Fund
Power Shares	Water Portfolio	2005	Tracks Palisades US water index
	Global Water Portfolio	2007	Tracks Palisades Global water index
KBC AM	Eco Water Fund	2000	Korean mirror fund
	Samsung Global Water Fund	2007	US-based global hedge fund
Summit Global	Summit Master Water Equity Fund	1999	US-based global hedge fund
Credit Suisse	PL100 World Water Trust	2007	Australian investment trust
Aqua Terra AM	Praetor Water Fund	2005	Euro-denominated managed fund
	Kinetics Water Inf. Fund	2007	US-denominated debt and equity fund
	Claymore Global Water UIT	2005	Investment trust with fixed global portfolio
	Claymore US Water UIT	2005	Investment trust with fixed US portfolio
Water AM	The Reservoir Fund	2006	US-based global hedge fund
Terrapin AM	Water Fund	2005	US-based global hedge fund
S&P Indices	Guggenheim S&P Global Water Fund	2007	US fund tracking S&P Water Index
	KDB S&P Global Water Fund	2007	Korean fund tracking S&P Water Index
	iShares Global Water Fund	2007	UK fund tracking S&P Water Index
	ABN AMRO Water Certificate	2005	Unit trust with 10 stocks selected by S&P
Wessex AM	Wessex Global Water Fund	2007	UK-based managed fund
MFS Aqua Man.	MFS Water Fund (Australia)	2007	Australian managed fund

Table

	WOWAX	S-Net	S&P	MSCI ACWI	Asia	Europe	Latin America	US	Pictet	KBC Eco
Full period: January 2004–October 2014
w	0.07	−0.12	−0.16	−0.00	−0.12	−0.07	0.04	−0.10	−0.00	−0.49
	(0.00)	(0.00)	(0.00)	(0.08)	(0.00)	(0.00)	(0.00)	(0.00)	(0.01)	(0.00)
β	1.00	0.98	0.98	0.99	0.17	0.99	0.94	0.99	0.99	0.74
	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)	(0.00)***	(0.00)***	(0.00)***	(0.00)***
	0.27	−0.01	−0.00	0.07	−0.01	0.00	0.10	−0.00	0.06	0.52
	(0.00)***	(0.07)*	(0.00)***	(0.35)	(0.07)*	(0.74)	(0.00)***	(0.73)	(0.00)***	(0.00)***
γ	0.11	0.11	0.15	0.00	0.17	0.10	−0.05	0.13	0.00	−0.03
	(0.00)***	(0.00)***	(0.00)***	(0.94)	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.18)	(0.00)***
Pre-GFC period: January 2004–December 2007
w	−0.11	−0.04	−1.05	−0.47	0.03	−3.79	0.16	0.11	−2.78	−1.16
	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)
β	1.00	0.03	0.25	0.60	0.97	−0.98	0.74	0.55	−0.72	0.49
	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***
γ	1.50	−0.02	−0.07	0.31	0.08	0.02	0.21	0.32	−0.04	0.60
	(0.00) ***	(0.02)**	(0.02)**	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.33)	(0.00)***
α	1.68	0.99	0.65	−0.00	0.04	−0.02	−0.04	0.08	−0.03	−0.06
	(0.00)***	(0.01)***	(0.00)***	(0.98)	(0.00)****	(0.00)***	(0.18)	(0.00)***	(0.21)	(0.05)**
GFC period: January 2008-December 2010
w	−14.44	0.00	−0.00	0.00	0.02	0.00	0.00	0.01	−0.95	−0.16
	(0.00)	(0.46)	(0.47)	(0.18)	(0.00)	(0.38)	(0.03)	(0.00)	(0.00)	(0.00)
β	−0.84	1.00	0.98	1.00	0.96	0.99	0.98	0.98	−094	0.57
	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***
γ	−0.07	0.07	0.12	0.06	0.30	0.06	0.03	0.18	−0.00	0.83
	(0.09)*	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)**	(0.00)***	(0.44)	(0.00) ***
α	−0.00	−0.00	−0.09	0.03	−0.01	−0.06	−0.07	−0.07	−0.06	−0.25
	(0.91)	(0.91)	(0.00)***	(0.00)***	(0.50)	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***
Post-GFC period: January 2008–October 2014
w	−0.11	−5.94	−3.10	−0.26	−0.04	−1.96	0.02	−0.16	−3.22	−1.58
	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)
β	1.00	−0.93	0.02	0.79	0.09	−0.83	0.94	0.79	−0.97	0.58
	(0.00)***	(0.00)***	(0.93)	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.00)***
γ	−0.89	0.05	0.25	0.19	0.03	0.04	0.03	0.28	−0.01	−0.08
	(0.00)***	(0.00)***	(0.00)***	(0.00)***	(0.01)**	(0.16)	(0.00)***	(0.00)***	(0.38)	(0.00)***
α	1.05	−0.04	0.03	0.03	0.97	0.01	−0.09	−0.01	0.00	0.49
	(0.00)***	(0.00)****	(0.43)	(0.17)	(0.00)	(0.64)	(0.00)***	(0.70)	(0.57)	(0.00)***