The Economics of the Greenium: How Much is the World Willing to Pay to Save the Earth?

Abstract

Sadly, not much. This paper provides a theoretical and empirical analysis of the greenium, the price premium the investor pays for green bonds over conventional bonds. We explain in simple economic terms why the price premium of a green bond essentially represents a combination of the non-pecuniary environmental benefit of the bond, as perceived by the investor, and the effective cost of issuing it, as measured by the additional issuing costs of the bond netted off a range of monetary and non-monetary benefits associated with the issuance. Our empirical model decomposes the greenium into a time-varying market component which is common to all green bonds and an idiosyncratic component which is specific to a certain green bond itself. Using the largest global green bond dataset compared to any previous studies, we find that the greenium on average amounts to, sadly, just over one basis point. However, it varies quite significantly among individual green bonds and our result suggests that a key factor underlying the variation is that they are subject to the risk of greenwashing to different extents.

Appendices

Appendix 1: Construction Methodology of our Green Bond Database

After collecting the raw data, we consolidate them based on the International Securities Identification Numbers (ISIN) of each green bond. This apparently straight forward task is actually formidable because the green bond information, such as the issue date, issuer name, credit rating, and issuer industry, can be missing and inconsistent among the three data sources. Therefore, we resort to a proprietary data massage algorithm, which validates the bond information, fills in missing values, standardizes values in different attributes, performs resolution strategies for inconsistent records among the three data sources, and removes duplicative records. Manual inspection is also performed on some subtle cases which cannot be rectified by the machine. Green bonds without ISIN are dropped to ensure no duplication.

Our green bond database has 6031 bonds with a total face value of USD767 billion, covering over 50 economies.³⁰ These numbers are much greater than those of Zerbib (2019). The database in his study has 1065 bonds with a total face value of USD 72 billion.

Appendix 2: Inseparable Individual and Time Fixed Effects in a Two-Way Fixed Effects Model

Consider the following two-way fixed effects model with both entity fixed effects and time fixed effects:

$$Y_{it} = \alpha_{i} + \beta_{t} + \gamma X_{it} + u_{it} ,\quad i = 1,2, \ldots ,N,\quad t = 1,2, \ldots ,T$$

(12)

where $\alpha_{i}$ and $\beta_{t}$ denote the individual and time fixed effects respectively.

From (12), we can derive the following three mean equations:

$$\overline{Y}_{i.} = \alpha_{i} + \overline{\beta } + \gamma \overline{X}_{i.} + \overline{u}_{i.}$$

(13)

$$\overline{Y}_{.t} = \overline{\alpha } + \beta_{t} + \gamma \overline{X}_{.t} + \overline{u}_{.t}$$

(14)

$$\overline{Y} = \overline{\alpha } + \overline{\beta } + \gamma \overline{X} + \overline{u}$$

(15)

where

$$\overline{Y}_{i.} = \frac{1}{T}\mathop \sum \limits_{t = 1}^{T} Y_{it} ,\quad \overline{Y}_{.t} = \frac{1}{n}\mathop \sum \limits_{i = 1}^{N} Y_{it} ,\quad \overline{Y} = \frac{1}{nT}\mathop \sum \limits_{t = 1}^{T} \mathop \sum \limits_{i = 1}^{N} Y_{it}$$

$$\overline{X}_{i.} = \frac{1}{T}\mathop \sum \limits_{t = 1}^{T} X_{it} ,\quad \overline{X}_{.t} = \frac{1}{n}\mathop \sum \limits_{i = 1}^{N} X_{it} ,\quad \overline{X} = \frac{1}{nT}\mathop \sum \limits_{t = 1}^{T} \mathop \sum \limits_{i = 1}^{N} X_{it}$$

$$\overline{u}_{i.} = \frac{1}{T}\mathop \sum \limits_{t = 1}^{T} u_{it} ,\quad \overline{u}_{.t} = \frac{1}{n}\mathop \sum \limits_{i = 1}^{N} u_{it} ,\quad \overline{u} = \frac{1}{nT}\mathop \sum \limits_{t = 1}^{T} \mathop \sum \limits_{i = 1}^{N} u_{it}$$

With $\hat{\gamma }$, we can derive the following three estimators:

• 1. $\overline{\alpha } + \overline{\beta } = \overline{Y} - \hat{\gamma }\overline{X}$ derived from (15)

• 2. $\widehat{{\alpha_{i} }} + \overline{\beta } = \left( {\widehat{{\alpha_{i} }} - \overline{\alpha }} \right) + \left( {\overline{\alpha } + \overline{\beta }} \right) = \overline{Y}_{i.} - \hat{\gamma }\overline{X}_{i.}$ derived from (13)

• 3. $\overline{\alpha } + \widehat{{\beta_{t} }} = \left( {\widehat{{\beta_{t} }} - \overline{\beta }} \right) + \left( {\overline{\alpha } + \overline{\beta }} \right) = \overline{Y}_{.t} - \hat{\gamma }\overline{X}_{.t}$ derived from (14)

Practically, there is no way to tease out $\overline{\alpha }$ and $\overline{\beta }$ individually, so we cannot estimate $\alpha_{i}$ and $\beta_{t}$, i.e. the individual fixed effects cannot be separately identified from the time effects, and vice versa (Hansen 2019).

Appendix 3: Average Liquidity and Volatility Premium Differentials Over Time

Figures 7 and 8 plot the average liquidity premium differential $(\hat{\gamma }\overline{{\Delta L}}_{t} )$ and the average volatility premium differential $(\hat{\varphi }\overline{{\Delta \sigma }}_{t} )$ over time respectively. $\overline{\Delta L}_{t}$ and $\overline{\Delta \sigma }_{t}$ are calculated as $\left( {\mathop \sum \nolimits_{i}^{{n_{t} }} \Delta L_{i, t} } \right)/n_{t}$ and $\left( {\mathop \sum \nolimits_{i}^{{n_{t} }} \Delta \sigma_{i, t} } \right)/n_{t}$ respectively, with $n_{t}$ equals to the available number of observations at time t.

Fig. 7

Time series plot of the average liquidity premium differential $(\hat{\gamma }\overline{\Delta L}_{t} )$

Fig. 8

Time series plot of the average volatility premium differential $(\hat{\varphi }\overline{\Delta \sigma }_{t} )$

As can been seen, $\hat{\gamma }\overline{{\Delta L}}_{t}$ has decreased in recent years, which means that green bonds have become more liquid compared to their conventional counterparts. This is consistent with the fact that green bond liquidity has improved due to growing average deal size, rising proportion of green bonds listed on exchanges, and increasing green bond exchange-traded funds (Meng et al. 2017; Filkova et al. 2019). Regarding $\hat{\varphi }\overline{{\Delta \sigma }}_{t}$, it fluctuates around zero and no obvious trend is observed. Both $\hat{\gamma }\overline{{\Delta L}}_{t}$ and $\hat{\varphi }\overline{{\Delta \sigma }}_{t}$ are very small in magnitude, implying that they play a negligible role in determining the yield spreads between green bond and conventional bond.

Appendix 4: Regression results for robustness check

	Dependent variable:$\Delta \tilde{y}_{i,t}$
	Pooled OLS (1)	Pooled OLS (2)	Pooled OLS (3)	Two-way FE (4)	Two-way FE (5)	Two-way FE (6)
$\Delta L_{i, t}$	0.092*** (0.005)		0.091*** (0.005)	0.111*** (0.005)		0.111*** (0.005)
$\Delta \sigma_{i, t}$		0.007*** (0.001)	0.006*** (0.001)		0.002*** (0.0004)	0.002*** (0.0004)
Constant	− 1.703*** (0.039)	− 1.695*** (0.039)	− 1.724*** (0.039)
Obs	78,304	78,304	78,304	78,304	78,304	78,304
R2	0.005	0.002	0.006	0.007	0.003	0.007
F Statistics	378.863*** (df = 1; 78,302)	124.675*** (df = 1; 78,302)	246.279*** (df = 2; 78,301)	533.973*** (df = 1; 76,669)	22.603*** (df = 1; 76,669)	278.882*** (df = 2; 76,668)

1. ***Statistical significance at 1%

Appendix 5: Replication of Zerbib (2019)’s Individual Fixed Effects Model

In order to do compare our estimates with those of Zerbib (2019), we re-estimate his individual fixed effects model with our data:

$$\Delta \tilde{y}_{i,t} = \alpha_{i} + \gamma\Delta L_{i, t} + \varepsilon_{i, t}$$

Table

Table 6 Descriptive statistics of the variables in the sample for replicating Zerbib’s empirical results (July 2013 to December 2017)

6 shows the descriptive statistics of the data available from July 2013 to December 2017, which is the sampling period used by Zerbib. In total, there are 134 GB–CB triplets and 37,675 observations in the sample, as compared with Zerbib’s 110 triplets and 37,504 observations.

Table

Table 7 Results of the individual fixed effects regression

7 summarizes the results of the individual fixed effects model. The coefficient of $\Delta L_{i, t}$ $(\gamma )$ is estimated at 0.174, which suggests that a one basis-point widening in the liquidity differential $(\Delta L_{i, t} )$ will lead to an increase of 0.174 basis points in the yield spread ${(\Delta }\tilde{y}_{i,t} {)}$. As mentioned, we believe our estimation is more intuitive as a higher $\Delta L_{i, t}$ (green bond being less liquid) should lead to an increase, instead of a decrease (suggested by Zerbib’s results), in the yield spread between green bond and conventional bond ${(\Delta }\tilde{y}_{i,t} {)}$.

Figure 

Fig. 9

Distribution of the idiosyncratic greeniums $(\hat{\alpha }_{i} )$ using Zerbib’s model

9 shows the distribution of the idiosyncratic greeniums $(\hat{\alpha }_{i} )$ estimated. The mean and median are − 1.7 and − 0.4 basis points respectively, which is very close to the estimates of Zerbib (− 1.8 and − 1.0 basis points).

Appendix 6: Robustness Check on the Impact of the Triplet Impurity

The Achilles heel of adopting a GB–CB triplet matching approach to estimating the yield spread between a green bond and its synthetic conventional counterpart is the potential errors caused by the impure matches of the bonds. Since it is almost impossible to find conventional bonds having identical features as the green bond, the GB–CB triplets are often impure, which may result in estimation errors in the yields of the synthetic conventional bonds $(\tilde{y}_{i,t}^{CB} )$. Given that the two matched conventional bonds do not share the same maturity date as the green bond, $\tilde{y}_{i,t}^{CB}$ may be over- or under-estimated by linearly interpolating or extrapolating the yields of the conventional bonds, as the curvature of the yield curve is not taken account. Different issue dates can also contaminate the estimation of $\tilde{y}_{i,t}^{CB}$. For example, bonds issued in different interest rate cycles, despite having similar remaining maturities, can arguably have very different coupon rates and sharply different degrees of convexity.

A simple solution to the problem is to remove the GB–CB triplets of higher impurity from our sample. However, doing so will inevitably reduce the sample size, as well as the variety of green bonds. For instance, if half of the GB–CB triplets are removed from our sample, green bonds from a number of countries and sectors will be completely excluded, rendering potentially a huge loss in important information. Hence, there is a trade-off between triplet purity and sample size. In view of this, we conduct a robustness check to examine the extent to which the inclusion of impure triplets distorts the estimates of the greenium.

First, we introduce two major impurity measures based on the maturity date (MD) and the issue date (ID) differences for each GB–CB triplet.For the former, the impurity is measured by the sum of the absolute values of the maturity date difference between the green bond and each of the two conventional bonds.³¹ The impurity arising from different issue dates is measured the same way.

$$Impurity_{i}^{MD} = \left| {MD_{i}^{GB} - MD_{i}^{CB1} } \right| + \left| {MD_{i}^{GB} - MD_{i}^{CB2} } \right|$$

$$Impurity_{i}^{ID} = \left| {ID_{i}^{GB} - ID_{i}^{CB1} } \right| + \left| {ID_{i}^{GB} - ID_{i}^{CB2} } \right|$$

With these measures, we rank the 267 GB–CB triplets by their impurity from the highest to the lowest and remove them one by one, starting with the most impure triplet, and we stop when there are only 10 triplets left. Each time when a triplet is removed, we re-estimate the augmented idiosyncratic greeniums $(\tilde{\alpha }_{i} )$ with our fixed effects model. Figures 

Fig. 10

Trajectories of the augmented idiosyncratic greeniums $(\widehat{{\tilde{\alpha }_{i} }})$ with the GB–CB triplets of the highest $Impurity_{i}^{MD}$ removed one by one

10,

Fig. 11

Trajectories of the augmented idiosyncratic greeniums $(\widehat{{\tilde{\alpha }_{i} }})$ with the GB–CB triplets of the highest $Impurity_{i}^{ID}$ removed one by one

11, and

Fig. 12

Trajectories of the augmented idiosyncratic greeniums $(\widehat{{\tilde{\alpha }_{i} }})$ with the GB–CB triplets of the highest average impurity removed one by one

12 show the trajectories of the mean, median, maximum, and minimum values of $\widehat{{\tilde{\alpha }_{i} }}$ estimated by the aforementioned approach, with the impurity of the triplets measured by $Impurity_{i}^{MD}$, $Impurity_{i}^{ID}$, and the average impurity respectively.³² As can been seen, the mean and median of $\widehat{{\tilde{\alpha }_{i} }}$ are very stable and close to zero. This suggests that our key finding of a negligible greenium on average is robust regardless of the degree of impurity of the sample.³³ However, the absolute values of the maximum and minimum $\widehat{{\tilde{\alpha }_{i} }}$ decrease substantially when impure triplets are removed, i.e., the distribution of $\widehat{{\tilde{\alpha }_{i} }}$ become more concentrated around zero. This indicates that the outliers in the distribution of $\widehat{{\tilde{\alpha }_{i} }}$ are possibly due to the inclusion of the impure GB–CB triplets.³⁴