Section 4: Data, empirical results and robustness checks
4.3 Robustness checks
In order to account for some of the shortcomings of the methodology (Section 3.2.3) performed thus far, as well as testing the sensitivity of the model to key variable changes, I perform three robustness checks. The first (4.3.1) implies shortening the length of the fiscal period under consideration, from 2003-2020 to 2010-2019. There are two reasons for doing this. Firstly, Table 5 showed that, prior to 2010, both ‘green’ and ‘brown’ portfolios contained fewer than twenty stocks, in fact less than ten prior to 2006. This is largely insufficient for the portfolios to be considered well-diversified, increasing the idiosyncratic bias incorporated by the ‘green’ factor (and, consequently, the premium). Secondly, in the extended timeframe, the financial crisis of 2007-2008 (stretching until 2009, when the S&P 500 reached the crisis’
low, at $676) may have impacted the ‘green’ factor’s average, due to the abnormally negative returns and high volatility. The year 2020 also constitutes an anomaly due to the beginning of the Covid-19 pandemic which, at least in its early months, shattered financial markets. The restricted timeframe therefore omits 2020. The second robustness check that I carry out (4.3.2) is the inclusion of an additional sorting variable, firm size (measured by market
capitalisation), to account for it in the construction of the ‘green’ and ‘brown’ portfolios.
Specifically, by sorting stocks of similar size by ‘greenness’, the size component should not contribute (as much) to observed performance differences between ‘green’ and ‘brown’
portfolios, allowing us to interpret the ‘green’ premium estimated in relation to the initial hypothesis. The third and final robustness check of my analysis (4.3.3) involves changing the relative weighting (𝛾) of the variables constituting the synthetic ‘greenness’ indicator. This way we can observe how the ‘green’ premium changes in relation to the relative weightings attributed to ‘GHG emission intensity’ and ‘E-score’.
Ø 4.3.1 Restricting the timeframe (2010-2019)
Shortening the length of the panel involves a compromise between lower stock return volatility (resulting from the exclusion of the ‘Great Recession’ and pandemic start) and fewer observations. However, since these diminishing quantities respectively make up the numerator and denominator of the risk factors’ standard errors27, we shouldn’t observe drastic changes in accuracy. On the contrary, we expect the factor averages to be more representative of their true expected values. More specifically, we expect the ‘green’ factor to incorporate less ‘idiosyncratic’ biases tied to limited diversification, and hence be more representative of performance differences associated with ‘greenness’. Provided that our expectations on standard errors are met, this is a worthwhile compromise.
Table 9 (next page) reports descriptive statistics for the risk factors (a) in fiscal period 2010-2019, along with the respective ‘green’ cross-sectional parameters and premia (b) obtained for the three linear factor models adopted thus far. We see that the average ‘green’ factor is 0.559% and not significant, while the ‘green’ premia are positive (0.602%, 1.513%, 0.985%) and not significant in all three specifications. Also, 𝜐𝑮 is now only significant in one model.
This is in stark contrast with the previous replication (Table 3 and Table 7), where the ‘green’
factor and premia were found to be negative and significant at the 1% level in all specifications.
27 𝑆𝑡𝑑. 𝑒𝑟𝑟𝑜𝑟 = =
√9 .
Table 9: (a) Average US risk factors (𝐸#𝑓",$$ or, equivalently, 𝑓%%%%",$) plus ‘green’ factor (𝑓𝑮), and (b) ‘green’ cross-sectional parameters (𝜐𝑮) plus resultant ‘green’ premia for distinct factor model specifications, for fiscal years 2010-2019. All quantities are reported in annualized % terms. Recall, from Eq.5., that the risk premium is the sum
of 𝐸#𝑓",$$ and 𝜐$, and note that the former (computed as a simple average) is independent of the choice of factor
model. Hence, unlike Table 7, the average risk factors are reported only once, in a), for simplicity. Also, b) only displays the ‘green’ cross-sectional parameters and premia, since these are the focus of the analysis. All risk factors, except for 𝑓𝑮 (constructed using the methodology in Sections 3.2.2-3), were downloaded in monthly terms from Kenneth French’s data library (2022). 𝜐𝑮 was obtained via the usual two-pass procedure described in Section 3.2.4. The only change, with respect to the initial replication, is the restriction of the timeframe. The annualization was obtained via simple multiplication by 12, while the annualization of monthly standard deviations required multiplication by √12. Standard errors of the resultant premia (not shown, but implicit to the obtainment of the t-statistics) have been calculated using the equation for the standard error of a sum shown previously in Table 7’s legend. All t-statistics are for a null hypothesis of zero. The asterisks *** indicate statistical significance at the 1% level.
a)
b)
We also note that, in line with expectations, the reduction in statistical significance is not driven by substantial increases in the standard errors. This appears to be a further indication that, by excluding years of low data availability (hence smaller portfolios), the ‘green’ factor and premia are now less prone to idiosyncratic bias. These firm and industry specific risks, perhaps exacerbated by periods of high volatility, appear to have had a substantial impact on the results obtained in Section 4.2, since both a change in the sign and significance of the
‘green’ premia are observed upon restricting the timeframe.
Unfortunately, this supposed reduction in idiosyncratic bias does not come hand in hand with a reduction in ‘systematic’ bias. Analogous tests to those performed in 4.2.1 and 4.2.2 show similar size differences in portfolio constituents’ (recall Table 4), with ‘green’ firms tending to be larger on average than ‘brown’ firms. Consequently, a similar negative dependence of the
‘green’ factor on SMB is found for 2010-2019 (in fact slightly larger, 𝛽31$ = −0.409 compared with −0.338 in Table 8). We had pointed out that such dependence likely
contributed to the negative ‘green’ premium observed in the initial replication, for which 𝐸[𝑓31$,#] was 1.415% and significant at the 1% level (Table 3). Since the dependence persists in the restricted timeframe, yet 𝐸[𝑓31$,#] ceases to be significant, it comes natural to question the extent to which changes in the significance of the ‘green’ premia are in fact a consequence of this. May we indeed interpret the estimates in Table 9b, in relation to earlier estimates in Table 7, as evidence that the premia ‘vanish’ once idiosyncratic biases are addressed? If so, this could in turn be seen as evidence that ‘climate’ risk is not being priced by the US market.
In the next section, I seek to answer this question by reducing the dependence of ‘greenness’
on SMB. This way, we can test whether the ‘green’ premia remain insignificant irrespective of the size factor, allowing us to interpret them in relation to the hypothesis (Section 3.1).
Ø 4.3.2 Bivariate portfolio sorting: ‘greenness’ conditional on firm size (2010-2019) After restricting the timeframe of the analysis, the next robustness check involved a change in the portfolio sorting methodology, to account for the relationship between 𝑓!, as initially determined using the methodology in 3.2.2-3, and 𝑓31$. The intention of this was to focus on the systematic excess returns associated with ‘greenness’ alone, as an independent distinguishing characteristic (supposedly) embodying an asset’s exposure to climate transition risk.
The portfolio sorts were performed dependently; for each year, firms were first sorted into size (market capitalisation) terciles, each of which was then sorted into quintiles by
‘greenness’. In other words, ‘greenness’ quantiles were determined conditional on firm size.
This ensured that ‘greenness’ was scaled on size, i.e. that ‘greenness’ breakpoints were not common across size terciles. This arrangement also increased portfolio sizes (hence further reducing the impact of undiversified idiosyncratic risk), since each ended up containing 13%
(-98) of the total number of firms in the cross-section, higher than the 10% for univariate replications (4.2 and 4.3.1). After sorting was complete, the following formula was used to construct the new version of the ‘green’ factor:
Eq. 9: 𝑓!,# = 0.5N𝑟#:%; ;<==>+ 𝑟#?@ABB ;<==>O − 0.5(𝑟#:%; :<CD>+ 𝑟#?@ABB :<CD>)
Eq.9 is equivalent to the ‘EMI3’ portfolio constructed by In et al. (2019), which itself follows closely from Fama & French’s (1993) own construction of the SMB and HML factors. This formulation seeks to capture only the excess returns associated with stocks being ‘greener’, since comparisons are made after controlling for size. Those generated by significant size differences should, supposedly, ‘cancel’ by symmetry (i.e. the systematic size effect in 𝑠𝑚𝑎𝑙𝑙 𝑔𝑟𝑒𝑒𝑛− 𝑏𝑖𝑔 𝑏𝑟𝑜𝑤𝑛 cancels with that in 𝑏𝑖𝑔 𝑔𝑟𝑒𝑒𝑛− 𝑠𝑚𝑎𝑙𝑙 𝑏𝑟𝑜𝑤𝑛 ). In this replication, the ‘green’ factor therefore consists of the difference between size combinations of ‘green’ and ‘brown’ portfolios. The ‘0.5’ coefficients in Eq. 9 ensure normalisation, to allow direct comparability with the formulation adopted so far (Eq. 1). Consistently with In et al.
(2019), who find that their EMI3 portfolio is the only exception generating no significant return in the period 2006-2015, Table 10 below shows that applying bivariate sorting in the restricted timeframe yields a ‘green’ factor of only 0.169%, with a t-statistic of 0.192. These are the smallest numbers obtained so far, respectively 6.5% those obtained in Section 4.2 and 30.2% those obtained in 4.3.1. Also, the standard error obtained (0.880) is the smallest among the replications, confirming that the small t-statistic is not determined by a reduction in statistical accuracy, but indeed by the non-pricing of ‘greenness’.
Table 10: Average US ‘green’ factor, 𝐸#𝑓+,$$, in annualized % terms, constructed via bivariate sorting by
‘greenness’ conditional on size (Eq.9), for fiscal years 2010-2019. The annualization was obtained via simple multiplication by 12, while the annualization of monthly standard deviations required multiplication by √12. The t-statistic is for a null hypothesis of zero mean. Note that the established risk factors (MKT, SMB, HML, MOM) are unchanged with respect to Table 9a, because the timeframe is the same, and (having been downloaded from Kenneth French’s data library) they are unaffected by the change in the sorting methodology introduced in the current section, which only affects 𝑓+ and the cross-sectional parameters 𝜐𝑮 (see Table 12 later). Hence, only 𝑓+ is reported below. Also recall that, as already mentioned in Table 9, 𝐸#𝑓+,$$ is independent of the choice of linear factor model (CAPM, Fama French and Carhart).
Table 11 (next page) shows the output of regressing the ‘green’ factor on other risk factors.
We see that the bcoefficient of the SMB factor is 44% smaller than the respective coefficient obtained for the initial replication (Table 8), and 54% smaller than that obtained for the first robustness check (mentioned at the end of 4.3.1). Further, it is only significant at the 10%
level. In other words, the bivariate sorting does appear to succeed in reducing the association between ‘greenness’ and SMB, however imperfectly.
Table 11: Outcome b coefficients of the OLS regression involving the bivariate ‘green’ factor (as constructed using Eq.9) on established risk factors, fiscal period 2010-2019. Robust standard errors of the coefficients are shown in parenthesis. This is the same test as the one performed for the initial univariate replication in the extended timeframe (Table 8), where a -0.338 dependence on SMB was found, significant at the 1% level. When restricting the timeframe to 2010-2019, while keeping the sorting methodology untouched, this dependence slightly increased to -0.409, still significant at the 1% level. Recall that this regression seeks to test the independence of the ‘green’ factor; in other words, the extent to which ‘greenness’ is the unique systematic characteristic associated with the observed ‘green’ premium. The 120 observations correspond to the number of months in the restricted timeframe. The asterisk * indicates statistical significance at the 10% level.
Therefore, notwithstanding the reduced impact of SMB, the ‘green’ factor has remained statistically insignificant, in fact at an even lower level and magnitude. Of course, 𝑓! could be related to other factors not included in Table 1128, but these are the most renown and established in the literature. Biases due to data inaccuracy are also likely to remain, despite an attempt being made to reduce their concentration through the use of a balanced synthetic
‘greenness’ indicator (recall Section 3.2.2).
Table 12 (next page) reports the 'green’ cross-sectional parameters 𝜐! and ‘green’ premia, obtained for the respective factor models, resulting from the current replication. With regards to 𝜐𝑮, following the reasoning in Section 4.2.2, the observed positive signs could be interpreted as an indication that investors’ expectations transcend and misalign with climate risk considerations. The interpretation of the parameter remains complicated however, especially as it is negative for the ‘Carhart + G’ model, which would revert the reasonings
28 For instance ‘quality’, though the problem with non-traditional risk factors is that a variety of competing definitions exists for them, as with ‘greenness’ itself.
presented in 4.2.2. Therefore, even though for completeness I choose to report the parameters alongside the resultant premia, I choose to focus my analysis on the latter.
Table 12: ‘Green’ cross-sectional parameters and resultant ‘green’ premia obtained from bivariate portfolio sorting by ‘greenness’ conditional on size (Eq.9), for different factor models, reported in annualized % terms, for fiscal years 2010-2019. Similarly to Table 9b in the previous section, only the ‘green’ estimates have been reported, since these are the focus of the analysis. The ‘green’ premia are the result of the sum between the average ‘green’ factor reported in Table 10 and the 𝜐𝑮 (obtained via the usual two-pass procedure described in Section 3.2.4) reported below. Standard errors of the resultant premia (not shown, but implicit to the obtainment of the t-statistics) have been calculated using the equation for the standard error of a sum shown previously in Table 7’s legend. The t-statistics are for a null hypothesis of zero. The asterisks *, **, *** indicate statistical significance at the 10%, 5% and 1% levels, respectively.
Like 𝑓𝑮, the ‘green’ premium remains statistically insignificant, and is by far smaller and less significant compared to both previous replications (Table 7 and Table 9b), except for the
‘Fama-French’ model, where it is significant but only at the 10% level. However, in the latter exception, the premium and t-statistic are very similar to those obtained for the first robustness check (Table 9b), where the t-statistic only just failed to exceed the 10% critical threshold. As such, small differences in magnitude and/or standard error can make a big impact on whether the 10% level is attained. Also, the 5% threshold is all that matters with respect to the hypothesis (3.1). We can therefore disregard the economic significance of this difference and focus on the main findings. Summarising them:
1) In the first replication (Section 4.2), for 2003-2020, negative ‘green’ premia estimates were obtained for all linear factor specifications (Table 7).
2) Having restricted the timeframe of the analysis (2010-2019), to address the issue of small portfolio sizes and exclude periods of high volatility (Section 4.3.1), the new
‘green’ premia estimates turned out positive and insignificant for all specifications (Table 9b).
3) Having now, in the current section, reduced the effect of size differences between
‘green’ and ‘brown’ firms, sorting stocks (2010-2019) by ‘greenness’ conditional on market capitalization, while concurrently increasing portfolio sizes by 3 p.p., the
resultant time-invariant ‘green’ premia remain statistically insignificant at the 5% (or lower) level.
The ‘green’ factor and premia were already insignificant after step 2, but they reduce to almost zero, in both magnitude and significance, after step 3, despite a substantial reduction in the dependence of 𝑓!on 𝑓31$. Further, in two out of the three factor models tested in step 3, the ‘green’ premia are close to zero on either side (0.358% and -0.233%), confirming that the negative (though insignificant) 𝐸[𝑓31$,#] has no determinant impact on them. These results suggest that the ‘green’ premia vanish (irrespective of b 31$) when idiosyncratic bias is addressed, and even more evidently if the dependence on SMB is controlled.
Such findings support my hypothesis (Section 3.1), allowing me to confirm that, indeed, there is no significant evidence of an association between ‘greenness’ and systematic returns.
Extrapolating, this suggests that climate transition risk is not being priced by the US equity market. However, the ‘green’ factor does not appear to be completely independent of existing risk factors; even conditional sorting only partially reduces its dependence on SMB, since b 31$ remains significant at the 10% level (recall Table 11). This weak dependence is, in my view, sufficient to conclude that the reiterated insignificance of the ‘green’ factor and premia is not determined by the relation to SMB. In other words, that the determinant is indeed the non-pricing of transition risk. Nonetheless, the results could alternatively be interpreted as evidence that, in fact, ‘greenness’ is not, as an independent characteristic, a determinant of an asset’s exposure to transition risk. Extending this reasoning further, the persistent dependence of 𝑓! on 𝑓31$ could be seen as an indication that, rather, it is the size of a firm which may embody this exposure. If this were true, transition risk could indeed be priced, but within 𝑓31$ (and the resultant 𝜆31$ ). Consequently, changes in the significance of the ‘green’ premium, 𝜆! , would simply be a direct effect of changes in the significance of 𝜆31$ , and/or in the strength of the dependence of 𝑓! on 𝑓31$. From an economic perspective, this alternative interpretation could perhaps be explained by the fact that small firms are less ‘equipped’ to face policy uncertainty (as implied by the potential implementation of stricter environmental regulations), hence being more exposed to climate transition risk. While unlikely to be robust, this interpretation is discussed further in Section
5. Figure 3 below shows a graphical comparison of the ‘green’ premia and respective t-statistics obtained for the three replications performed so far, summarizing the main results.
This way it is easier to visualize the progressive impact of methodological changes on the resulting ‘green’ premia.
Figure 3: Graphical comparison of the ‘green’ premia and respective (absolute) t-statistics, obtained for the three replications performed so far (univariate 2003-2020, Section 4.2, univariate 2010-2019, Section 4.3.1, and bivariate 2010-2019, the current section), for each of the factor model specifications (CAPM+G, Fama-French 3-factor + G, Carhart + G). The latter make up the categorical ‘bins’ on the horizontal axis, while the primary axis (left) measures the ‘green’ premium (in annualised, % terms), and the secondary axis (right) measures the absolute value of the t-statistic. The horizontal red line marks the 5% statistical significance threshold, corresponding to a t-statistic of 1.96. Note that the dashed lines in between the bins are just drawn for ease of visualisation; only the points vertically above the bins retain economic meaning. Some of the colours hereby used to distinguish between the replications are preserved in the upcoming section (specifically, in Table 14 and Figure 4), so should ideally be kept in mind.
We see that, indeed, the ‘green’ premium is negative and statistically significant at the 5%
(or lower) level only when issues related to small portfolio sizes and systematic dependencies of 𝑓! on existing risk factors are unaddressed (green). When portfolios of < 20 firms are dropped, and periods of high market volatility excluded, the ‘green’ premium turns out positive and no longer significant (orange). When, in addition to this, ‘greenness’ sorts are performed conditionally on firm size (blue), the ‘green’ premium reverts to zero and is even less significant, except for the ‘Fama-French + G’ specification where its t-statistic nonetheless remains below the 5% threshold.
t=1,96
0 0,5 1 1,5 2 2,5 3 3,5
-3 -2,5 -2 -1,5 -1 -0,5 0 0,5 1 1,5 2
CAPM + G 3FF + G CAR + G
|t-statistic|
Green premium
Univariate 2003-2020 Univariate 2010-2019 Bivariate 2010-2019
|t-stat| |t-stat| |t-stat|
A final note should be made on the change from ‘greenness’ deciles to quintiles, concurrent with the robustness check performed in this section. While the change inevitably results in an average reduction of ‘greenness’ heterogeneity between quantiles, it is done to ensure that
‘green’ and ‘brown’ portfolios are sufficiently large (in fact, they are 3 p.p. larger than in the univariate replications). Maintaining deciles would have reduced each portfolio’s size (from 10%) to <7% of the total cross-section, with a consequent increase in the level of undiversified idiosyncratic risk. While recognizing that the reduction in the number of ‘greenness’ quantiles may in part concur to the observed reduction in magnitude and significance of the ‘green’
premium upon bivariate sorting (Figure 3), it is unlikely to be the determinant cause. After all, a big drop in significance was already observed in 4.3.1 (which involved no change in the portfolio sorting methodology), suggesting that the choice of percentiles should indeed not be determinant.
Ø 4.3.3 Sensitivity analysis for 𝛾: the relative weighting of ‘greenness’ determinants After shortening the timeframe of the analysis, to reduce the impact of undiversified idiosyncratic ‘noise’ on the ‘green’ premium, and after varying the sorting methodology to account for the significant size differences between ‘green’ and ‘brown’ firms, I performed a sensitivity analysis for the 𝛾 weight assigned to the inverse ranking of ‘GHG intensity’ (Ki,y ) in the construction of the synthetic ‘greenness’ indicator (Eq. 7, Section 3.2.2). Recalling Eq. 7, since the sum of constituents’ weights is one, increasing 𝛾 will on one hand increase the influence of a better ‘carbon efficiency’29 and, by symmetry, decrease the influence (1 − 𝛾) of a better environmental transparency, on the overall ‘greenness’ score. Conversely, a 𝛾 value of zero implies that all the weight is placed on environmental transparency. It is important to recall that, so far, 𝛾 was fixed at 0.5 for all replications.
The initial univariate replication (Section 4.2) and the bivariate replication (4.3.2) were, respectively, iterated for discrete values of 𝛾 between 0 and 1, based on the ‘Carhart + G’30
29 Recall that Ki,y is the inverse ranking by emission intensity, which in effect is equivalent to the ranking by
‘carbon efficiency’. In this context, ‘carbon efficiency’ is defined as the reciprocal of ‘emission intensity’, i.e.
how much output (revenues) is generated per tonne of CO2 equivalent emissions.
30 The Carhart + G model was preferred, to be used in the two-pass procedure to obtain 𝜐&, because it is the most extensive model among those applied in my research.
multi-factor model. The output ‘green’ premia, and constituents, are reported in Table 13 below.
Table 13: Sensitivity analysis for 𝛾. Recall that 𝛾 is the weight applied to the inverse rank of ‘GHG intensity’ in the construction of the ‘greenness’ indicator (Eq.7). De facto, this means that 𝛾 measures the importance attributed to ‘carbon efficiency’ (which can be seen as the reciprocal of intensity) in defining ‘greenness’. 1- 𝛾 is instead the weight applied to the rank by ‘Environmental Pillar Score’, which measures a firm’s environmental transparency.
This table reports the ‘green’ factor average 𝐸#𝑓+,$$, cross-sectional parameter 𝜐+, and total ‘green’ (G) premium, obtained by iterating each of the replications described in Sections 4.2 and 4.3.2 for discrete weights 𝛾 = {0, 0.2, 0.5, 0.8, 1}, using the ‘Carhart + G’ linear multi-factor specification. Recall, from Eq. 5, that the (time-invariant) premium estimate is obtained from the sum of 𝐸#𝑓+,$$ and 𝜐+. All values are reported in annualised, % terms. The first set of observations refers to the 2003-2020 univariate sorting replication (4.2), while the second set refers to the 2010-2019 bivariate sorting replication (4.3.2). Note that the values displayed for 𝛾 = 0.5 correspond to those reported, for the ‘Carhart + G’ model, in Table 7 and Table 12 respectively, since 𝛾 = 0.5 was used for all replications prior to the current section. Standard errors of the resultant premia (not shown, but implicit to the obtainment of the t-statistics) have been calculated using the equation for the standard error of a sum shown previously in Table 7’s legend. All t-statistics are for a null hypothesis of zero. The asterisks *, **, ***
indicate statistical significance at the 10%, 5%, and 1% levels, respectively.
The first thing to note is that, for the univariate replication, the ‘green’ premium is statistically and economically significant at the 1% level for all 𝛾, although its sign changes from negative to positive when 𝛾 > 0.5. In contrast to this, the ‘green’ premium obtained in the bivariate replication is comparatively smaller and less significant for all 𝛾 (except 0.2). This is coherent with the results obtained in Section 4.3.2, showing that differences with respect to the initial replication are robust to changes in 𝛾. Surprisingly though, the premium is significant at the 1% level in two instances, 𝛾 = {0.2, 1}, but I later show that there are underlying factors which can explain this. For the univariate replication, we see a clear positive relationship
between 𝛾 and the premium (while, for the bivariate case, a trend is less marked). Even Alessi et al. (2021, p.8) find a similar trend, though much less pronounced. The implication of this is that, when ‘greenness’ is defined more strongly in terms of carbon efficiency (i.e. increasing 𝛾), ‘green’ firms earn higher premia. This is interesting, since it suggests that only by increasing the weight of environmental transparency (i.e. decreasing 𝛾) do we obtain negative premia, which are in line with theoretical predictions. However, this trend is in fact likely to (at least partly) result from changes in the systematic characteristics of ‘green’ and ‘brown’
portfolio constituents (recall Table 4), depending on the chosen weight 𝛾. For instance, further tests show that ‘green’ constituents defined prevalently on intensity terms (i.e. 𝛾 >
0.5) are smaller31 on average than ‘green’ constituents defined prevalently on transparency terms (i.e. 𝛾 < 0.5), while there is little difference in the sizes of alternative ‘brown’
constituents. The consequence of this is that the effect of SMB on 𝑓!, discussed in Section 4.2 and 4.3, reduces with 𝛾. For the univariate replication, this results in a decreasingly negative effect of SMB on the ‘green’ premium (since 𝐸1𝑓31$,#2 is positive and significant between 2003-2020). For the bivariate replication instead, there is no significant consequence, since size differences are controlled and 𝐸1𝑓31$,#2 is also not statistically significant between 2010-2019.
By running regressions of the ‘green’ factor, constructed for different values of 𝛾 in the separate replications, on other factors (recall Table 8 and Table 11), Table 14 (next page) confirms that an increase in 𝛾 reduces the dependence on size (i.e. b31$decreases). It also shows that there are other risk factors at play when 𝛾 is allowed to vary. We note that for 𝛾 ≠ 0.5 there is always at least one factor that is statistically significant at the 1% level. For example, 𝛾 = 1 generates a ‘green’ factor that is positively dependent on the market (MKT) risk factor (b12+ = 0.558 and 0.376, respectively), whose average (𝐸1𝑓12+,#2) is itself strongly positive in both timeframes (recall Table 3 and Table 9). Unsurprisingly then, 𝛾 = 1 results in positive ‘green’ premia for both replications. Contrarily, 𝛾 = 0 generates a ‘green’ factor that, in the univariate case, is positively related to HML and negatively related to SMB (whose
31For 𝛾=1, the average market capitalisation of a ‘green’ portfolio constituent between 2003-2020 was found to be $68 billion, compared to $92 billion for 𝛾=0. More specifically, the average was calculated as the mean (2003-2020) of the yearly mean market capitalisations of ‘green’ constituents, in order to account for time-varying portfolio sizes.
averages are respectively negative, positive and significant, Table 3), while, in the bivariate case, is negatively related to ‘MKT’ and ‘MOM’ (whose averages are positive and significant, Table 9). Unsurprisingly then, 𝛾 = 0 results in negative ‘green’ premia for both replications.
These findings explain the premium’s change of sign as 𝛾 is increased. Most importantly, they are evidence that, for an unequal weighting of ‘greenness’ constituents, the estimated ‘green’
premia are strongly driven by underlying risk factors, hence incorporating large proportions of ‘systematic’ biases. It is difficult to interpret these excess returns from the perspective of climate risk, since they cannot be explained in terms of ‘greenness’ as an independent characteristic. Hence, it is not possible to interpret their significance as evidence against the hypothesis (3.1).
Table 14: Outcome b coefficients of OLS regressions involving the ‘green’ factor, as constructed in the extended univariate (Section 4.2) and restricted bivariate (Section 4.3.2) replications respectively, on established risk factors, for the set 𝛾 = {0, 0.5, 1}. Not all the values of 𝛾 used in the complete sensitivity analysis (Table 13) are reported, due to limited space. Note that the outcomes for 𝛾 = 0.5 correspond to the analogous tests performed in Section 4.2.2 (Table 8) and Section 4.3.2 (Table 11), since 𝛾 = 0.5 was used for all replications until the current section. Recall that these regressions seek to test the independence of the ‘green’ factor; in other words, the extent to which ‘greenness’ is indeed the unique systematic characteristic associated with the observed ‘green’
premium. Robust standard errors of the coefficients are shown in parenthesis. The asterisks *, **, *** indicate statistical significance at the 10%, 5%, and 1% levels, respectively.
Interestingly, for both univariate and bivariate replications, the least ‘systematic’ bias appears to occur for 𝛾 = 0.5, where only b31$is significant (respectively at the 1% and 10% levels). A balanced weighting of ‘greenness’ therefore seems to do better at limiting its dependency on established risk factors, thereby allowing us to better assess the association between
‘greenness’, as an independent characteristic, and systematic excess returns. This finding appears to confirm the importance of incorporating environmental transparency into measures of ‘greenness’ (recall Section 2 and 3.2.2), finding a right balance between firm-reported emissions and data vendors’ ESGs. Not only does this address the inaccuracies in reporting and ensures diversification in the sourcing of data, it also appears to generate a unique ‘greenness’ indicator which is least dependent on existing risk factors. The fact that the smallest premia and significance levels, among all replications, are indeed obtained for 𝛾=0.5, when the ‘green’ factor is least dependent on existing factors and, for the bivariate replication, idiosyncratic bias has also been addressed, is reinforcing evidence that an unbiased estimate of the time-invariant ‘green’ premium is not statistically significant in the S&P 500. This confirms the hypothesis (3.1), while suggesting, by implication, that climate transition risk has thus far not been priced by the US equity market.
However, the results may alternatively be interpreted as evidence that ‘greenness’ itself is not, in essence, an independent characteristic determining an asset’s exposure to climate transition risk, since even with 𝛾 = 0.5 it remains dependent on SMB. After all, we have merely supposed, but not proven, the relationship between ‘greenness’ and transition risk. In fact, we could extend such reasoning further, to hypothesise that, depending on their correlations with ‘greenness’, it may be the established risk factors that are capturing (different shades of) this exposure. This would also explain why, when the dependency of 𝑓! on other factors is minimised, the estimated ‘green’ premium is smallest and least significant.
If such an interpretation were true, climate risk could indeed be priced, but by combinations of existing risk factors. Figure 4 (next page) provides a graphical representation of the sensitivity analysis performed in this section, summarising how a more balanced weighting indeed tends to result in a smaller, less significant ‘green’ premium.
Figure 4: Graphical representation of the sensitivity analysis for 𝛾, as reported in Table 13. The primary axis (left) measures the ‘green’ premia for iterations of the ‘Carhart + G’ model in the univariate 2003-2020 (Section 4.2) and bivariate 2010-2019 (Section 4.3.2) replications respectively, for the set 𝛾={0, 0.2, 0.5, 0.8, 1} which runs on the horizontal axis. The secondary axis (right) compares the respective absolute values of the t-statistics. The horizontal red line marks the 5% statistical significance threshold, corresponding to a t-statistic of 1.96. Since 𝛾 is a continuous variable, trends can be inferred in the ‘green’ premia and t-statistics. Note that the colours used to distinguish between replications correspond to those used previously in Table 14 and Figure 3.
t=1.96
0 1 2 3 4 5 6 7 8
-8 -6 -4 -2 0 2 4 6 8 10
𝛾= 0 𝛾= 0.2 𝛾= 0.5 𝛾= 0.8 𝛾= 1
|t-statistic|
Green premium
Univariate 2003-2020 Bivariate 2010-2019
|t-stat| |t-stat|
Section 5: Discussion and Conclusions
My research sought to find evidence against the systematic pricing of climate transition risk in the United States’ equity market, in light of the ambiguous results obtained by the asset pricing literature on the existence of a ‘green’ risk premium. Coherently with the time-invariant definition by Gagliardini et al. (2016), the premium was defined as the sum between the average of its associated ‘green’ factor (𝐸1𝑓!,#2) and a cross-sectional parameter (𝜐!, accounting for market imperfections) obtained from a two-pass multi-factor regression approach. To define ‘greenness’, I used an analogous methodology to Alessi et al. (2021), whom, coherently with predictions by classical asset pricing theory, had obtained a negative
‘green’ premium for the European market. Indeed, if the risk-return paradigm holds, the prospect of tighter environmental regulations should, ceteris paribus, lead investors to expect lower compensation for holding ‘greener’ assets, due to the lower associated transition risk.
However, a key aspect arising from a review of the literature is that, individually, ESGs or firm-level emissions are unlikely to be good proxies for an asset’s exposure to such risk. There are several causes of this, from the heterogeneity in estimation methodologies, to the over-comprehensiveness of ESGs and self-reporting biases. These fallacies are reflected in the mixed research findings regarding the systematic pricing of climate risk, not just in the United States. Hence, the motivation of my research was to construct a ‘greenness’ indicator, as defined by Alessi et al. (2021), equally weighted for both firm-reported emission intensity and third-party-assessed environmental transparency (‘E-score’), to test for the existence of a
‘green’ premium in the US equity market. This balanced definition of ‘greenness’ would ideally address biases in the data, allowing me to better interpret the estimated premium from the perspective of transition risk. The reference methodology was adapted, both for practical purposes and to ensure greater randomness in the sorting procedure, such that ‘green’ and
‘brown’ portfolios were respectively defined as the 10th and 1st ‘greenness’ deciles of the S&P 500 index. The performance difference between such portfolios was then defined as the
‘green’ factor, from which an estimate of the time-invariant ‘green’ premium could be obtained. By observing European and US trends in environmental policy stringency (Figure 1), denoting a comparative laxness by US policymakers, I speculated that this would be reflected in market participants’ expectations on transition risk. Therefore, I hypothesised that an