Green bonds move with equities when diversification matters most. In Hussain, Zafar and Khan's estimates, four of the six counterpart markets have positive and significant coefficients in the joint bearish cell of the quantile-on-quantile surface. The S&P 500 records 0.142. The DAX records 0.164.
A green bond is ordinary fixed income carrying a use-of-proceeds restriction. Its proceeds finance renewable energy, energy efficiency, clean transport and similar projects. Sustainable finance investors buy the label, though they would also like the bonds to justify their allocation through covariance. This paper tests that claim. Its economic case comes from Markowitz (1952): portfolio variance depends on covariance between holdings, and low or negative covariance can reduce risk even when an asset's own return is unremarkable.
The authors describe green bonds as state-contingent, low-volatility diversifiers. They decline to present them as a universal hedge or safe haven. Their abstract says the portfolios "do not show universal hedging or safe-haven performance." The estimates support the negative half of that conclusion, I think. Evidence for the positive half remains thin for the reasons below.
Inside the quantile surface
The authors use quantile-on-quantile regression in the Sim and Zhou form. For every pair of quantiles, it fits a local linear quantile regression. Choose green-bond quantile θ and counterpart quantile τ, then estimate the slope of green-bond returns on counterpart returns. A Gaussian kernel weights each day according to the distance between the counterpart's empirical CDF value and τ. The baseline bandwidth is h = 0.05. Its grid is {0.10, 0.25, 0.50, 0.75, 0.90}, producing 25 cells for each pair and six pairs altogether.
The sample contains 2,857 daily closes and 2,856 log returns times 100. It runs from 2 January 2014 to 30 April 2026 and covers seven indices. Five are quoted in USD: the S&P Green Bond Index, the S&P 500, the S&P Bitcoin Index, the S&P Global Clean Energy Index and the S&P GSCI. The Clean Energy index comprises renewable-energy and clean-technology companies. Because the green-bond index is a price return series, coupon income is excluded. Yahoo Finance supplies the DAX in EUR and the SSE Composite in CNY. The authors align dates complete-case, discard Bitcoin's weekend-only observations and perform no currency conversion anywhere.
The grid matters because an OLS slope blends the left tail with the middle. Mean beta cannot reveal whether green bonds decouple on days when equities fall two percent. For the portfolio exercise, the authors use a closed-form long-only two-asset minimum-variance weight bounded at 0 and 1. Each pair comes with annualized return and volatility, a zero risk-free Sharpe, and variance reduction relative to holding the counterpart alone.
The portfolio table mostly ranks volatility
Green bonds have daily volatility of 0.4721%. The corresponding figures are 1.1149% for the S&P 500, 1.2456% for the DAX, 1.2940% for Shanghai, 1.4565% for GSCI, 1.6664% for Clean Energy and 4.2714% for Bitcoin. Pairwise correlations with green bonds range from 0.008 (GSCI) to 0.164 (Clean Energy). Put a near-zero correlation and a volatility ratio between 2.4x and 9x into the closed form, and the resulting allocation is 86.8% to 99.3% green bonds. Reported variance reductions span 84.0% to 98.8%.
The authors acknowledge the mechanism. The paper says the portfolios allocate this way "mainly because green bonds are much less volatile than the counterpart markets in the sample." Once the volatility ratio is removed, little remains for the portfolio section to establish.
The return column is more revealing. Green bonds paired with the S&P 500 produce the best result: 1.47% annualized at 7.08% volatility, for a Sharpe of 0.207. The Bitcoin pair gives the largest variance reduction, 98.8%, while returning 0.13% a year with a Sharpe of 0.017. Clean Energy returns 0.06%, with 0.008. Every portfolio finishes within a narrow annualized volatility band of 7.07% to 7.48%. Despite its 98.8% variance reduction, the Bitcoin pair ends at 7.48%, above the S&P 500 pair's 7.08% after an 84.0% reduction. The larger reduction uses a much more volatile counterpart as its benchmark, so both figures describe nearly the same portfolio.
Table 12 includes the note "The risk free rate would be zero for the reported Sharpe ratio." Those Sharpes span a 2014 to 2026 period containing substantial positive cash rates. With any cash rate above 1.47%, the best of the six becomes negative. Table 2 identifies the green-bond series as price return, and its mean daily return is -0.0006%. Both return and variance therefore exclude coupon income. The authors list six limitations, without including that return basis among them.
We previously made a related point about a connectedness-based allocation study in which plain minimum variance held up against the connectedness portfolios (our review). With green bonds at 0.4721%, in-sample minimum variance largely becomes a volatility ranking when the ratio ranges from 2.4x for the S&P 500 to 9x for Bitcoin.
Does the bearish tail hedge equities?
For the S&P 500, the joint bearish (0.10, 0.10) coefficient is 0.142, CI [0.057, 0.227], p =.001. The joint bullish coefficient is 0.166 [0.082, 0.250], p =.000, while joint normal is -0.083, p =.577. Clean Energy records 0.198 bearish and 0.143 bullish, with 0.061 and insignificant at the median. GSCI has a bearish coefficient of 0.058, p =.026; its normal and bullish cells are indistinguishable from zero. The DAX is 0.164 bearish, p =.000, with nothing elsewhere on the diagonal. Bitcoin is insignificant across all three diagonal states. Shanghai is also insignificant in all three, including a joint bearish cell of 0.010 at p =.720.
Shanghai's striking significant result lies off the diagonal: -0.362 at green-bond quantile 0.90 against market quantile 0.25. The DAX and Shanghai coefficients occupy local-index-return space, EUR and CNY. They are local-currency estimates, so a USD investor would experience a different result.
A safe haven should have a zero or negative lower-tail coefficient. Four of the six coefficients are positive. The paper's conclusion counts three and names the S&P 500, Clean Energy and DAX. GSCI is the fourth, at 0.058 with p =.026, small and significant at the 5% level.
The paper says the calculations "do not result in safe-haven behavior in an external crisis," echoing the abstract. Its remaining claim is state-contingent diversification. Table 10 reports six diagonal triples. Four of the six joint bearish cells are significant, whereas the median cell is statistically zero in every case. For the S&P 500, the joint bullish coefficient of 0.166 exceeds the joint bearish one. Dependence appears in both tails and disappears in the middle. That shape runs against a smooth beta and sits awkwardly with a flight-to-quality account.
Clean Energy has both the highest green-bond correlation, 0.164, and the strongest joint bearish coefficient, 0.198. Among all pairs studied, the two sustainability-labelled assets provide the least diversification.
An ESG allocator pairing green bonds with clean-energy equity buys the tightest of the six relationships.
Precision is also weakest in the median cells. For the S&P 500, the median CI is [-0.376, 0.210], a width of 0.586, compared with 0.170 for the joint bearish interval. Shanghai's median interval is [-0.429, 0.035]. Across bearish and bullish tails, the intervals are roughly a third as wide as those around the median cells.
DAX signs survive only 56% of one bandwidth change
The authors recalculate every matrix at h = 0.03 and h = 0.07, then report sign agreement. At h = 0.03, agreement is 56% for DAX, 68% for GSCI, 72% for Bitcoin and 76% for the S&P 500. Mean absolute changes reach 0.111 for the S&P 500 and 0.128 for Shanghai. Agreement returns to 80-92% at h = 0.07. The paper prints these results in a table rather than hiding them. When almost half the DAX cell signs reverse after a bandwidth change, cell-level directional interpretation carries little weight. The tail diagonals are the cells worth quoting because their intervals are about a third as wide as those for the median cells.
Inference uses the asymptotic kernel-sandwich approximation, without a bootstrap. Green-bond returns have skewness of 4.462 and kurtosis of 105.243, alongside a Jarque-Bera statistic of 1,249,047.5. Table 3 reports a daily range from -4.4419% to +10.3928%. In practice, that is how kurtosis of 105 appears in a bond index. The authors flag block-bootstrap intervals as a possible extension. Across six matrices, 150 cells are tested individually, and the paper describes no multiplicity adjustment. Shanghai's isolated significant off-diagonal coefficient of -0.362 offers too little to build on.
We did not rebuild the portfolios
The green-bond leg is an index that nobody can hold. The DAX and SSE legs are quoted in EUR and CNY, while the other five use USD. For this reason, the authors call those two portfolio rows local-currency illustrations and apply the same qualification to the DAX and Shanghai QQR estimates. Repeating the exercise with US-listed ETF proxies and platform crypto prices would introduce fees, tracking error, different trading hours and an FX leg. The estimator would change, preventing a replication of their 84-99% figures.
Rolling QQR would change my view if the joint bearish coefficients became negative within a defined stress window and block-bootstrap intervals surrounded them. The authors identify rolling estimation as the next step. For now, these 2,856 days say something simpler. Green bonds are a 0.47%-volatility index. In the joint bearish tail they move with US and German equities, at 0.142 and 0.164, while the Shanghai estimate is 0.010 at p =.720. Give that asset to a minimum-variance optimizer, and the Bitcoin pair holds 0.7% Bitcoin while the Clean Energy pair holds 3.4% clean energy.