A green bond is a type of fixed-income security that raises money to invest in predetermined climate and environmental projects, in contrast to conventional debt instruments, where the use of  proceeds is not specified in the terms. The difference in yield between a green bond and an otherwise identical non-green bond of the same issuer and with the same terms is called the greenium. In this paper, we investigate this yield differential between green and conventional bonds. We estimate the greenium on the basis of the bond's asset swap spread (ASW) to investigate whether, consistent with a non-pecuniary motive for holding green assets, green labels are associated with a negative or positive yield gap with respect to ordinary bonds. We calculate and compare several descriptive statistics of green bonds and conventional bonds. Then, several statistical tests are implemented to analyze potential statistical differences between their return distributions. In our analysis, synthetic non-green bonds are constructed via interpolation of the ASW curve of non-green bonds. There are several findings: (1) From a statistical point of view, no difference between the overall distribution, the mean or median of ASW changes is detected on individual bond pairs. However, our estimation of an overall greenium exhibits a level fluctuating near zero over time with an overall average around -7 bps. (2) In addition, we see indications that the volatility of some green-bonds is lower than their non-green counterparts. (3) We see a lagging effect between the greenium and stress in financial markets. This could indicate that sustainable investments like green bonds are potentially more immune to systemic crises.