*This post has been updated and moved to the blog’s new domain, **conductunbecoming.ie**, and you can find it here.*

After my post a few weeks ago proposing a form of emissions-linked government bond which I called a ‘green bond’, I’ve realised an unintended benefit that the green bonds would bring to any government that issues them: they would reduce long-term borrowing costs. This actually surprised me when I realised it, as it certainly wasn’t one of the intended consequences of issuing the bonds, but after considering the matter, it’s actually quite clear that borrowing costs would be lower for governments offering green bonds, subject to a couple of conditions.

I’m not going to go over a formal mathematical proof here (I like to think my blog hasn’t become quite *that* nerdy yet), but here’s the reasoning behind my claim:

Assume creditors are buying ten-year government bonds at an interest rate * n*. Now, if they also have the option of buying a ten-year green bond from the government, that green bond is going to have a base interest rate

*, which would be increased by*

**m***if the government goes over its promised allocation of emissions permits by some given amount. We’ll assume that the market of creditors will place a probability*

**r****on the government actually having to pay out the higher**

*p***+**

*m***interest rate. The only reason that**

*r**would be zero would be if the markets had absolute and complete confidence that a government would never renege on its promises. We know that’s not true, so we can say that*

**p****is nonzero.**

*p*The expected interest payment for the green bond will be the base rate ** m** plus the increment

**times the probability**

*r***that the increment will have to actually be paid. That is, expected interest will be**

*p***+ (**

*m*

*p****. Given the choice between either the regular government bond or the green bond, if one has an expected interest rate which is higher than the other, then creditors will simply all buy the one with the higher rate. This means that, in an efficient market, the expected rate for both should be equal, ie**

*r*)*=*

**n****+ (**

*m******

*p***). Now, we know that both**

*r***and**

*p***are nonzero (if**

*r***was zero, then it would just be a regular bond), and are both positive. This means that**

*r***must be less than**

*m***for the market for both bonds to operate. That is, the base interest rate on the ten-year green bond has to be lower than the interest rate on standard government bonds. Which means that, so long as the government doesn’t actually deviate from its proposed emissions limits, issuing green bonds is going to be a definitively cheaper way to raise cash.**

*n*Of course, this is a simplified explanation; there would actually be a range of possible ** r**s depending on how far over the emissions schedule the government went, and then a range of possible

**s for the expected probabilities of each of those**

*p***s being paid out. However, the principle remains the same; markets are going to be willing to accept a lower base interest rate on green bonds so long as there is some non-zero probability that a higher interest rate will have to be paid out instead.**

*r*Interestingly, what a government would actually be doing with this scheme is betting on its own trustworthiness. The government is assuming with certainty that it will stick to its promises, whereas the markets don’t have the same faith. By issuing green bonds, a government can actually leverage this lack of trust in the form of lower interest rates. Of course, to benefit from these lower base rates, the government would actually have to stick to its promises, and can it really be that confident of itself?