Fair value from the issuer's own curve, the concession a conventional deal would have paid, and the framework costs that come off the saving.
The greenium is the green bond's spread minus the fair value of a conventional bond of the same issuer at the same maturity, read off its secondary curve. On an illustrative seven-year euro green bond priced at mid-swaps plus 112 bp, against a conventional curve that interpolates to 116.00 bp, the greenium is minus 4.00 bp. Against what a conventional deal would actually have cleared at, concession included, the issuer saved 7.00 bp, worth EUR 2,106,944 on EUR 500 million, or EUR 1,620,753 after the cost of the green framework.
Worked in full in Capital Markets by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
A green bond has no twin. The issuer's conventional bonds sit at other maturities, and the green bond is priced on a day when no conventional deal was printed. So the greenium is never observed: it is a spread against an estimate, and it inherits every choice made in building that estimate. The three that matter are the interpolation, whether a concession is added to the counterfactual, and whether the issuer's extra costs are netted off. Each is worth more than the greenium itself on some deals.
| Input | Value |
|---|---|
| Conventional bond A: maturity, spread over mid-swaps | 5.5 years, 104 bp |
| Conventional bond B: maturity, spread over mid-swaps | 8.5 years, 128 bp |
| New green bond: maturity, reoffer spread | 7 years, 112 bp |
| Seven-year mid-swap rate | 2.80% |
| Size | EUR 500,000,000 |
| Concession a conventional deal would have paid | 3 bp |
| Second-party opinion and framework, upfront | EUR 125,000 |
| Allocation and impact reporting with assurance, a year | EUR 60,000 |
Fair value = SA + (T − MA) / (MB − MA) × (SB − SA)
Greenium = green spread − fair value
Saving at issue = (fair value + concession) − green spread
Value of 1 bp = size × 0.0001 × (1 − (1 + y)−T) / y
Excel: =B2+(7-A2)/(A3-A2)*(B3-B2) for the fair value, =500000000*0.0001*PV(3.92%,7,-1) for the basis point.
Step 1, fair value. Seven years sits exactly halfway between 5.5 and 8.5, a weight of 0.5000. The curve rises 24 bp over that gap, so a conventional seven-year bond is worth 104 + 0.5000 × 24 = 116.00 bp.
Step 2, greenium. 112 less 116.00 is minus 4.00 bp. The green bond trades 4 bp inside where the issuer's conventional paper says it should. This is the figure most research and dealer screens report, and it is a secondary-market comparison.
Step 3, the issuer's saving. The issuer's question is different: what would a conventional seven-year deal have cost on the same day? New issues usually price at a concession to the secondary curve. At 3 bp, the counterfactual reoffer is 119.00 bp and the green deal saved 7.00 bp. The concession is an assumption, and it is three sevenths of the answer.
Step 4, into euros. At a reoffer yield of 3.92 per cent the seven-year annuity factor is 6.0198, so one basis point on EUR 500 million is worth EUR 300,992. The saving of 7.00 bp is EUR 350,000 a year and EUR 2,106,944 in present value.
Step 5, the costs of being green. The second-party opinion and framework cost EUR 125,000 upfront and the annual reporting EUR 60,000 a year, EUR 361,190 discounted at the same yield. Together EUR 486,190, which is 23.1 per cent of the gross saving. The net saving is EUR 1,620,753, and the break-even saving, below which the label costs money, is 1.62 bp.
Credit curves are usually concave, so interpolating in the square root or the logarithm of maturity is as defensible as a straight line. Each moves the fair value, and therefore the greenium.
| Convention | Fair value, bp | Greenium, bp | Saving at issue, bp | Net saving, EUR |
|---|---|---|---|---|
| Linear in maturity | 116.00 | −4.00 | 7.00 | 1,620,753 |
| Linear in square root of maturity | 116.65 | −4.65 | 7.65 | 1,815,950 |
| Linear in log of maturity | 117.30 | −5.30 | 8.30 | 2,010,770 |
The span is 1.30 bp, worth EUR 390,017 at this size. That is about a third of the measured greenium, and it comes from a modelling choice, not from investors. The same arithmetic, applied to the concession on a conventional deal, is in how to calculate a new issue concession, where four conventions produce answers 4.97 bp apart.
| Saving at issue, bp | Gross, EUR | Net of framework costs, EUR |
|---|---|---|
| 0 | 0 | −486,190 |
| 1 | 300,992 | −185,198 |
| 2 | 601,984 | 115,794 |
| 4 | 1,203,968 | 717,778 |
| 7 | 2,106,944 | 1,620,753 |
| 10 | 3,009,920 | 2,523,729 |
The costs are mostly fixed, so the break-even falls with size. On EUR 250 million one basis point is worth EUR 150,496 and the issuer needs 3.23 bp to break even; on EUR 1 billion, 0.81 bp. A small issuer with a modest greenium can pay for the label rather than be paid for it.
Without the concession, the saving is just the 4.00 bp greenium: EUR 1,203,968 gross and EUR 717,778 net. Whether to add a concession depends on whether the green deal itself priced flat to its own fair value. If it also carried one, the two cancel and the greenium is the saving.
Comparing the green bond with a single conventional bond. Bond A, the shorter of its two neighbours, trades at 104 bp, and against it the green bond looks 8 bp wide: a premium paid, not a greenium earned. The curve rises 8 bp a year, and the green bond is 1.5 years longer, which is 12 bp of slope. Once maturity is adjusted, the sign flips. A greenium quoted without its curve and its interpolation is not a number; state both, as you would for a G-spread or an I-spread.
The second error is to report the greenium as the issuer's saving without netting the framework, the reporting and the assurance. On a benchmark size they are nearly a quarter of the gain; on a small issue they can be all of it.
The interpolation, the concession and the cost a bond carries without an invoice are the subject of Capital Markets, and the free workbook for this case runs the four readings of one curve on your own quotations.
Not quite. The greenium compares the green bond with the issuer's secondary curve, minus 4.00 bp in the illustrative case. The issuer's saving compares it with what a conventional deal would have cleared at, which normally includes a new issue concession. With a 3 bp concession the saving is 7.00 bp, and after framework and reporting costs of EUR 486,190 it is worth EUR 1,620,753 on EUR 500 million.
Divide the present value of the extra costs by the value of one basis point. With EUR 125,000 upfront and EUR 60,000 a year of reporting, the costs are EUR 486,190 over seven years. On EUR 500 million one basis point is worth EUR 300,992, so the break-even is 1.62 bp; on EUR 250 million it is 3.23 bp.
Because no conventional bond sits at the green bond's maturity, its fair value has to be estimated. Interpolating linearly in maturity gives 116.00 bp, in the square root of maturity 116.65 and in the log of maturity 117.30. The greenium moves from minus 4.00 to minus 5.30 bp, a span worth EUR 390,017 on EUR 500 million.
This article is one calculation from Capital Markets. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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