Pricing GDP-linked bonds

Fernando Eguren-Martin

GDP-linked bonds are sovereign debt instruments with repayments linked to the evolution of a country’s GDP. Originally proposed by Shiller in the 90s, they have recently been re-invoked in the debate around the policy response to the Covid-19 pandemic. These instruments present an obvious attraction for issuers: repayments are lower at times when the economy is growing relatively slowly, which typically coincides with lower tax earnings. A greater share of the risk of weak growth is then transferred to investors, who will require a compensation given they are typically risk-averse. Therefore, while the design is attractive ex-ante, a relevant question facing sovereigns willing to issue this type of instrument is `at what cost?’. In this post (and in an underlying Staff Working Paper) we provide some tentative answers.

GDP-linked bonds

Although the idea of having GDP-linked debt is not new, several policymakers have expressed an interest in them in recent years as a potential means for promoting financial stability, including in response to the current Covid-19 pandemic. The last decade has seen the emergence of a substantial body of analysis of these bonds’ features and desirability (see this CEPR e-book for a summary). However, there is an issue that remains unsettled: pricing. Having an estimate of the price of these bonds is a central consideration for sovereigns considering the cost-benefit analysis of issuing them relative to conventional bonds.

The pricing question

Holders of GDP-linked bonds will bear a greater share of the risk of low growth outcomes than holders of conventional bonds. Therefore, they will require a risk premium as a compensation.

Estimating this`GDP risk premium’ has proven elusive to previous attempts. Existing approaches have significant limitations: some papers rely on CAPM-type frameworks (for example, Borensztein & Mauro (2004), Kamstra & Shiller (2009) and Bowman & Naylor (2016)), while Barr et al. (2014) rely on modelling investors risk preferences explicitly within a macroeconomic model. However, it is well established that both these approaches have difficulties in matching risk properties of existing assets, so hopes of them delivering in terms of an asset for which we do not currently observe prices are not clear.

In a recent Staff Working Paper we propose a new framework for pricing GDP-linked bonds, which is based on a flexible no-arbitrage approach which constitutes the current workhorse model for pricing bonds. The model innovates by using data on equity yields to extract information about GDP expectations. The framework is applied to the pricing of a simple GDP-linked bond with no coupon payments, and which principal is tied to the cumulative growth of nominal GDP. This structure can be thought of as comparable to that of existing inflation-linked sovereign bonds. Our framework is general enough such that it could accommodate different bond structures, including coupon payments also linked to GDP, but for the sake of simplicity we stick with zero-coupon bonds.

The yields and premia of GDP linkers

A useful exercise when thinking about pricing of GDP-linked debt is to compare the estimated yields to those of plain-vanilla nominal bonds. The difference between these two rates can be referred to as `breakeven rate’; if this breakeven rate is positive, it means the yield GDP-linked bonds would have to offer is smaller than that of conventional nominal bonds, and hence they would be cheaper to issue.

It is also useful to consider the two components of the breakeven rate separately; that is, the two drivers of the price difference between GDP-linked bonds and plain nominal bonds. On the one hand there is the expectation of GDP growth over the lifespan of the bond; if the outlook for GDP improves, the price of a GDP-linked bond increases (as investors reap benefits from the increase in value), its yield goes down and the breakeven rate increases (GDP-linkers become cheaper to issue than plain nominal bonds). On the other, there is the `GDP risk premia’ investors require as a compensation for bearing GDP risk; an increase in these premia pushes down on the price of GDP-linked bonds (up on their yield), which decreases the breakeven rate (GDP-linkers become more expensive to issue than plain nominal bonds). These premia will be a combination of real GDP- and inflation- risk premia. In sum, the overall relative cost of conventional versus GDP-linked debt will be the result of the relative strength of these two forces.

Figure 1 shows the evolution of the estimated breakeven rate at the 7-year maturity over 2010-2017 for a bond tied to the evolution of US GDP (using US Treasuries as a benchmark), together with a decomposition into its components. It can be seen that over the sample the breakeven rate is typically positive: that is, the yield GDP-linked bonds would have had to offer was below that of conventional bonds. This is the result of (the absolute value of) GDP risk premia estimates being below the expectations of average annualised GDP growth over the lifespan of the bond. In plain words, for the US it would have been cheaper to issue this type of debt instead of nominal Treasuries, as expectations of US GDP growth would more than have compensated the risk premium required by investors to hold this type of debt.

Figure 1: 7-y GDP-linked bond breakeven rate and components

Another useful exercise is to look at average estimates of GDP risk premia at different maturities. Figure 2 plots these for maturities ranging from 6 months to 10 years. The figure shows a clear term structure: while premia are more elevated in absolute value at the short-end of the curve (at around -700 basis points), they decrease to around -100 basis points at the 10-year horizon. This means that, in principle, it is cheaper to issue GDP-linked debt at longer maturities as larger negative premia measures push up on the required yield of GDP-linkers at shorter maturities. One possible explanation of this observation is that shocks to GDP tend to have relatively low persistence, which makes them less important over the lifespan of bonds with longer maturities.

Figure 2: Population GDP risk-premia estimates at different maturities

In sum, our framework allows for an estimation of the yields GDP-linked bonds would have to offer at different maturities, including a quantification of the risk compensation required by investors. The post set out to answer the question of what cost prospective issuers would need to pay to reap the benefits of having their debt burden tied to the evolution of GDP. The answer is that, typically in our sample period (looking at the US between 2010 and 2017), GDP-linked bonds would have offered yields below those of conventional Treasury bonds and would therefore have been cheaper to issue, although this may not apply in other circumstances. More generally, this framework could be of interest to sovereigns considering the issuance of such instruments.

Fernando Eguren-Martin works in the Bank’s Global Analysis Division, International Directorate.

If you want to get in touch, please email us at or leave a comment below.

Comments will only appear once approved by a moderator, and are only published where a full name is supplied. Bank Underground is a blog for Bank of England staff to share views that challenge – or support – prevailing policy orthodoxies. The views expressed here are those of the authors, and are not necessarily those of the Bank of England, or its policy committees.

2 thoughts on “Pricing GDP-linked bonds

  1. In this interesting article the probability distribution of estimated future growth rates is shown as symmetrical. The fluctuation around the trend of GDP have two components, relatively small fluctuations around the underlying trend, and the effects of occasional major effects such was the present one (called major recessions by Christopher Dow) of which the effect is emphatically asymmetrical. Taking both these effects into account in projections of GDP shows clearly that the distribution of growth rates to some future date are also asymmetrical.

  2. The most efficient structure we have found is to start in constant purchasing power, calculate the equivalent number of nominal units for the pays and receipts. Amortize. Do not accrete. Long stated maturities deliver compounded benefits for borrower and the lender. Inflation uncertainty premia is eliminated. Known real payments are matched to the expected real incomes.
    Federal Reserve of St. Louis data from 1917 to present applied to the inflation/economic activity measure.

Comments are closed.