EUTERPE

EUTERPE
 EUropean TERm Premium Estimation

About

“What does the historically unusual behavior of long-term yields imply for the conduct of monetary policy? The answer, it turns out, depends critically on the source of that behavior. To the extent that the decline in forward rates can be traced to a decline in the term premium, ... the effect is financially stimulative and argues for greater monetary policy restraint, all else being equal. ... However, if the behavior of long-term yields reflects current or prospective economic conditions, the implications for policy may be quite different - indeed, quite the opposite”.

Ben Bernanke, Chairman of the Federal Reserve

What is EUTERPE?

The Great Financial Crisis and, more recently, the pandemic shock have threatened the stability of the euro and have posed new challenges on the path to strengthening the European Union. The European Central Bank (ECB) has been forced to adopt unconventional monetary policy measures, such as negative interest rates and asset purchases, in order to stabilize financial markets and stimulate economic growth. Recent developments in the world economy and financial markets seem to indicate that interest rates are likely to remain low for a relatively long time. Such a scenario, commonly referred to as the “new normal”, is particularly evident in Europe, with the yield on long-term German Bunds sinking into negative territory and the forward guidance of the ECB monetary policy signalling a renewed expansionary attitude. A “low-for-long” scenario poses considerable challenges to the business models of many financial institutions, primarily banks and insurance companies, as it could weaken their profitability at the same time that it encourages institutions to “reach for yield”, a combination which represents a serious source of vulnerability for the financial system. Moreover, a low-for-long environment is challenging for the conduct of monetary policy of the ECB as well as other central banks, since in the event of adverse shocks the presence of a near-zero lower bound on nominal interest rates can prevent the monetary authorities from moving the policy rate to sufficiently low levels.

The low-for-long scenario turns out to be a topical issue because of the current global health emergency and the consequent widespread negative effects of the pandemic on the world economy. Therefore, a clear understanding of the forces underlying the movements in interest rates has become a timely and very relevant matter for central bankers and investors.

The yield curve is vital for the transmission of monetary policy, as it has a significant influence on asset valuations and is the main driver of the investment and saving decisions of households and firms. From a theoretical viewpoint, nominal yields combine the investors’ expectations on the average short rate over the maturity of the bond with a risk premium component, the term premium, representing the additional compensation they demand to hold a longer-term bond relative to a series of shorter-term bonds and, therefore, reflecting their uncertainty on future interest rates. In turn, these two components can be splitted further depending on whether they are driven by inflation or real factors: the expectation of the average short-term interest rate reflects the sum of the expected inflation over the term of the bond and the expected path of short-term real interest rates, whereas the term premium comprises the real term premium and the inflation risk premium. The latter represents the compensation for bearing the risk of unanticipated changes in future inflation perceived by investors holding nominal government bonds, and implicitly gives a measure of their confidence in the ability of the central bank to meet inflation targets.

The decomposition of yields cannot be inferred directly from market prices and identifying the drivers of yield curve movements in real time is a challenging task. Although extensive theoretical and empirical work has been devoted to this issue, thus far there is neither a commonly accepted framework nor agreement on empirical regularities. The purpose of the EUTERPE (EUropean TERm Premium Estimation) research project is to provide timely and reliable estimates of the term premium for government bonds of the Euro Area. EUTERPE not only delivers an academic contribution but also has the ambition to produce a new analytical tool with various applications in the practice of European policymakers and the financial industry.


Methodology

EUTERPE proposes a model for the estimation of term premia in the Euro Area (EA) that relies on an affine term structure framework with interrelations between yields, volatility and macroeconomic factors. The set of the underlying state variables includes both country-specific and global (eurozone-specific) factors, whose dynamics is described by stochastic processes with time-varying volatility. The term premia of the different countries are interrelated and the strength of those connections depends on the sensitivity of each country to the global factors. From a policymaker perspective, this information is crucial in order to better understand the mechanism of transmission of macro, volatility and global shocks to the risk premium components of bond yields within the EA.

The model explicitly disentangles the convexity effect from the expectation and risk premium components. This convexity effect is particularly important for long-term bonds, as it is large and negative at long maturities and is responsible for the persistent downward slope in the term structure of forward rates that is observed in the data. The size of the effect depends on the volatility of long-term yields and, as this varies significantly over time, a term structure model with stochastic volatility is necessary to account for it.

Using data on euro inflation swaps and the ECB survey for inflation forecasts, separate estimates of the inflation risk premium and the real term premium can be obtained along with estimates for the term structure of real interest rates and inflation expectations in the EA. As a result, the model endogenously provides an estimate for the long-run equilibrium real rate, defined as the average expected real short rate over a five-year period starting five years ahead. The equilibrium real rate, which is a proxy for the so-called “natural” o “neutral” interest rate, is relevant in many respects. For central bankers, it represents a benchmark to calibrate the stance of monetary policy. To the extent that the central bank targeting rule can be traced (directly or indirectly) to this natural rate, the monetary policy is expansionary if the short-term real rate lies below the equilibrium rate and contractionary if it lies above. For investors, the level of the natural rate represents a reference point for the prediction of the future discount rates that are applied in the valuation of financial assets.

The global dimension of the structural model allows to study the co-movement of yield curves, calculate their degree of connectedness and build the implied network structure. The analysis can be extended to the components of yields and thus can provide a picture of the cross-country connections for expected short rates and term premia, both in real and inflation terms. This allows to determine the global impact of macro and volatility shocks on sovereign bonds of the EA and may have relevant implications for measuring systemic risk and predicting contagion effects.

The connectedness analysis based on single type of relationships between countries has some limitations which have become increasingly evident over the past few years since the emergence of strongly interconnected financial markets with multiple channels of shock transmission. For this reason, a network with multiple connectivity layers (different countries, different maturities of yields and/or different components of yields) represents a better tool to understand the dynamics of the underlying interactions. In particular, EUTERPE proposes a network analysis based on a multilayer Bayesian graphical VAR model, where the temporal and contemporaneous causal structures of the structural VAR are represented by two different graphs and an efficient Markov chain Monte Carlo algorithm is used to estimate jointly the causal structures and the parameters of the reduced-form VAR model.


Data

Download Estimates

This file contains estimates of the term structure of term premia and short rate expectations for ten countries of the Euro Area and the Euro Area as a whole.

file odsEstimates
Last update: 01/05/2021
632 K

Euro Area term premia curve

This graph shows the evolution of the estimated term structure of term premia in the Euro Area
Term structure of term premia in the Euro Area

This graph shows the evolution of the estimated term structure of term premia in the Euro Area

This graph shows the evolution of the estimated term structure of short rate expectations in the Euro Area
Term structure of short rate expectations in the Euro Area

This graph shows the evolution of the estimated term structure of short rate expectations in the Euro Area

Term premia  
Time series estimates of 10-year term premium

This graph shows the time series estimates of the 10-year short rate expectations for the Euro Area, Austria, Finland, France, Germany and Netherlands

This graph shows the time series estimates of the 10-year term premium for the Euro Area, Austria, Finland, France, Germany and Netherlands

This graph shows the time series estimates of the 10-year term premium for the Euro Area, Belgium, Ireland, Italy, Portugal and Spain

This graph shows the time series estimates of the 10-year term premium for the Euro Area, Belgium, Ireland, Italy, Portugal and Spain

Short rate expectations  
Time series estimates of 10-year expected short rate

This graph shows the time series estimates of the 10-year short rate expectations for the Euro Area, Austria, Finland, France, Germany and Netherlands

This graph shows the time series estimates of the 10-year short rate expectations for the Euro Area, Austria, Finland, France, Germany and Netherlands

This graph shows the time series estimates of the 10-year short rate expectations for the Euro Area, Belgium, Ireland, Italy, Portugal and Spain

This graph shows the time series estimates of the 10-year short rate expectations for the Euro Area, Belgium, Ireland, Italy, Portugal and Spain


Research

Related articles and working papers

Inflation risk premia, yield volatility, and macro factors

Inflation risk premia, yield volatility, and macro factors
A. Berardi and A. Plazzi
Journal of Financial Econometrics, 2019, vol. 17, pp. 397-431

We incorporate a latent stochastic volatility factor and macroeconomic expectations in an affine model for the term structure of nominal and real rates. We estimate the model over 1999–2016 on U.S. data for nominal and TIPS yields, the realized and implied volatility of T-bonds, and survey forecasts of GDP growth and inflation. We find relatively stable inflation risk premia averaging at 40 basis points at the long end, and which are strongly related to the volatility factor and conditional mean of output growth. We also document real risk premia that turn negative in the post-crisis period, and a non-negligible variance risk premium. We incorporate a latent stochastic volatility factor and macroeconomic expectations in an affine model for the term structure of nominal and real rates. We estimate the model over 1999–2016 on U.S. data for nominal and TIPS yields, the realized and implied volatility of T-bonds, and survey forecasts of GDP growth and inflation. We find relatively stable inflation risk premia averaging at 40 basis points at the long end, and which are strongly related to the volatility factor and conditional mean of output growth. We also document real risk premia that turn negative in the post-crisis period, and a non-negligible variance risk premium.

Mind the (convergence) gap: bond predictability strikes back!

Mind the (convergence) gap: bond predictability strikes back!
A. Berardi, M. Markovich, A. Plazzi and A. Tamoni
Management Science, 2020

We show that the difference between the natural rate of interest and the current level of monetary policy stance, which we label Convergence Gap (CG), contains information that is valuable for bond predictability. Adding CG in forecasting regressions of bond excess returns significantly raises the R2, and restores countercyclical variation in bond risk premia that is otherwise missed by forward rates. Consistent with the argument that CG captures the effect of real imbalances on the path of rates, our factor has predictive ability for real bond excess returns. The importance of the gap remains robust out-of-sample and in countries other than the U.S. Furthermore, its inclusion brings significant economic gains in the context of dynamic conditional asset allocation.

Dissecting the yield curve: the international evidence

Dissecting the yield curve: the international evidence
A. Berardi and A. Plazzi
Under Review (R&R)

Nominal yields can be expressed as the sum of an expectation, term premium, and convexity component, and in turn of their real and inflation counterparts. We extract these terms from the yield curve of the U.S., Euro Area, U.K., and Japan using a term structure model that explicitly captures the interrelation between yield factors and macroeconomic conditions while allowing for aggregate stochastic volatility. We find that the bulk of yield dynamics comes from short rate expectations. Term premia vary over time and increase with maturity, but account for a smaller fraction of yield level and variance than previously documented. Over time, we observe a sustained decline in short real rate expectations and significant convexity effects. With regard to yield comovement, the U.S. and U.K. generate the strongest spillovers at the long-end of the yield curve, in particular through term premia, whereas the Japanese market is the least connected.

Bond risk premia: the information in really long-maturity forward rates

Bond risk premia: the information in really long-maturity forward rates

A. Berardi, R. Brown and S. Schaefer

Long term forward rates contain information that greatly improves the precision with which expectations of future short rates can be distinguished from risk premia in the term structure. Indeed, in affine models, the slope of the term structure of risk premia for long maturities is very closely approximated by the sum of (i) the slope of the forward rate curve and (ii) a term that depends only of yield volatility and maturity ("convexity"), two quantities that can easily be estimated independently of the details of model specification. Key to extracting the risk premium information in long-term forward rates is capturing the dynamics of convexity, which requires a model with time-varying volatility. Using a four-factor ATSM, we find that risk premia on long term bonds are almost entirely driven by volatility. Short rate expectations in our model account for a much larger fraction of the volatility of yields than is typically reported, a result that we show is mainly the result of econometric bias in some estimates of Gaussian models. We also show - using Monte Carlo simulation - that including data on long-term yields in the estimation of term structure models greatly improves the precision of estimated values of short rate expectations, term premia and risk premia. Compared with benchmark estimates that use yield data up to 25 years, excluding data on yields longer than 10 years results in the standard errors of both estimated means and volatilities roughly tripling in size.

A Bayesian graphical VAR model for connectedness in international yield curves

A Bayesian graphical VAR model for connectedness in international yield curves

A. Berardi, M. Billio and R. Casarin

This research explores the time-varying behaviour of the degree of connectedness among the yield curves of seven currency areas (Australia, Canada, Germany, Japan, Switzerland, UK and US). We decompose yields into expected short rates and term premia using a Gaussian ATSM integrated with long-term yield expectations. We find that the dependence structure of both yields and their components can be significantly different for short and long maturities. The empirical analysis is based on a Bayesian graphical VAR model, where the contemporaneous and temporal causal structures of the structural VAR are represented by two different graphs and an efficient Markov chain Monte Carlo algorithm is used to estimate jointly the two causal structures and the parameters of the reduced-form VAR model.