How do zero-coupon inflation swaps predict inflation rates in the euro area? Evidence of efficiency and accuracy on 1-year contracts

It should be noted that the data on ZCISR date back to June 2004. If we consider contracts with longer maturities, we have a reduced number of observations to test the EMH. However, an empirical work with a reduced sample is pointless since it does not allow us to draw robust conclusions. In view of this constraint, concentrating the analysis on short-term contracts is a standard practice (see, e.g., Casiraghi and Miccoli 2015).

The results of the different studies may not be directly comparable owing to differences in sample periods, instruments and methods used (Grishchenko and Huang 2013; Bekaert and Wang 2010). Though, it can also be an indication that the inflation risk premium is time-varying, depending on the inflation level and on the uncertainty about future inflation rates.

Deacon et al. (2004), Kerkhof (2005) and García and van Rixtel (2007) are examples of authors who provide information on the evolution, size and composition of the inflation derivative market.

Theoretically, in a frictionless world where agents are endowed with rational expectations and there are no risk premia, inflation expectations taken from inflation swaps and other inflation-linked instruments should be similar and discrepancies among alternative measures are supposed to be quickly adjusted. Otherwise, any difference of this kind constitutes an arbitrage opportunity that can be exploited by agents who have access to the diverse markets. In practice, on the back of the failure of these principles and other technicalities, some instruments may be more prone to generate better forecasts.

So, a potential failure of the risk-neutral EMH can be due to the presence of a risk premium or to a failure of rational expectations. Also, it is necessary to admit the possibility of information inefficiencies as well as a possible disagreement on inflation expectations. Furthermore, one may conjecture a supply-demand imbalance in the inflation swap market. All these factors may cause inefficiencies in inflation swap markets and speculators may exploit them by operating simultaneously in the swap market and in other markets for inflation-linked securities.

When analyzing regression (4) one should have in mind the concept of speculative efficiency which postulates that a market is speculatively efficient if excess returns from speculation are not economically significant. Therefore, in practice, \(\alpha \) and \(\beta \) do not always have to correspond to the standard values under the null hypothesis and deviations from these figures might occur as long as these do not allow for large profit opportunities (Wagner 2012).

Surveys correspond to the most direct source of inflation expectations since they put specific questions to particular groups designed for this purpose. Thus, results are directly observed rather than estimated or inferred. For the euro area, various survey-based measures of inflation expectations are available. Since the ECB SPF is one of the main focus of attention (it is free, provides point forecasts of inflation expectations at various horizons and also offers a quantitative assessment of uncertainty surrounding the reported point forecasts), we favor this source. Given that the ECB SPF is conducted on a quarterly basis, we convert these data into monthly series via linear interpolations.

Market-based measures of inflation expectations have the advantage of being forward looking, timely and frequently updated for a wide range of maturities, summarizing the view of market participants that are willing to risk money based on their beliefs. Besides the use of inflation swaps, the simplest way to measure expected inflation by means of financial data is to consider information on BEIR that, even in the case of comprising some risk premia, are broadly determined by expectations of future inflation rates (see, e.g., Strohsal and Winkelmann 2015). In the derivation of euro area inflation expectations from BEIR we draw on bonds issued by the French Treasury taking into consideration (1) the date of the first issuance and the consequent data availability to proceed with the empirical analysis; (2) the number of inflation-linked bonds and large range of maturities; (3) the amount outstanding available in the market and the higher degree of liquidity; (4) creditworthiness concerns (non-peripheral States).

In particular, if the two components are orthogonal, the decomposition is exact.

It is reasonable to consider that investors base their expectations on this source since it corresponds to one of the most direct measures of inflation expectation (with real-time updates). In this line, Bernanke (2004) states that “inflation-indexed securities would appear to be the most direct source of information about inflation expectations and real interest rates”.

It is not strictly correct to interpret this coefficient as a departure from risk neutrality because \(\beta ^{RP}\) will be null if there is a constant risk premium. Indeed, in the case that the risk premium is constant, \(\rho _t =\rho \) and, consequently, \(\hbox {var}\left( {\rho _t } \right) =\hbox {var}\left( \rho \right) =0\). In this special situation: \(\beta =1\). This fact underlines the importance of the complete evaluation of the EMH beyond the simple validation of the unbiasedness hypothesis.

Caparole et al. (2012) realize that inflation uncertainty has declined steadily since the inception of euro area, while short-run uncertainty has stabilized.

Considering data on the US market, Fleming and Sporn (2014) conclude that the ZCIS market is reasonably liquid and transparent. In this sense, knowing that the euro area has the most active inflation swap market, the concerns about liquidity should be even smaller, especially for maturities with a higher negotiation.

As is standard for swaps contracts, there are no up-front costs to either party of entering into the contract. In addition, as mentioned by Schulz and Stapf (2014), collateralization mitigates the problem of credit risk and has become increasingly popular among OTC derivatives during the last years.

In effect, this result provides compelling evidence that the assumptions underlying the financial theory hold since, in a context with perfect markets, it is expected a substitution between BEIR and ZCISR and, as a result, inflation curves derived from both instruments should be identical. Against this backdrop, several authors have been studying the relationship between inflation expectations extracted from inflation swaps and inflation-bond markets (see e.g., Devlin and Patwardhan 2012; Schulz and Stapf 2014; Grothe and Meyler 2015).

Based on expression (14) the coefficient \(\varphi \) corresponds to the deviation of the risk-neutral EMH due to systematic expectational errors. So, regression (19) will allow us to check if the value found for \(\beta ^{RE}\) is statistically different from zero.

In practice, regressions (21) and (23) are estimated taking into account information from time \(t-1\) because, at moment t, agents only know the realized inflation rate and the rational expectations forecast errors of the previous month.

Similar tests with other variables known at the time that inflation swaps are traded provide analogous conclusions.

Using the time series plot of ACF and PACF to determine the order of the SARMA model, we select a SARMA (1,1) (1,1)\(_{12}\) as an appropriate specification to forecast euro area inflation.

Timmermann and Granger (2004) study the relationship between the forecasting activity and the EMH, documenting that the practice of searching for predictable patterns and exploiting trading opportunities affects market prices. In consequence, stable forecasting patterns are unlikely to persist for long periods of time and will self-destruct when discovered by a large number of agents.