Futures Contracts Rates as Monetary Policy Forecasts

Transcription

1 Futures Contracts Rates as Monetary Policy Forecasts by G. Ferrero and A. Nobili Bank of Italy, Economic Research Department (This version: October 2005) JEL classification: E43, E44, E58. Keywords: futures rates, monetary policy, risk-premium. Abstract Many central banks currently use futures contracts rates to assess financial markets expectations about future monetary policy. We provide evidence that futures contracts rates are upward biased forecasts of short-term interest rates. The resulting ex-post excess returns, that are predictable using business cycle indicators, are procyclical in the euro area and countercyclical in the United States. We also show that they embody two different components: the effective ex-ante risk premium required by the investor at the moment of futures price settlement and the ex-post systematic forecast error, which is related to the expectation formation process. We find this second component to be more important in explaining overall excess returns in the euro area, while in the United States the riskpremium dominates. These results have important policy implications for central banks in assessing the efficacy of their communication and transparency of the monetary policy strategy. 1 Introduction As short-term interest rates are to a large extent influenced by monetary authority decisions, financial markets provide useful information regarding expectations of future monetary policy stance. This information plays also an important role for central banks in order to check the efficacy of the communication, as well as the transparency of the strategy. 1 Recent studies for the United States have compared the information content of several financial instruments, finding that yield curves and futures contracts on short-term interest rates are useful predictors of the path of monetary policy decisions both in the short and medium run. 2 Among these, Gurkaynak, Sack and Swanson (2004) showed that federal funds futures rates perform better at shorter forecast horizons, while futures contracts rates on eurodollar deposits are so far the best predictors at forecast horizons over six months. Using asset prices and derivatives to assess future monetary policy has some advantages with respect to other techniques, such as VARs, DSGE models or ARIMAs. First, there is no issue of forecasting model 1 What do markets expect about the future course of monetary policy? The question is important to policymakers, not because we are concerned necessarily that we should meet the market s expectations but as a check on the efficacy of our communication, speech of governor Ben Bernanke at the Society of Analysts for Investments of Chicago held on April 15th See Gurkaynak, Sack and Swanson (2004) and Piazzesi and Swanson (2004a, 2004b). 1

2 selection (e.g. there is no need to fully specify an equilibrium model); second, forecasts are based on real-time rather than revised data; third, under the rational expectations hypothesis market participants use all information available at the moment that the contract is settled. 3 Finally, with respect to other measures of market agents expectations, such as survey data, they are available on a more frequent basis. Nevertheless, some caution is required in evaluating the predictive power of quoted futures rates. Given the aversion to risk of market participants, futures rates will also reflect both a risk and a term premium. Such premia may distort the information embodied in forward rates. A number of papers (e.g. Krueger and Kuttner 1996, Sack 2002 and Durham 2003) provided evidence of such distortions for the United States, showing that short-term interest rates implied in futures contracts are upward biased estimators of ex post realized spot rates. In addition, Piazzesi and Swanson (2004) show, for the US economy, that these positive excess returns are time-varying and predictable by means of business cycle indicators, such as nonfarm payroll employment, yield spreads and corporate bond spreads. These findings are consistent with the failure of the expectations hypothesis in its stronger version, according to which, excess returns should not be predictable. In this paper we provided new evidence on the information content of futures rates for the euro area, allowing for a comparison with the United States. Ex-post excess returns computed on euro area short-term interest rates are found to be positive, time-varying and, differently from the United States, procyclical. Therefore, in the euro area, futures rates adjusted for the time-varying excess return are, on average, better predictors during booms than in recessions, as opposed to the United States. Previous literature on adjusted measures of futures rates, such as Piazzesi and Swanson (2004), uses the label risk premium to refer to predictable excess returns on the short-term interest rate, without taking any particular stance on their structural interpretation. We analyze more in detail ex-post excess returns and show that they can be divided into two components. The first is the ex-ante risk premium required by the investors at the moment of buying or selling the financial contract. The second is the ex-post systematic forecast error, which is independent from the financial instrument considered and provides information about the efficacy of the monetary policy communication and the transparency of policy decisions. Excess returns decomposition has important implications for central banks. Even if futures rates adjusted for both components are the best interest rates forecasts, they do not coincide anymore with financial markets view. In order to correctly assess market expectations about the future path of monetary 3 For example, Krueger e Kuttner (1996) showed that, in the United States, forecasts based on federal funds futures rates are efficent, in the sense that the resulting forecast errors are not significantly correlated with any other variable known to the agents at the moment they establish the futures contract price. 2

3 policy, quoted futures rates should be adjusted only by the risk premium, as the sistematic prediction error reflects part of the expectations formation process. Our empirical analysis shows that both components are predictable and positively correlated with the business cycle in the euro area. Systematic prediction errors are by far more important in explaining overall excess returns at horizons up to one year and a half, even if they tended to decline significantly over recent years. A similar decomposition for the United States leads to opposite results. Both components are found to be predictable and countercyclical, but, risk-premia represent by far the larger fraction of whole ex-post excess returns. The remainder of the paper is organized as follows. In section 2 we provide evidence on the size and predictability of ex-post excess returns computed on short-term interest rates futures for the euro area, allowing a comparison with the United States. In section 3 we show how to decompose ex-post realized excess returns, while in section 4 we point out the main implications for central banks. Section 5 presents some concluding remarks. 2 Forecasting excess returns on short-term interest rates 2.1 Constant excess returns In this section we check whether futures contracts rates are unbiased predictors of the euro area short-term interest rates during the period from January 1992 to December We restrict our attention to daily yields on futures contracts traded on the London International Financial Futures Exchange (LIFFE), which have quarterly maturities, extending out to 18 months. In particular, for the pre-emu period ( ), we select contracts based on the spot three-month LIBOR euromark time deposits, while, for the EMU period ( ), we consider contracts based on the spot three-month Euribor. 4 This choice reflects the idea that the corresponding interest rates underlying the contracts basically account for the monetary policy stance in the considered sample period. Therefore, let f (n) t denote the interest rate on a futures contract quoted at quarter t with expiration occurring at quarter t+n. Letalsor t+n denote the corresponding realized spot three-month interest rate prevailing on the day of expiration of the future contract. We define the ex-post excess return realized 4 We focus on the March, June, September and December futures contracts, which are by far the most actively traded. The expiration on these contracts is around the third tuesday of the third month of the indicated quarter. 3

4 from holding the n-quarter-ahead contract to maturity as x (n) t+n = f (n) t r t+n. (1) Under the expectations hypothesis (in its stronger formulation) and under the assumption of a riskneutral representative agent, in absence of arbitrage opportunities, futures rates coincide with the expected future spot interest rates; therefore the realized excess returns are just equal to the forecast errors made by market participants and should be, on average, equal to zero. Figure 1 shows the excess return on futures contracts on 3 month euribor, expiring after 3, 6, 9, 12, 15 and 18 months. The ex-post differences between the implied expected rate and the realized spot interest rate are, on average, positive and increase with the forecast horizon. To check whether the mean excess return has been significantly different from zero and, therefore, to reject the expectation hypothesis in its stronger version, we run the following regressions for the forecast horizons n =3, 6, 9, 12, 15, 18 5 x (n) t+n = α(n) + (n) t+n. (2) We summarize results in Table 1(A). The average ex-post realized excess returns is significantly positive over the considered sample period, ranging from 10 to 120 basis points in the euro area; in addition, longer-horizon contracts have larger excess returns. Buying the four-quarter-ahead contract and holding it to maturity is a strategy that generates an excess return of 70 basis points per year on average, 7 time bigger than buying and holding to maturity the one-quarter-ahead contract. Similar conclusions are reached in the corresponding analysis for the United States, using the eurodollar futures contacts rates traded on the Chicago Mercantile Exchange, which are settle based on the spot three-month LIBOR eurodollar time deposit rate (Figure 2; see also Piazzesi and Swanson, 2004). In order to compare the size of the excess returns, in Table 1(B) we report the results of the regressions (2) for the United States, in the same sample period. Average excess return has been significantly positive and larger than those of the euro area at all forecast horizons considered. Precisely, it has been greater on average by 10 basis points at shorter horizons (up to 6 months) and by 20 basis points at longer ones (from 9 up to 18 quarters). 5 Standard errors are computed by means of the Newey-West heteroskedasticity and autocorrelation consistent procedure, in order to take into account the futures contract overlap. 4

5 2.2 Time varying excess returns We have obtained our previous results under the assumption that excess returns are constant over time. Now we allowexcess returns to be time-varying and check wether they can be predicted by means of business cycle indicators. We run the following regressions x (n) t+n = α (n) + β (n) y (c) t + (n) t+n (3) where y (c) t is the business cycle component of the euro area real GDP growth rates 6. The estimated coefficients for the euro area suggest that excess returns are time-varying and significantly procyclical at forecast horizons longer than six months (Table 2A) 7. Splitting the sample between periods of booms and recessions, we notice that excess returns are about 1.5 to 2.5 times lower in recessions than they are on average in expansions; precisely, in the former case, excess returns are about 16, 42 and 75 basis points, respectively, at the forecast horizons of 6, 12 and 18 months; in the latter, they are about 35, 107 and 184 basis points at the same horizons. On the contrary, for the United States, in the same sample period, excess returns are significantly countercyclical; in recessions they are about 1.5 to 3 times larger than in other periods (see Table 2b). At forecast horizons of 6, 12 and 18 months they are, respectively, about 65, 125 and 160 basis points in recession, while they are about 20, 70 and 125 during expansions. As official real GDP data are frequently revised and usually released with different delays in the two regions, these results may be affected by the differences on the information set available to market participants at the moment that contract prices are settled. Therefore, we investigate the predictability of the excess returns running regressions of the form x (n) t+n = α (n) + β (n) z t + γ (n) f (n) t + (n) t+n (4) where z t is a business cycle proxy known to operators in real time and not subject to ex-post revisions. 8 In particular, we select two different sets of variables: first, we use (one at the time) the year-on-year change 6 The business cycle component is extracted by means of a Band Pass filter a la Baxter and King (1996). We select frequencies between 6 and 40 quarters and set up the control size of symmetric moving average equal to 8. All results outlined in this section are robust to the use of alternative filters, such as a Band-Pass (8,32,8) or a Hodrick-Prescott (1600) one. 7 We notice that the size of the business cycle component of real GDP in the sample period is ranging between 0,1 and 1,8 in economic expansions, while, between -0,1 and -2,1 in recessions. 8 The estimated regressions also include the futures rate itself as additional predictor. It would represent a scale variable, based on the idea that the excess returns are lower when the level of interest rates is lower, and vice versa. Results suggest that this variable is not significant at forecast horizons up to 6 months, while at longer horizons the estimated coefficients are significantly positive. 5

6 of the percentage balances referring to the replies collected in the surveys of the European Commission for the manufacturing industry, consumers, the construction and the retail trade sectors 9.Asallthesedata are not released until the last week of the month, in order to perform predictive regressions in real-time, we use those referring to the second month of the indicated quarter. As an alternative, we use the time series for real GDP growth rate expectations measured by the quarterly Consensus Forecasts survey. These variables, by definition, do not depend on future monetary policy shock realizations, therefore, they can be considered contemporaneously predetermined in the corresponding predictive regressions of type (4), avoiding problems of spurious correlations. 10 In Table 3a we only report the results obtained using as predictive regressor the employment expectations for the months ahead collected in the survey of manifacturing industry, as we find this variable to have the best properties in terms of significance and goodness of fit (higher values for the statistic R 2 ) among the entire set of potential explanatory variables. The slope coefficients confirm the view that the excess returns are positively correlated with the business cycle in the euro area; precisely, they are significantly positive and increase with the forecast horizon. The fitted values imply that estimated excess returns are ranging between 15 and 170 basis points, on average, during expansions, while they are between 5 and 70 basis points during recessions. In particular, at a one-year horizon they are, respectively around 100 and 35 basis points. Similar results are obtained using the other business cycle indicators (see Table A3 of the Appendix). In general, among the entire set of variables, we find confidence indicators collected from the survey in the manifacturing industry, as well as the expectations on future real GDP by Consensus Economics, to be good candidates for excess returns predictive regressions. 11 In Table 3b we report the results of the regression (5) fortheunitedstates,inthesamesampleperiod, using the quarterly year-on-year change in nonfarm payrolls as business cycle indicator, as suggested by Piazzesi and Swanson (2004). 12 The countercyclicity of the U.S. excess return is still confirmed, but, 9 For each survey we consider separately the overall index and the components one by one, because some of them may have better indicator properties than their corresponding overall index. In order to screen a narrower set of variables among the large amount of available survey data, we performed a preliminary cross correlation analysis at business cycle frequencies between each of them and real GDP. This roughly search allowed us to select the leading and coincident indicators and drop the lagging ones. When a variable is found to be leading by n quarters, we compared the results obtained by including this variable as lagged (by up to n lags) or contemporaneous. 10 As suggested by Piazzesi and Swanson (2004) for the United States, we also checked for the predictive power of some term spreads. We find weak leading properties of term spreads for forecasting the euro area short-term interest rates, in line with some previous studies. Davis and Fagan (1997), Berg and Van Bergejik (2000) and Nicoletti-Altimari (2001), found that the slope of the yield curve has no marginal predictive content for output growth and inflation using bivariate regressions. Recently, Nobili (2005) argued that these results still hold in a multivariate context using bayesian VAR models with time-varying coefficients. 11 We also run alternative regressions including simultaneously two or more business cycle indicators as explanatory variables. Results in terms of both goodness of fit are very similar to those obtained using a single regressor and gains in out-of-sample forecast accuracy are tiny or negligible. 12 The authors also provide evidence about the significant predictive power of yield spreads and corporate bond spreads for U.S. excess returns. We do not report results obtained with alternative regressors in order to save space. We only notice 6

7 differently form Piazzesi and Swanson (2004) the magnitude of the slope coefficient increases with the forecast horizon. In recessions excess returns are higher by 1.2 to 1.8 times than in periods of booms. At a one-year horizon they are, respectively, about 100 and 70 basis points. Finally, we check the robustness of our results at shorter horizons (up to 9 quarters ahead) substituting the future-based excess returns with those implicit in the term structure of interest rates, both in euro and dollars. 13 Forward rates may embody different risk premia with respect to futures rates because of the nature of the underlying contracts. As futures contracts are marked to market every day, cash-flow movements connected with payments or withdrawing to reconstituite the collateral margins, may imply a spread between futures and forward rates. The terms of a forward contract are settled exclusively by the two parties, meaning that the buyer of the contract may face off asignificant credit risk; the size of credit risk implied in a futures contract can be supposed to be negligible beacuse of the role of the clearinghouse during the trade. The estimated coefficients are reported in Table A1 and A2 of the Appendix. Ex-post excess returns based on forward rates are still, on average, positive and significanlty different from zero both in the euro area and the United States; in addition, they seem to be higher than their counterparts based on futures rates at all forecast horizons considered. Regressions based on business cycle indicators provide further evidence on the prociclicity of excess returns in the euro area and counterciclicity in the United States. Remarkably, the magnitude of the slope coefficients is close to the one obtained using futures rates. 2.3 Forecasts accuracy In the previous sections we have seen that excess returns are significantly different from zero, time-varying and predictable by means of business cicle indicators. Now, we investigate the gains in out-of-sample forecast accuracy using adjusted futures rates. The design of the experiment is based on rolling endpoint regressions. An initial estimate of excess returns at the different horizons is obtained using the sample period 1992q1-1993q4; we use the estimate to compute a set of out-of-sample forecasts for future interest rates up to 18 months E t (i t+n )=f (n) t E t (bx (n) t+n). (5) that, despite the euro area, expectations on future U.S. real GDP growth rates collected from Consensus Forecasts survey seem to be not a good candidate in the sample period we considered. 13 Precisely, the 3-months forward rate prevailing n-quarters ahead can be computed as fw (n) t = r (n) t r (n 1) t where r (n) t is the yield of a risk-free bond quoted at time t and expiring t + n quarters ahead. Due to the lack in financial markets of bonds expiring from 15 to 18 quarters ahead,we cannot build directly 3-months forward rates prevailing at horizons over 9 quarters. An alternative could be offered by the interpolation method developed by Nelson and Siegel. 7

8 Then, we add a new observation and repeat the forecasting exercise, until the end of the sample period. Overall we collect a set of 44 out-of-sample predictions at each forecast horizon. In Table 4 we report some summary statistics on forecast accuracy, such as the mean error (ME) and the root-mean-squared error (RMSE). We perform a Diebold-Mariano test, in order to check whether the errors obtained under the adjusted predictions are significantly different from their counterparts obtained with unadjusted futures rates. 14 For completeness, we allow a comparison with the forecasting performance of some alternative techniques used in the literature, namely, a random walk, an ARIMA and a Bayesian VAR. 15 For the euro area, unadjusted future rates tend to predict short-term interest rates better than the three alternative competitors only at shorter horizons (up to two quarters ahead), while at longer ones they perform relatively poorly. 16 Constant-adjusted futures rates already produce lower root-mean-squared errors at all forecast horizons, even if the gains in forecast accuracy are small and often not significant. Adjusting futures rates for the business cycle improves further our predictions: the associated squared errors are, on average, lower by an amount that increases with the forecast horizon and ranges between 10 and 45 per cent with respect to unadjusted futures rates. For the United States the picture is similar. Unadjusted futures rates strongly outperform the alternative models up to two quarters ahead but generate larger squared forecast errors at longer horizons. Correcting market forecasts for the predictable components of the excess returns leads to gains in predictive accuracy, which are significantly larger when we adjust for time-varying component (the RMSE is between 20 and 50 per cent lower than under the unadjusted futures rates). Notice that these gains are, on average, larger for the United States than in the euro area, at all forecast horizons. This result may depend on the fact that excess returns are countercyclical in the former and procyclical in the latter. Indeed, during expansions, futures adjusted for the time-varying excess return subtract, in addition to the constant term, a positive component from the quoted future in the euro area, while they add it in the United States. The opposite occurs in recessions: business cycle 14 See Diebold and Mariano (2002). This test statistic is essentially a t-statistic in a regression of the differences in the root-mean-squared errors for two alternative forecasts on a constant term. 15 Specifically, we set trivariate domestic BVAR models comprising the short-term interest rate, the inflation rate (based on the HCPI index for the euro area and the CPI index for the U. S.) and a measure of real economic activity (employment expectations in the manufactoring sector for the euro area and nonfarm payrolls for the U.S.). In order to perform a real-time forecasting exercise, for the last two variables we used their year-on-year changes referring to the second month of the indicated quarter. 16 Notice that, the ARIMA model seems to produce better forecasts than the BVAR. This result in part confirms the view that more sophisticated model are not good candidate forecasts for euro area short-term interest rates. Recently Neri and Secchi (2004) found that the predictions of the euro area short-term interest rates (computed as quarterly averages of daily data) up to four quarters ahead provided by unadjusted futures rates strongly outperform those derived by means of a simple DSGE model and a BVAR-DSGE approach a la Del Negro and Schorfheide (2004). On the contrary, at longer horizons the forecasting performances of these competitor models become very similar and not far from those obtained using a naive random walk. 8

9 adjusted forecasts subtract a negative term from the futures rates in the United States, while they add an equivalent one in the euro area. As a result, squared errors are lower in booms (recessions) than in recessions (booms) in the euro area (United States). Table 5 shows that gains in forecast accuracy in expansion periods in the euro area and in recessions in the United States are on average by about the same amount (respectively 41 and 48 basis points). On the contrary, in periods of expansions in the US and recessions in the euro area - when adjusted forecasts are less accurate in both countries - the corresponding gains are larger in the former. 3 Excess returns decomposition The existing literature on risk-adjusted measures of financial instruments uses the term risk premium to refer to the predictable excess return on the short-term interest rate. In this section we ask whether it is possible to identify the risk premia with the predictable excess returns of the previous sections. We start by assuming that the ex-post excess return realized from holding the n-quarter-ahead contract to maturity can be separated in two different components: x (n) t+n = θ (n) t + σ (n) t+n (6) where and θ (n) t = f (n) t E(i t+n I t ) (7) σ (n) t+n = E (i t+n I t ) i t+n (8) The first, θ (n) t,representstheex-ante risk-premium required by the investors at the moment they settle the futures contract price. It is defined as the difference between the futures contract rate and the market s expectation about future short-term interest rate, conditionally to the information set available to the agents. The second, σ (n) t+n,defined as the difference between the conditional expectation on future rate and the ex-post realized spot rate, represents an ex-post systematic forecast error which is not linked to the nature of the financial contract. The assessment of this second component is a relevant issue in terms of credibility and transparency of the monetary policy. Being this part of the excess return connected to the process of formation of expectations, it is clearly affected by the efficacy of communication and it can represent a measure of how monetary policy decisions are perceived by market agents. 9

10 The main difference between E(i t+n I t ) and f (n) t is that the former is a measure of expectations that is not related directly to any financial contract and therefore should not include neither risk nor liquidity premium. As a proxy for E(i t+n I t ) we use three different measures that can be considered, by definiton, as cleared by the ex-ante risk premium. Precisely, we consider the time series of professional forecasters expectations on future short-term interest rate collected in the survey by Consensus Forecasts, the forecasts obtained with the ARIMA model and those resulting from a BVAR. In Tables 6 we report estimates of the two identified components by running the following regressions σ (n) t+n = α (n) σ + (n) t+n (9) θ (n) t = α (n) θ + η (n) t. Note that, by construction, the sum of the two estimated components, bα (n) σ the same amount of the estimated constant excess return reported in Table 1 (bα (n) ). and bα (n) θ,hastobeby The decompositions implied by the different proxies provide similar results. In the euro area, the computed systematic prediction errors are significant at all forecast horizons and, on average, much larger than the corresponding risk premia. When we use interest rates expectations obtained from Consensus Forecasts, the ex-ante risk premium ranges from 5 to 30 basis points, while the systematic prediction error is between 5 and 95 basis points. Therefore the latter component accounts by about 70 per cent of the overall predictable excess returns, at horizons larger than 3 months. The presence of large systematic prediction errors implies the violation of the rational expectations hypothesis and may be explained with learning phenomena connected to structural changes in the economy, as the process of convergence to EMU. For the United States opposite results arise. Risk premia are significantly positive and much larger than the corresponding systematic errors at all forecast horizons. Precisely, they represent a fraction of overall excess returns, which is decreasing with the forecast horizon and ranges between 90 and 60 per cent. In order to investigate the business cycle properties and the predictability of the two components σ (n) t+n and θ (n) t, we report in Table 7 the estimates of the following regressions σ (n) t+n = α (n) σ θ (n) t = α (n) θ + β (n) σ + β (n) θ 10 z t + γ (n) σ z t + γ (n) θ f (n) t f (n) t + (n) t+n (10) + η (n) t

11 Intheeuroareabothcomponentsareprocyclical. The empirical evidence that the difference between the conditional expectations on future rates and the ex-post realized spot rates is bigger in periods of economic expansions could be interpreted as exuberance phenomena: market agents tend to over-estimate future economic conditions when they face booms and underestimate them in periods of recessions. Precisely, ex-post systematic errors are during expansions higher by an amount ranging between 60 and 70 basis points at horizons over one year. In the United States both risk premia and systematic errors are instead found to be countercyclical, as the overall excess return. 4 Assessing monetary policy expectations Results outlined in the previous section have important implications for the central banks. Even if futures rates adjusted for both the risk premium and the systematic prediction error are the best predictors of future monetary policy decisions, they do not coincide anymore with financial markets expectations. Therefore, the correct assessment of financial markets view about the path of monetary policy should be conducted by policymakers using quoted futures rates adjusted only by risk premia, as systematic forecast errors represent part of agents expectations formation process. The spread between risk-adjusted futures rates and spot interest rates can be considered an ex-post measure of the efficacy of monetary authorities communication, as well as the transparency of their policy strategy. In order to provide some practical examples, we compare the term structure of interest rates implied in adjusted and unadjusted futures rates 17 with the ex-post realized pattern of spot rates over time, on two illustrative dates. In the upper panel of Figure 3 we report euro area short-term interest rates forecasts on September On that date, the spot three-month interest rate was close to 3.75 per cent and the euro area was experiencing an expansion phase. Therefore, according to the quoted futures prices, the short-term interest rates were expected to gradually rise in the subsequent periods, reaching a value of 4.5 per cent. As the ex-post realized spot rate declined at 2.75 per cent, futures based forecasts were very misleading on that date. Notice that both constant-adjusted and overall-adjusted futures rates would have implied more accuarate forecasts, but market agents view about future monetary policy signalled rising interest rates because of the large systematic prediction error. 17 Precisely, using z t and f (n) t as predictive regressors, we derive the implied forecasts on the short-term interest rates as E t (i t+n )=f (n) t (bα (n) OLS + β b (n) OLS z t + bγ (n) OLS f (n) t ). 11

12 On the other hand, the lower panel suggests that, in March 2002, when the United States faced a slowdown of real economic activity, futures rates signaled a gradual and persistent rise of future interest rates over time, by about 100 basis points within one year and a half, while the spot rate pattern was declining. Both constant and overall-djusted futures rates implied stable interest rate, consistently with financial markets expectations. 5 Concluding remarks In this paper, we provided new evidence that futures contracts rates are biased forecasts of future shortterm interest rates. We found large and time-varying excess returns on three-months interest rates futures in the euro area, confirming the results obtained by Piazzesi and Swanson (2004) for the United States. We find that, excess returns are predictable using business cycle indicators avaialble to market participants in real-time, in both regions, but they are procyclical in the euro area and countercyclical in the United States. Therefore, futures rates adjusted for the time-varying excess returns generate lower prediction errors in the euro area during booms and in the United States during recessions. We also showed that ex-post excess returns can be divided into two different components. The first is the effective ex-ante risk premium required by the investors at the moment of buying or selling the financial contract. The second is the ex-post systematic forecast error, which is independent from the financial instrument considered and provides useful information about the efficacy of the monetary policy communication and the transparency of policy decisions. The empirical analysis reveals that both components are predictable and positively correlated with the business cycle in the euro area. Among them, the systematic prediction error was by far more important in explaining overall excess returns, suggesting the presence of both exuberance and lerning phenomena. A similar decomposition for the United States leads, instead, to opposite results. The two identified components are both countercyclical and the risk-premium represents by far the larger fraction of the overall excess return. From the point of view of the central bank, the main implication is that a correct assessement of market agents expectations about the path of monetary policy should be conducted using quoted futures rates adjusted only for the risk premium, as the sistematic prediction error represents part of the expectation formation process. Indeed, futures rates adjusted for both components are better forecasts of future monetary policy actions but they do not coincide anymore with finanacial markets view. 12

13 Table 1 EX-POST CONSTANT EXCESS RETURNS (A) EURO AREA n α (n) 9.8** 24.3** 45.5** 70.8** 96.7** 122.7** (2.5) (2.8) (3.2) (3.4) (3.7) (4.0) R (B) UNITED STATES n α (n) 17.9** 39.5** 63.9** 89.9** 116.3** 138.9** (2.9) (2.9) (2.9) (2.7) (2.7) (2.7) R Notes: the sample period is 1992:1-2004:4. Excess returns are measured in basis points. Estimation by OLS. Newey-West HAC t-statistics are reported in parentheses. denotes significance at 10 per cent confidence level. denotes significance at 5 per cent confidence level. 13

14 EX-POST TIME-VARYING EXCESS RETURNS AND THE BUSINESS CYCLE Table 2 (A) EURO AREA n α (n) 9.7** 24.2** 45.6** 71.5** 97.9** 124.1** (2.6) (2.9) (3.4) (3.8) (4.2) (6.5) β (n) * 36.8** 52.1** 62.5** (0.6) (1.3) (1.8) (2.3) (2.7) (3.5) R (B) UNITED STATES n α (n) 18.9** 41.6** 66.1** 91.5** 116.8** 138.8** (3.3) (3.3) (3.3) (3.0) (2.9) (3.8) β (n) -14.1** -29.5** -38.0** (-2.3) (-2.5) (-2.0) (-1.4) (-0.7) (-0.5) R Notes: the sample period is 1992:1-2004:4. Excess returns are measured in basis points. Estimation by OLS. Newey-West HAC t-statistics are reported in parentheses. denotes significance at 10 per cent confidence level. denotes significance at 5 per cent confidence level. 14

15 Table 3 EX-POST TIME-VARYING EXCESS RETURNS AND BUSINESS CYCLE INDICATORS (A) EURO AREA (employment expectations) n α (n) (0.8) (0.3) (-0.4) (-1.2) (-1.2) (-1.9) β (n) 0.5** 1.2** 1.9** 2.3** 2.5** 2.2** (2.9) (3.9) (4.6) (4.4) (4.0) (4.2) γ (n) * 0.12** 0.26** 0.38** 0.51** (0.8) (1.8) (3.0) (4.2) (3.4) (4.4) R (B) UNITED STATES (nonfarm payrolls) n α (n) -11.7** -60.0** ** ** ** ** (-1.1) (-3.3) (-3.8) (-4.6) (-4.0) (-4.3) β (n) -0.2** -0.6** -0.8** -1.1** -1.2** -1.2** (-4.5) (-7.7) (-9.0) (-9.1) (-7.8) (-7.7) γ (n) 0.2** 0.4** 0.6** 0.9** 1.1** 1.3** (3.6) (6.1) (6.5) (6.9) (5.8) (6.3) R Notes: the sample period is 1992:1-2004:4. Excess returns, nonfarm payroll employment growth and futures rates are measured in basis points. Estimation by OLS. Newey-West HAC t-statistics are reported in parentheses. denotes significance at 10 per cent confidence level. denotes significance at 5 per cent confidence level. 15

16 Table 4a OUT-OF-SAMPLE FORECASTS OF SHORT-TERM INTEREST RATES EURO AREA futures rates based unadjusted constant business cycle adjusted adjusted n ME RMSE ME RMSE ME RMSE alternative models based random walk ARIMA BVAR Consensus n ME RMSE ME RMSE ME RMSE ME RMSE Notes: the sample period used for the out-of-sample exercise is 1994:1-2004:4. ME is the Mean Error, RMSE is the Root-Mean-Squared Error, expressed in basis points. and are referred to the results of a Diebold-Mariano test; they denote the rejection of the null hypothesis that there is no difference in the forecasting precision between the indicated model and the unadjusted futures, at a significance level, respectively, of 10 and 5 per cent. 16

17 Table 4b OUT-OF-SAMPLE FORECASTS OF SHORT-TERM INTEREST RATES UNITED STATES futures rates based unadjusted constant business cycle adjusted adjusted n ME RMSE ME RMSE ME RMSE alternative models based random walk ARIMA BVAR Consensus n ME RMSE ME RMSE ME RMSE ME RMSE Notes: the sample period used for the out-of-sample exercise is 1994:1-2004:4. ME is the Mean Error, RMSE is the Root-Mean-Squared Error, expressed in basis points. and are referred to the results of a Diebold-Mariano test; they denote the rejection of the null hypothesis that there is no difference in the forecasting precision between the indicated model and the unadjusted futures, at a significance level, respectively, of 10 and 5 per cent. 17

18 Table 5 GAINS IN FORECAST ACCURACY AND THE BUSINESS CYCLE EURO AREA n expansions recessions average UNITED STATES n expansions recessions average Notes: gains in forecast accuracy are computed as the differences in the Root-Mean- Squared Errors between forecasts obtained using business cycle-adjusted futures rates and those using constant-adjusted futures rates (expressed in basis points). 18

19 CONSTANT EXCESS RETURN DECOMPOSITION (A) EURO AREA α (n) θ α (n) σ Table 6 α (n) n ARIMA BVAR Consensus ARIMA BVAR Consensus ** 14.5** ** ** 29.7** 17.6* 24.3** ** 44.8** 35.0** 45.5** ** 59.9* 55.3** 70.8** * 77.1** 73.1* 73.0** 96.7** ** 91.2** 86.2* 94.3** 122.7** α (n) θ (B) UNITED STATES α (n) σ α (n) n ARIMA BVAR Consensus ARIMA BVAR Consensus ** 15.0** 38.7** ** 17.9** ** 34.4** 46.7** ** ** 57.9** 57.3** ** ** 81.7** 66.4** ** ** 105.7** 78.1** ** ** 125.7** 87.2** ** Notes: the sample period is 1992:1-2004:4. Excess returns are measured in basis points. Estimation by OLS. t-test are based on Newey-West HAC t-statistics. denotes significance at 10 per cent confidence level. denotes significanceat5percentconfidence level. 19

20 Table 7a TIME-VARYING EXCESS RETURN DECOMPOSITION - EURO AREA (employment expectations) n α (n) θ (0.8) (0.2) (-0.2) (-0.8) (-0.9) (-1.2) β (n) θ ** 0.9** 1.0** 1.0** 0.8* (1.5) (2.0) (2.0) (2.2) (2.1) (1.9) γ (n) θ * (-0.2) (0.3) (0.7) (1.2) (1.3) (1.9) R n α (n) σ (-0.1) (0.1) (-0.1) (-0.7) (-0.8) (-1.3) β (n) σ ** 1.3** 1.5** 1.4** (0.7) (1.3) (2.3) (2.7) (2.8) (2.7) γ (n) σ ** 0.27** 0.36** (0.6) (0.7) (1.4) (2.5) (2.6) (3.3) R Notes: the sample period is 1992:1-2004:4. Excess returns are measured in basis points. Estimation by OLS. Newey-West HAC t-statistics are reported in parentheses. denotes significance at 10 per cent confidence level. denotes significance at 5 per cent confidence level. 20

21 Table 7b TIME-VARYING EXCESS RETURN DECOMPOSITION - UNITED STATES (nonfarm payrolls) n α (n) θ ** -75.2** ** ** (0.2) (-1.6) (-2.3) (-3.9) (-4.2) (-6.0) β (n) θ * -0.16** -0.18** -0.18** (0.6) (-0.9) (-1.6) (-2.2) (-2.5) (-2.9) γ (n) θ 0.08** 0.17** 0.24** 0.32** 0.39** 0.48** (2.3) (3.7) (4.6) (6.4) (7.3) (9.2) R n α (n) σ * -69.8* ** ** ** (-1.0) (-1.7) (-1.7) (-2.3) (-2.1) (-2.2) β (n) σ -0.26** -0.54** -0.73** -0.95** -1.05** -1.07** (-3.7) (-4.5) (-4.8) (-5.7) (-5.4) (-5.8) γ (n) σ ** 0.39** 0.58** 0.74** 0.80** (1.3) (2.6) (2.9) (3.5) (3.2) (3.5) R Notes: the sample period is 1992:1-2004:4. Excess returns are measured in basis points. Estimation by OLS. Newey-West HAC t-statistics are reported in parentheses. denotes significance at 10 per cent confidence level. denotes significance at 5 per cent confidence level. 21

22 Table A1 EX-POST EXCESS RETURNS BASED ON FORWARD RATES EURO AREA constant business cycle α (n) 14.4** 42.6** 44.4** 14.4** 42.5** 44.5** (4.0) (4.1) (3.0) (4.0) (4.2) (3.4) β (n) ** (0.6) (1.2) (2.5) γ (n) R employment expectations real GDP expectations α (n) (0.5) (-1.1) (-1.1) (1.4) (-0.6) (-0.2) β (n) 0.48** 1.16** 1.89** 9.46** 21.86** 38.92** (2.8) (3.6) (4.6) (2.2) (2.2) (3.3) γ (n) 0.25** 0.14** 0.16** ** 0.12* (1.8) (3.9) (4.2) (1.2) (4.2) (1.8) R Notes: the sample period is 1992:1-2004:4. Excess returns are measured in basis points. Estimation by OLS. Newey-West HAC t-statistics are reported in parentheses. denotes significance at 10 per cent confidence level. denotes significance at 5 per cent confidence level. 22

23 Table A2 EX-POST EXCESS RETURNS BASED ON FORWARD RATES UNITED STATES constant business cycle α (n) 26.7** 51.4** 82.5** 27.9** 53.7** 84.7** (4.1) (3.6) (3.7) (4.7) (4.2) (4.1) β (n) ** -31.7** -37.2** (-2.6) (-2.8) (-2.1) γ (n) R nonfarm payrolls real GDP expectations α (n) ** ** (-1.3) (-3.5) (-4.1) (0.7) (-0.1) (-0.5) β (n) -0.25** -0.61** -0.86** ** ** * (-4.5) (-7.5) (-8.9) (-3.0) (-2.9) (-1.9) γ (n) ** 0.66* 0.05* 0.12** 0.20** (4.1) (6.6) (7.1) (1.8) (2.2) (2.6) R Notes: the sample period is 1992:1-2004:4. Excess returns are measured in basis points. Estimation by OLS. Newey-West HAC t-statistics are reported in parentheses. denotes significance at 10 per cent confidence level. denotes significance at 5 per cent confidence level. 23

24 Table A3 TIME-VARYING EXCESS RETURNS AND BUSINESS CYCLE INDICATORS EURO AREA industrial confidence indicator (export order books) α (n) ** β (n) 0.46** 1.05** 1.63** 2.00** 2.13** 1.94** γ (n) ** 0.24** 0.36** 0.50** R industrial confidence indicator (overall index) α (n) ** β (n) 0.59** 1.33** 2.10** 2.70** 3.07** 3.02** γ (n) ** 0.27** 0.39** 0.52** R consumer confidence indicator (general economic situation over next 12 months) α (n) β (n) 0.43* 1.10** 1.49** 1.78** 1.66** 1.29 γ (n) * 0.22** 0.35** 0.50** R expected real GDP (Consensus Forecasts) α (n) β (n) 7.93* 23.48** 38.10** 46.17** 47.11** 41.43** γ (n) * 0.37** 0.51** R Notes: the sample period is 1992:1-2004:4. Excess returns are measured in basis points. The industrial confidence (both the overall index and the export book level) and the consumer confidence are measured in annual percentage changes based on the original percentage balances. The expected real GDP is the business cycle component of expected year-on-year growth rates, extracted by means of a Band-Pass filter considering cycles between 6 and 40 quarters and a size for the symmetric moving average equal to 8. All the regressors included in the estimated equations are lagged by one quarter. Estimation by OLS. Newey-West HAC t-statistics are reported in parentheses. denotes significance at 10 per cent confidence level. denotes significance at 5 per cent confidence level. 24

25 Ex-post excess returns on euro area futures contracts (basis points) Figure n= n= n= n= n= n=

26 Ex-post excess returns on U.S. futures contracts (basis points) Figure n= n= n= n= n= n=

27 Euro area short-term interest rates forecasts (19th September 1997) Figure unadjusted futures ex-post spot rates constant-adjusted risk-adjusted overall-adjusted 3m 6m 9m 12m 15m 18m United States short-term interest rates forecasts (18th March 2002) unadjusted futures ex-post spot rates constant-adjusted risk-adjusted overall-adjusted 3m 6m 9m 12m 15m 18m References [1] Baxter, M. and R. G. King (1995), Measuring Business Cycles: Approximate Band-Pass Filters for Economic Time Series, NBER Working Paper, No [2] Berk, J. M. and P. Van Bergeijk (2000), Is the Yield Curve a Useful Information Variable for the Eurosystem? European Central Bank, Working Paper Series, No

28 [3] Davis, E. P. and G. Fagan (1997), Are Financial Spreads Useful Indicators of Future Inflation and Output Growth in EU Countries, Journal of Applied Econometrics, Vol. 12, No. 6, pp [4] Del Negro, M. and F. Schorfheide (2004), Priors from General Equilibrium Models for VARs, International Economic Review, Vol. 45, No. 2, pp [5] Diebold, F. X. and R. S. Mariano (2002), Comparing Predictive Accuracy, Journal of Business & Economic Statistics, Vol. 20, No. 1, pp [6] Durham, B. (2003), Estimates of the Term Premium on Near-Dated Federal Funds Futures Contracts, Federal Reserve Board, FED Working Paper, No. 19. [7] Gurkaynak Refet S., Sack B. and E. Swanson (2004), Market-Based Measures of Monetary Policy Expectations, Board of Governors of the Federal Reserve System, Division of Monetary Affairs, mimeo. [8] Krueger, J. T. and K. N. Kuttner (1996), The Fed Funds Futures Rate as a Predictor of Federal Reserve Policy, Journal of Futures Markets, Vol. 16, No. 8, pp [9] Kuttner, K. N. (2001), Monetary Policy Surprises and Interest Rates: Evidence from the Federal Funds Futures Market, Journal of Monetary Economics, Vol. 47, No. 3, pp [10] Neri, S. and A. Secchi (2005), Bayesian Forecasting Models for the Euro Area: New Evidence on the Information Content of M3, Banca d Italia, mimeo. [11] Nicoletti-Altimari, S. (2001), Does Money Lead Inflation in the Euro Area?, European Central Bank, Working Paper Series, No. 63. [12] Nobili, A. (2005), Forecasting Output Growth and Inflation in the Euro Area: Are Financial Spreads Useful?, Banca d Italia, Temi di Discussione, No [13] Seppala, J. (2004) The Term Structure of Real Interest Rates: Theory and Evidence from UK Index-Linked Bonds, Journal of Monetary Economics, Vol. 51, pp [14] Piazzesi, M. and E. Swanson (2004), Futures Prices as Risk-Adjusted Forecasts of Monetary Policy, NBER Working Paper, No [15] Rudebusch, G. D. (1998), Do Measures of Monetary Policy in a Var Make Sense?, International Economic Review, Vol. 39, No. 4, pp