Keywords: forward rates, sensitivity puzzle, affine term structure model, risk premia
Abstract:
The purpose of this paper is to separate the reaction of U.S. Treasury forward rates to macroeconomic news into components attributable to term premia and expected future short rates. The analysis employs the decomposition of forward rates into expected future short rates and term premia made possible by a standard affine, noarbitrage, threefactor model of the term structure. Such modelling permits a closer look at the nature of interest rate sensitivity than recent research whose scope has been confined to nominal forward rates. I confirm that distanthorizon nominal forward rates are sensitive to current economic news and monetary policy surprises but show that movements in term premia, not expected future short rates, account for most of the reaction.
Specifically, movements in term premia account for about three quarters of the reaction of nominal forward rates 10 to 15 years hence in response to a range of important macroeconomic surprises. This has strong implications for the interpretation of interestrate sensitivity, namely, that longhorizon expectations of inflation and real rates are reasonably well anchored in the United States, contrary to recent conjecture by Gürkaynak, Sack, and Swanson (2005) (GSS). Why term premia exhibit such sensitivity to economic news and monetary policy surprises is not clearcut. It may represent changing uncertainty (a change in the quantity of risk), a change in the price of risk, or a behavioral overreaction to new information.
These findings are relevant to what is meant by "wellanchored expectations". Are interestrate expectations well anchored when expectations of future nominal policy rates mean revert at reasonable horizons following the release of new information? Or must uncertainty about longrun interest rate expectations also be fairly insensitive to current macroeconomic surprises? The results shown in this paper suggest that the second condition is not met in U.S. Treasury markets. The paper is structured as follows. Section 2 gives a brief overview of the affine termstructure model used to generate the decompositions, describes the data and presents the estimation strategy. Section 3 presents and discusses the results and considers an alternative estimate of the term premium and Section 4 concludes.
The model of the nominal term structure is the implementation by Kim and Orphanides (2005) of a model proposed by Duffie (2002) using three underlying latent factors to describe the timeseries behavior of the U.S. yield curve. As is standard in affine termstructure models, the model hinges on the fundamental asset pricing condition
where is the gross nominal return on a zerocoupon bond at time and is a stochastic discount factor derived from a standard utility maximization problem of a representative investor. The simple nature of zerocoupon bonds allows the price of an period bond to be expressed recursively asThe financial data for the analysis consist of zerocoupon yields and forward rates from an estimated nominal Svensson yield curve for U.S. Treasuries. The zerocoupon yields are used to estimate the parameters of the affine factor model described above, and once estimated, the model provides decompositions of forward rates into expected future nominal short rates and term premia. Daily changes in the oneyear forward rates and their components are then employed as dependent variables in announcement regressions.
The macroeconomic data consist of the surprise elements of thirteen major U.S. data releases and a monetarypolicy target surprise. The macroeconomic surprises are nearly identical to those of GSS (2005) but the sample enddate has been extended from December 2002 to October 2005 and missing observations replaced.^{3} Following GSS, the surprise component of a macroeconomic data release is measured as the released value less the market expectation reported the prior Friday by Money Market Services (MMS, provided by Action Economics), and each surprise series is divided by its standard error. To facilitate comparison with earlier results, the macroeconomic variables included in the regressions are the subset of releases deemed by GSS to be significant determinants of the oneyear forward rate ending one year hence; namely, capacity utilization, consumer confidence, core CPI, civilian employees' employment cost index, advance GDP, initial jobless claims, index of leading indicators, ISM PMI index (NAPM), new home sales, change in nonfarm payrolls, core PPI, retail sales and the unemployment rate.^{4} The monetary policy surprise is measured as the daily change in the current or next month's futures contract around an FOMC announcement, as recommended by Kuttner (2001).
Daily changes in forward rates, expected nominal short rates and term premia from the affine factor model are regressed at various horizons on the surprise components of macroeconomic data releases. The equations to be estimated take a simple form:
(2)  
(3)  
(4) 
Two points are worth making here. First, the fit of the factor model is sufficiently good that coefficient estimates from regressions using the fitted forward rates are indistinguishable from those using the Svenssoncurve forward rates. Second, while there may be measurement error present in and , as long as this measurement error is uncorrelated with the surprise components of the data releases, it will not bias the coefficient estimates but just sacrifice precision.
Table 1 presents the estimated coefficients from equation (2) from regressing daily changes in Svensson forward rates and the fitted factormodel forward rates on economic news variables for the sample January 1990 to December 2002. The columns marked GSS report the results published in GSS (2005). The coefficients estimated from fitted forward rates are very similar to the Svensson forward rates and the standard errors remain small, testimony to the good fit of the threefactor model. Only the coefficient on advance GDP differs noticeably, with the replacement of missing data points lowering the estimated response by one third. Table 2 presents the same regressions updated to include data to endOctober 2005, also plotted as the solid black line in Figures 2 to 4 (95 percent confidence intervals are shown as dashed lines). Extending the sample has little effect on the coefficients or standard errors.
Table 3 presents the results of equations (3) and (4) for expected future short rates and term premia. The coefficient estimates are summarized in Figures 2 to 4 along with 95 percent confidence intervals. Several points are worth making. First, as expected, the estimated coefficients on the expected short rate and term premium sum to the coefficient on the nominal forward rate at each maturity. Second, it is immediately clear that the majority of the sensitivity of longhorizon forward rates is due to the response of term premia to macroeconomic surprises. Between 70 and 80 percent of the total response at 10 years can be attributed to movement in term premia. Expected nominal short rates respond strongly to macroeconomic shocks in the near term but the response then declines smoothly over the forecast horizon to a small (but precisely estimated) response 10 years hence. The minimal response of expected future nominal short rates at long horizons suggests that the sum of longrun inflation expectations and the perceived equilibrium real rate is reasonably well anchored in the United States.
The term premia response at long horizons dominates the expected shortrate response for all economic news variables used as regressors. Positive inflation surprises and realside surprises cause expected future short rates to rise in the near term, while term premia dominate in the longer run. Notably, nonfarm payrolls surprises seem to elicit a larger response of expected nominal short rates than other variables, suggesting that this important release prompts the most revision to longrun expectations. Weakerthanexpected inflation and realside news are associated with lower term premia. One possible reason for this is that investors may demand less compensation for inflation risk when news indicates that inflation outcomes are likely to be lower, consistent with the positive correlation between the level and volatility of inflation discussed by Svensson (1997) and Mishkin and Westelius (2006), among others.
The reaction of forward rates to a monetarypolicy surprisedefined as the unexpected target surprise of an FOMC decisionis particularly interesting. Positive policy surprises elicit a small rise in nominal shortrate expectations in the near to medium term, but short rates are then projected to revert slowly to their preshock level within a decade. In contrast, a positive policy surprise is associated with a decline in the term premium at all horizons, sufficient to offset the rise in nominal short rate expectations. The connection between tighter monetary policy with a lower market price of risk, or a larger market appetite for assets, could be consistent with monetarypolicy tightening lowering market uncertainty, especially the compensation that investors demand for inflation risk.
Cochrane and Piazzesi (2005) estimate bond term premiums by regressing excess bond returns on the term structure of forward rates, where excess bond returns are measured as the return on holding an year bond over the return on holding a oneyear bond for a holding period of one year. Their resulting forecasting factor shares a high correlation (0.71) with the term premium on a oneyear forward rate 5years hence estimated by the threefactor model. Thus it comes as no surprise that estimating equation (3) on daily changes in the return forecasting factor reveals significant reactions to the same news surprises that move term premia (see Table 4). And because excess returns at different horizons are proportional to the return forecasting factor, this implies that the response does not diminish with maturity, the same property seen clearly in Figures 2, 3 and 4 for the affine factor model's term premia.
An important question to ask at this point is whether the results are an artifact of the construction of the threefactor model. The factors of the arbitragefree model are estimated as unobservable, latent factors without macroeconomic data input, and as such the regressions presented here do not exploit preconstructed relationships between expected interest rates, term premia and economic news. Therefore, the assumption that any measurement error in the term premium and expected future shortterm rates estimated by the threefactor model should be uncorrelated with the MMS surprises seems reasonable. Similar results to those presented here are obtained using the forwardrate decomposition from a threefactor model augmented with Blue Chip survey inflation expectations (Kim and Orphanides, 2005). These survey expectations presumably incorporate information about macroeconomic surprises comparable to that in MMS expectations used to derive the surprise regressors and, accordingly, the results differ little.
The affine termstructure model also has the characteristic that its latent factors are stationary. However, the half life of the most persistent factor is over 10 years, so gradual that fitted term premia and expected short rates can be far from their means for very long periods. The coefficients, and thus the decomposition of the sensitivity puzzle, are quite insensitive to increasing the persistence of the most persistent factor as done by Wright (2006). It is also important to remember that term premiums and expected short rates are fitted jointly in the model and as such, both are functions of the same three factors. Freely estimated coefficients determine the affine combination of factors that represent the best fit of the data.
This paper has shown that expectations of the central bank's policy rate account for only a small fraction of the response of longhorizon forward rates to news. The finding casts doubt upon explanations of long forwardrate sensitivity that posit that data surprises prompt changes in perceptions of the central bank's inflation target, or perceptions of equilibrium real interest rates. Such explanations overlook the role of adjustment of risk premia in response to new information, which appear to dominate the response at long horizons.
Term premia at all maturities rise in response to strongerthanexpected real and inflation news, and in response to surprise policy easings. This is true of both the term premia estimated by the affine factor model and Cochrane and Piazzesi's (2005) return forecasting factor. This procyclicality contrasts with the common finding that term premia are somewhat countercyclical. The two are not necessarily at odds, however, as countercyclicality is found at the businesscycle frequency and need not reflect the highfrequency reaction of term premia in short windows around macroeconomic news announcements.
Indeed, the nature of the termpremium response to newsdeclining with weakerthanexpected macroeconomic data and tighter monetary policyis suggestive of a role for inflation risk premia. Paired with the findings of Gürkaynak, Levin, and Swanson (2005), that longhorizon inflation compensation (comprising expected future inflation and an inflation risk premium) also responds to macroeconomic news, it seems likely that inflation risk premia are variable in the United States. However, to accurately parse out the effect of news announcements on inflation risk premia and real risk premia requires termstructure models that can identify both quantities and is the subject of ongoing research.
Macroeconomic data releases and Monetary Policy Surprises  Ending 1 year ahead  GSS  Ending 1 year ahead  Threefactor model  Ending 5 years ahead  GSS  Ending 5 years ahead  Threefactor model  Ending 10 years ahead  GSS  Ending 10 years ahead  Threefactor model 

Capacity utilisation  ($1.33)  ($1.32)  ($1.57)  ($1.57)  ($1.61)  ($1.61) 
Consumer confidence  ($1.40)  ($1.40)  ($1.56)  ($1.52)  ($1.54)  ($1.51) 
CPI (core)  ($1.42)  ($1.40)  ($1.60)  ($1.54)  ($1.66)  ($1.52) 
Employment cost index  ($1.89)  ($1.86)  ($1.13)  ($1.98)  ($1.93)  ($1.87) 
GDP (advance)  ($1.42)  ($1.24)  ($1.19)  ($1.62)  ($1.82)  ($1.43) 
Initial Claims  ($1.24)  ($1.41)  ($1.29)  ($1.41)  ($1.27)  ($1.33) 
Leading Indicators  ($1.34)  ($1.33)  ($1.57)  ($1.53)  ($1.58)  ($1.55) 
NAPM  ($1.51)  ($1.49)  ($1.54)  ($1.53)  ($1.63)  ($1.54) 
New home sales  ($1.39)  ($1.42)  ($1.54)  ($1.56)  ($1.51)  ($1.51) 
Nonfarm payrolls  ($1.57)  ($1.56)  ($1.91)  ($1.90)  ($1.97)  ($1.87) 
PPI (core)  ($1.45)  ($1.43)  ($1.56)  ($1.51)  ($1.50)  ($1.51) 
Retail sales  ($1.72)  ($1.68)  ($1.03)  ($1.90)  ($1.92)  ($1.87) 
Unemployment Rate  ($1.51)  ($1.47)  ($1.73)  ($1.66)  ($1.66)  ($1.63) 
Monetary Policy Surprises  ($1.10)  ($1.08)  ($1.14)  ($1.10)  ($1.07)  ($1.09) 
Notes: NeweyWest standard errors. *** indicates significance at the 1percent level, ** at the 5percent level and * at the 10percent level. Coefficients in columns labelled 'GSS' are values reported in GSS
(2005). The estimated coefficients represent the basispoint repsonse of the oneyear forward rate per standard deviation of the macroeconomic release surprise and per basispoint surprise in monetary policy announcements. Constant terms not shown.
Macroeconomic data releases and Monetary Policy Surprises  Ending 1 year ahead: Jan 1990  Dec 2002  Ending 1 year ahead: Jan 1990  Oct 2005  Ending 5 years ahead: Jan 1990  Dec 2002  Ending 5 years ahead: Jan 1990  Oct 2005  Ending 10 years ahead: Jan 1990  Dec 2002  Ending 10 years ahead: Jan 1990  Oct 2005 

Capacity utilisation  ($1.32)  ($1.29)  ($1.57)  ($1.48)  ($1.61)  ($1.52) 
Consumer confidence  ($1.40)  ($1.37)  ($1.52)  ($1.51)  ($1.51)  ($1.48) 
CPI (core)  ($1.40)  ($1.36)  ($1.54)  ($1.48)  ($1.52)  ($1.46) 
Employment cost index  ($1.86)  ($1.89)  ($1.98)  ($1.03)  ($1.87)  ($1.83) 
GDP (advance)  ($1.24)  ($1.98)  ($1.62)  ($1.30)  ($1.43)  ($1.16) 
Initial Claims  ($1.41)  ($1.30)  ($1.41)  ($1.32)  ($1.33)  ($1.27) 
Leading Indicators  ($1.33)  ($1.34)  ($1.53)  ($1.48)  ($1.55)  ($1.50) 
NAPM  ($1.49)  ($1.42)  ($1.53)  ($1.50)  ($1.54)  ($1.49) 
New home sales  ($1.42)  ($1.31)  ($1.56)  ($1.43)  ($1.51)  ($1.39) 
Nonfarm payrolls  ($1.56)  ($1.50)  ($1.90)  ($1.81)  ($1.87)  ($1.75) 
PPI (core)  ($1.43)  ($1.34)  ($1.51)  ($1.39)  ($1.51)  ($1.40) 
Retail sales  ($1.68)  ($1.59)  ($1.90)  ($1.82)  ($1.87)  ($1.73) 
Unemployment Rate  ($1.47)  ($1.45)  ($1.66)  ($1.65)  ($1.63)  ($1.61) 
Monetary Policy Surprises  ($1.08)  ($1.08)  ($1.10)  ($1.10)  ($1.09)  ($1.09) 
Notes: NeweyWest standard errors. *** indicates significance at the 1percent level, ** at the 5percent level and * at the 10percent level. The estimated coefficient indicates the basispoint repsonse of the oneyear forward rate per standard deviation of the macroeconomic release surprise and per basispoint surprise in monetary policy announcements. Constant terms not shown.
Macroeconomic data releases and Monetary Policy Surprises  Ending 1 year ahead: Short rate  Ending 1 year ahead: Term premium  Ending 5 years ahead: Short rate  Ending 5 years ahead: Term premium  Ending 10 years ahead: Short rate  Ending 10 years ahead: Term premium 

Capacity utilisation  ($1.29)  ($1.18)  ($1.35)  ($1.10)  ($1.44) 

Consumer confidence  ($1.37)  ($1.19)  ($1.37)  ($1.09)  ($1.41) 

CPI (core)  ($1.36)  ($1.15)  ($1.36)  ($1.08)  ($1.40) 

Employment cost index  ($1.89)  ($1.40)  ($1.71)  ($1.20)  ($1.73) 

GDP (advance)  ($1.98)  ($1.41)  ($1.05)  ($1.23)  ($1.03) 

Initial Claims  ($1.30)  ($1.13)  ($1.23)  ($1.06)  ($1.24) 

Leading Indicators  ($1.34)  ($1.16)  ($1.38)  ($1.07)  ($1.46) 

NAPM  ($1.42)  ($1.21)  ($1.38)  ($1.10)  ($1.43) 

New home sales  ($1.31)  ($1.14)  ($1.33)  ($1.07)  ($1.35) 

Nonfarm payrolls  ($1.50)  ($1.24)  ($1.63)  ($1.14)  ($1.65) 

PPI (core)  ($1.34)  ($1.15)  ($1.29)  ($1.07)  ($1.35) 

Retail sales  ($1.59)  ($1.28)  ($1.58)  ($1.15)  ($1.62) 

Unemployment Rate  ($1.45)  ($1.22)  ($1.50)  ($1.11)  ($1.54) 

Monetary Policy Surprises  ($1.08)  ($1.03)  ($1.07)  ($1.02)  ($1.07) 
Notes: NeweyWest standard errors. *** indicates significance at the 1percent level, ** at the 5percent level and * at the 10percent level. The estimated coefficient indicates the basispoint repsonse of the oneyear forward rate per standard deviation of the macroeconomic release surprise and per basispoint surprise in monetary policy announcements. Constant terms not shown.
Macroeconomic data releases and Monetary Policy Surprises  Response 

Capacity utilisation  ($1.08) 
Consumer confidence  ($1.08) 
CPI (core)  ($1.11) 
Employment cost index  ($1.43) 
GDP (advance)  ($1.69) 
Initial Claims  ($1.66) 
Leading Indicators  ($1.02) 
NAPM  ($1.30) 
New home sales  ($1.06) 
Nonfarm payrolls  ($1.82) 
PPI (core)  ($1.99) 
Retail sales  ($1.79) 
Unemployment Rate  ($1.27) 
Monetary Policy Surprises  ($1.23) 
Notes: NeweyWest standard errors. *** indicates significance at the 1percent level, ** at the 5percent level and * at the 10percent level. The estimated coefficient indicates the repsonse of Cochrane and Piazzesi's return forecasting factor per one standarddeviation macroeconomic release surprise and per basispoint surprise in monetary policy announcements. Constant terms not shown.