Abstract
In recent years, the concept of term premia has become a focus of attention for academics, policy makers as well as the investment community. This heightened attention was initially triggered by the puzzling behavior of long-term interest rates in the Unites States and in other industrialized countries (Greenspan, 2005). The interest-rate conundrum manifested itself in stable and even falling long-term bond yields despite a reversal in the short-term FED funds cycle. Over the period between June 2004 and February 2005, the FED decided to increase the target rate by over 120 basis points. Over the same time, the 10-year treasury rate lost temporarily over 100 basis points. Among the global saving glut, declining inflation expectations, reduced global macroeconomic and financial uncertainty were cited as explanations attempts, shrinking bond term premia though were the most promising fact to capture the conundrum within a coherent macroeconomic framework (Kim and Wright, 2005; Rudebusch et al., 2006; Backus and Wright, 2007).
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Notes
- 1.
See, for instance, Kohn (2005), Bernanke (2006), Plosser (2007) and Trichet (2008) among others for the United States and the euro area.
- 2.
For example, the Bundesbank identifies four main channels through which the financial crisis spread: (1) recklessness in securitization, (2) low risk perception, (3) slack lending standards and (4) high credit expansion in the aftermath of 2003 (Zeitler, 2009).
- 3.
At least in Keynes (1936), Chap. 13.
- 4.
The problem is that specific numerical values of the underlying parameters give rise to the same term structure. In this respect, invariant transformations of the original ATSM, by restricting and normalizing specific parameter constellations before the estimation, is a procedure to guarantee identification of the model and to present it in its canonical form. Dai and Singleton (2000) show that if one restricts a specific set of parameters, this allows to treat the more “interesting” parameters to the econometrician as free parameters.
- 5.
Most work on affine term structure models rely on US data. See for instance, Dai and Singleton (2002), Duffee (2002), Dai and Philippon (2005), Kim and Orphanides (2005), Kim and Wright (2005), Lemke (2006), Bolder (2006), Rudebusch and Wu (2007), D’Amico et al. (2008b), Pericoli and Taboga (2008) and Adrian and Wu (2009). For Germany, studies have been carried out by Cassola and Lus (2003), Fendel (2005) and Mayer (2008) and for the UK by Bianchi et al. (2009).
- 6.
See Singleton (2006) and Nyholm and Vidova-Koleva (2010) for the admissibility and identification conditions.
- 7.
The presence of latent factors make the model invariant to affine transformations. To identify the model, it is normalized by imposing the following restriction: (1) ϕ is upper-triangular, (2) Σis diagonal, (3) the mean μ of the latent factors are zero and (4) the loadings δ1on the short rate are each set to one. Furthermore, the parameter δ0is set to the long-run mean of the short rate in order to reduce the number of parameters to be estimated. The a-priori restrictions follow Dai and Philippon (2005).
- 8.
See Appendix B for details on the estimation.
- 9.
Especially, the diagonal elements of ϕ need to be smaller than 1 for stationarity. This is guaranteed by introducing ϕiiaux = − log(. 999 ∕ ϕii − 1). In addition, the covariance matrix Σneeds to be strictly positive which is derived by setting Σiiaux = log(Σii). Converting the two auxiliary matrices back in its original form reveals that the true values always fulfil the admissibility restrictions.
- 10.
A similar, but much more intensive hands-on procedure is proposed by Duffee (2009).
- 11.
The Matlab function to calculate the standard errors is partly provided by Piazzesi and Schneider (2007).
- 12.
As a test for robustness, the log-likelihood function also has been modified in the line of Chernov and Mueller (2008) by adding a term premium component to the log-likelihood function. It introduces an additional burden and uses term premia as a “last resort” in fitting yields. It basically means that the model first tries to fit yields via the expectations hypothesis. If this does not work, it allows term premia to do so. It turned out that the penalty did not alter results at all.
- 13.
One line of technical defense is that standard errors calculated with Matlab tend to be higher than with other software programs such as Fortran (Duffee, 2009).
- 14.
The US yield curve decomposition is not reported here but a similar result can be found in Rudebusch et al. (2007) for comparison.
- 15.
The authors build a modified affine term structure model based on monthly data. Their findings can be hardly captured in the quarterly frequency of the estimated model in this section.
- 16.
These findings are supported by Diebold et al. (2008). The authors identify a significant “global” yield curve factor that accounts for much of the variation in international yield curve dynamics.
- 17.
If the model is estimated with the assumption that λ1has zero entries in its off-diagonal elements or if it is even empty, the risk-adjusted coefficients would not lie near βEH.
- 18.
The restricted model implies a diagonal matrix of ϕ. The LR statistic is χ2with 1 degree of freedom. The 5 and 1% critical values are 3.84 and 6.64.
- 19.
Similar to the literature on default-free affine bond pricing of the previous Sect. 4.2, PDs from historical data refer to the physical probability measure; whereas PDs derived from bond prices are related to the risk-neutral measure. The difference results from the market price of credit risk per unit of this risk and it describes the systematic default risk which can not be diversified in portfolio optimization.
- 20.
The credit-risk literature attributes excess returns on defaultable bonds to a number of factors, including systematic, non-diversifiable risk, risk due to an insufficient number of defaultable bonds in portfolio allocation, liquidity risk, tax effects, contagion or a misspecified risk-free interest rate. See among others Longstaff (2004), Hull et al. (2005) and Collin-Dufresne et al. (2010).
- 21.
Typically, this fee is quoted in basis points per annum and payments follow a quarterly or semi-annul payment basis.
- 22.
For a review of recent sovereign lending episodes and default events see Andritzky (2006). The analysis of country risk, more generally, can be classified into (1) models of early-warning indicators, (2) studies on sovereign yield spreads and (3) studies on countries’ credit ratings; see Edwards (1986), Kaminsky and Reinhart (1999), Reinhart (2002), Pan and Singleton (2008) and Hilscher and Nosbusch (2010).
- 23.
Longstaff et al. (2007) find that two-third of sovereign credit risk can be linked to global factors whereby sovereigns spreads are related to US stock and corporate bond markets as well as global risk premia. Local economic measures matter less because there is little country-specific compensation for bearing local risk. Excess returns are earned for bearing global macroeconomic risk.
- 24.
Remolona et al. (2007) decompose international sovereign bond spreads into expected losses and risk premia. They find that risk premia account for a larger part of spreads so that international risk aversion as imbedded in the price of risk of unexpected losses play an important force in valuing government debt.
- 25.
See Codogno et al. (2003), Manganelli and Wolswijk (2009) and Favero et al. (2010) and the following Sect. 4.4on liquidity risk.
- 26.
See Bernoth et al. (2004), Sgherri and Zoli (2009) and Favero et al. (2010). International risk appetite is often proxied by the spread of US corporate bonds over US Treasury bonds.
- 27.
For a detailed approach to the risk-taking channel of monetary transmission see Chap. 7.2.
- 28.
This holds especially for Greece, Portugal, Spain and to some extend to Italy (European Comission, 2010).
- 29.
For the problem of real and nominal divergence and adjustment failures within the euro area see Geiger and Spahn (2007) and Wickens (2007).
- 30.
See Sgherri and Zoli (2009), Mody (2009), Haugh et al. (2009), Attinasi et al. (2009), Ejsing and Lemke (2009) and Schuknecht et al. (2010).
- 31.
Asset pricing deals with optimal pricing given a conditional information set. Agents require a higher return in case of increasing illiquidity costs. In contrast, realized (ex-post) returns depend positively on liquidity; they are greater if the liquidity of the asset is higher (than initially expected when the asset has been priced).
- 32.
A similar implication has been found in a model version of Holmström and Tirole (2001) and it is documented by Pastor and Stambaugh (2003) in US stock markets.
- 33.
The OIS spread is defined as the difference between the 3-month EURIBOR and the 3-month EONIA swap rate.
- 34.
The 3-month government interest rate is provided by ECB and it is the cross-country average of national government bonds with best credit-rating quality.
- 35.
As stated, changing interest-rate expectations might also have a significant influence on the EURIBOR spread. A positive spread could then be interpreted within a rising short-rate environment. However, the period under consideration clearly does not allow for such considerations. If anything, markets were expecting falling policy rates which should have narrowed the spread between current overnight and 3-month rates rather than increased it.
- 36.
For a theory of interest-rate determination within the portfolio and the stock of wealth setting see Spahn (1994).
- 37.
Many theories on liquidity preference build up on this theme. Hahn and Solow (1995, 144) point out that “there is thus a probability that a portfolio, once made, is not optimal in light of what will be learned. This consideration, when combined with transaction costs, leads to a premium on ‘liquid’ or low-transaction-cost assets. This premium is in nature of an option purchase.” Similarly, the user cost of money can be defined as the value of potential gains or losses that has been forgone or avoided by parting with money (Kregel, 1998). Likewise, Hicks (1974, 57) gives liquidity a social function as “it gives time to think.” Finally, Jones and Ostroy (1984, 13) highlight the possible liquidation costs associated with re-allocating a portfolio, in particular out of non-monetary positions: “The more variable are a decision maker’s beliefs, the more flexible is the position he will choose.”
- 38.
This transmission mechanism is closely related to the risk-taking channel of Chap. 7.2.
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Geiger, F. (2011). A Systematic View on Term Premia. In: The Yield Curve and Financial Risk Premia. Lecture Notes in Economics and Mathematical Systems, vol 654. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21575-9_4
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