The 15 reference contexts in paper Christopher F. Baum, Basma Bekdache (1995) “Modeling Returns on the Term Structure of Treasury Interest Rates” / RePEc:boc:bocoec:288

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    BaumBasma Bekdache Department of EconomicsDepartment of Economics Boston CollegeWayne State University Chestnut Hill MA 02167Detroit MI 48202 June 1996 Introduction In this paper, we test the multivariate model of securities’ excess returns formulated by
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    Engle et al. (1990)
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    on an expanded set of maturities. By applying their methodology to the entire Treasury term structure, we consider the applicability of a parsimonious common factor approach to the dynamics of short-, medium-, and long-term interest rates.
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    zero to 12 months’ tenor discount bills, which are readily available from CRSP as the “Fama files.” In this study, we consider the entire Treasury term structure–for bills, notes, and bonds–so that both money market and capital market returns may be modeled. We make use of a set of monthly estimates of Treasury market spot yields constructed from coupon securities’ quotations by
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    Coleman et al. (1993,
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    CFI). Our work is based on the spot yields for the 14 specific tenors analyzed by CFI for their sample period of 1955 through 1992,1 transforming them into estimated one-month holding period returns.2 We model excess return series, created by subtracting the annualized holding period return on a one-month Treasury from the holding period return for each longer tenor.
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    term structure suggest that a workable term structure model should explicitly consider time variation in the second moments of residual series as well as capture the interaction among tenors. The following section presents such a model in which we have implemented time variation in the second moments, as well as asymmetry in the modelled conditional variances, using the approach of
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    Gourieroux and Monfort (1992).
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    2. Estimates of Factor-GARCH models for the Treasury term structure Term structure modelling has followed two broad strands of development: general equilibrium models, such as those pioneered by Cox, Ingersoll and Ross (1985), and no-arbitrage partial equilibrium models.
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    Estimates of Factor-GARCH models for the Treasury term structure Term structure modelling has followed two broad strands of development: general equilibrium models, such as those pioneered by
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    Cox, Ingersoll and Ross (1985), and
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    no-arbitrage partial equilibrium models. In this paper, we consider a model of the latter genre, developed by Engle et al. (1990), and extend it to the consideration of the complete Treasury term structure rather than just its short end.
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    Estimates of Factor-GARCH models for the Treasury term structure Term structure modelling has followed two broad strands of development: general equilibrium models, such as those pioneered by Cox, Ingersoll and Ross (1985), and no-arbitrage partial equilibrium models. In this paper, we consider a model of the latter genre, developed by
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    Engle et al. (1990), and
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    extend it to the consideration of the complete Treasury term structure rather than just its short end. In this framework, we consider whether time-varying volatility in asset returns is a meaningful determinant of excess returns in the medium and long-term sectors of the Treasury market.
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    The term structure literature contains scattered evidence that conclusions drawn from Treasury bill data do not readily extend to the medium and long term sectors of the Treasury market. For instance,
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    Engsted and Tangaard (1994)
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    extend the work of Hall, Anderson and Granger (1992) and study the cointegration properties of the term structure of interest rates, using 2-, 5-, and 10-year yields from McCulloch and Kwon’s (1993) data.
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    The term structure literature contains scattered evidence that conclusions drawn from Treasury bill data do not readily extend to the medium and long term sectors of the Treasury market. For instance, Engsted and Tangaard (1994) extend the work of
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    Hall, Anderson and Granger (1992) and
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    study the cointegration properties of the term structure of interest rates, using 2-, 5-, and 10-year yields from McCulloch and Kwon’s (1993) data. They find that the breakdown in the cointegrating relationship between short rates that occurs during the 1979-1982 Federal Reserve operating policy shift does not appear in the longer maturity term structure.
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    This suggests that risk premia behave differently over the maturity structure, and that the explanation that term premia become nonstationary with a regime shift may not hold true for longer maturities. Similar evidence is found in a study by
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    Froot (1989),
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    where survey data on interest rate expectations are used to study the relative importance of time-varying term premia and expectational errors in explaining rejections of the pure 3 The moving correlations are computed annually from 36 monthly observations; the date on the horizontal axis is the left endpoint of the three-year spa
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    They conclude that there are “nontrivial differences in the risk characteristics in agents investing at different maturities” (p. 64) and suggest that a segmented markets approach may be warranted.
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    Engle et al. (1990,
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    henceforth ENR) argue that a multivariate approach to the modelling of asset returns is clearly justified, since even in static asset pricing models, the full covariance matrix of asset returns is required to derive estimates of a single asset’s risk premium.
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    weighted bond portfolio and a pure stock portfolio–as sufficient, and apply a recursive representation where -4the stockmarket portfolio’s excess returns are generated in a univariate model, but the bond portfolio’s excess returns depend as well on the stockmarket portfolio’s behavior. 2.1 Excess returns for Treasury and stockmarket index portfolios We use the
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    henceforth CFI) yields to construct estimates of one-month holding period returns. Comparable returns on a diversified stock portfolio are derived from the CRSP value-weighted index for the NYSE/AMEX, which is first available in July 1962.
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    Although the number of significant eigenvalues does not specifically indicate the number of dynamic factors appropriate for our model, it would appear that a two-factor model might be able to capture the behavior of the excess returns series. 2.2 Asymmetric GARCH models of portfolio excess returns Following
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    p.223), we do not attempt to determine portfolio weights within the model, but rather specify weights for two factor-representing portfolios: an equally-weighted bond portfolio and a portfolio containing only the stockmarket index.
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    As noted above, the set of tenors for Treasuries in our data imply that the equally-weighted bond portfolio will have risk characteristics approximately equal to a 5.5-year tenor security. In fitting a GARCH model to the portfolio excess returns series, we considered various asymmetric forms of the basic GARCH model. Other researchers (cf.
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    Gourieroux and Monfort (1992))
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    have found support for asymmetries in either the mean equation or the conditional variance equation of the GARCH formulation. In the context of the factor-representing portfolios’ excess returns, we might expect the conditional variance to respond differently to increases and decreases in risk.
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    In a first application, we model the security excess returns as a linear function of the two portfolios’ excess return series, with a conditional variance given by a linear function of the two portfolios’ conditional variances. This model (analogous to
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    Engle et al., (1990,
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    p.226)) may be written as: Ri,t=iλ+iBondβtBondˆR+iStockβtStockˆR+i,tυ υi,tt−1ℑ~N0,i,th() hi,t=iσ+iBond 2 β Bondt θˆ+ Stocki 2 β Stockt θˆ (4) This model incorporates a constant, λ, in the mean equation, to capture nontime-varying components of the individual security’s risk premium (for instance, the “on-the-run” effect that newly auctioned Treasury securities exhibit, in which their
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    While the β coefficients are highly significant for all tenors, examination of their asymptotic standard errors indicate that the direct effect of the stockmarket portfolio’s excess returns and conditional variance is of considerable importance for short-term Treasury returns, but never meaningful for tenors greater than two years. In contrast to
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    p.226), we found that the stockmarket index has significant direct effects on the 3-12 month segment of the yield curve. Since the stockmarket factor does not appear to play a direct role in the individual securities’ excess returns and conditional variances for medium or long tenors, we respecify the model as a single-factor model in which the estimated excess return and con
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    We are investigating the feasibility of this approach, which is computationally burdensome. -10the model should be contrasted with the general equilibrium models of the term structure, such as that of
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    Cox, Ingersoll and Ross (1985),
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    which generate perfect correlations among rates at all tenors. The correlations of these predicted values are quite consistent with the original excess return series to which they are fit; for instance, the correlations between 3-month securities’ excess returns and those of 1-, 2-, 5- and 20-year securities are 0.768, 0.685, 0.550, and 0.381 over the full sample, wh
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