Yield Curve Predictability, Regimes, and Macroeconomic Information: - PowerPoint PPT Presentation

COMPSTAT 2010, Paris Yield Curve Predictability, Regimes, and Macroeconomic Information: A Data-Driven Approach Francesco Audrino and Kameliya Filipova University of St. Gallen August 26, 2010 F. Audrino and K. Filipova COMPSTAT 2010 – 1 / 32

Overview ⊲ Overview � Introduction Introduction [Motivation, Related literature, Open issues] Modeling framework Model estimation � Modeling framework Empirical Results [Conditional dynamics] Conclusion � Estimation procedure [Best subset selection, Threshold estimation] � Empirical results [Optimal structure, Stylized facts, Forecasting] � Conclusion F. Audrino and K. Filipova COMPSTAT 2010 – 2 / 32

Overview ⊲ Introduction Motivation Example Two views Related literature Open questions Contributions Regimes Introduction Threshold models Modeling framework Model estimation Empirical Results Conclusion F. Audrino and K. Filipova COMPSTAT 2010 – 3 / 32

Motivation Overview Modelling the time-varying dynamics of interest rates is crucial Introduction for many diverse task, such as ⊲ Motivation Example � pricing assets and their financial derivatives; Two views Related literature Open questions � managing financial risk; Contributions Regimes Threshold models � conducting monetary policy; Modeling framework � forecasting. Model estimation Empirical Results To describe the term structure behavior, a wide variety of Conclusion methods has been proposed. Why yet another term structure model? F. Audrino and K. Filipova COMPSTAT 2010 – 4 / 32

A first look at the data Overview 16 Introduction Motivation 14 ⊲ Example Two views 12 Related literature 15 Open questions 10 Contributions 10 Yield Regimes 8 Threshold models 5 Modeling framework 6 2002 120 Model estimation 84 1994 60 1986 36 4 Empirical Results 24 1977 12 Time Maturity 1969 6 Conclusion 3 2 0 U.S. monthly Treasury Bill data taken from CRSP database for the period January 1961 - June 2005. F. Audrino and K. Filipova COMPSTAT 2010 – 5 / 32

Two views of the term structure Finance view: Overview � latent factor models - aim at perfectly fitting the term structure Introduction at any point in time in order to ensure that no arbitrage Motivation Example opportunities exist ⊲ Two views � but ... factors are latent. They don’t model how yields respond Related literature Open questions to macro variables. Contributions Regimes Affine Term Structure Models (ATSMs) [Duffie and Kan (1996); Dai Threshold models and Singleton (2000)] and their extensions - “essentially” ATSMs Modeling framework [Duffee (2002)], “extended” ATSMs, Quadratic Term Structure Models Model estimation (QTSMs), Dynamic Term Structure Models (DTSMs), . . . Empirical Results Macroeconomic view: Conclusion � short rate is set by the central bank, which adjusts the rate to achieve its economic stabilization goals � but ... they fit the historical interest data poorly. Dynamic Stochastic General Equilibrium (DSGE) models, Taylor (1993) rule and its extensions Clarida, Gali and Gertler (2000). F. Audrino and K. Filipova COMPSTAT 2010 – 6 / 32

Macro-finance models Main Idea: Since macroeconomic variables are correlated with Overview yields, incorporating these economic factors into a pure finance Introduction Motivation model usually improves the predictive performance and provides Example macroeconomic linkage. Two views ⊲ Related literature Common setup: reduced-form no-arbitrage models with Open questions Contributions continuous-time or discrete time (mostly Gaussian) diffusions, Regimes Threshold models following the tradition of DTSMs (ATSMs, QTSMs) Modeling framework Related Literature: Ang and Piazzesi (2003); Dewachter, Model estimation Lyrio, and Maes (2006); Dewachter and Lyrio (2006); Hoerdahl, Empirical Results Tristani, and Vestin (2006); Rudebusch and Wu (2007); Ang, Conclusion Boivin, and Dong (2007); Ang, Bekaert, and Wei (2007); Kim and Wright (2005); Buraschi and Jiltsov (2007); DAmico, Kim, and Wei (2008) among many others. However, the question how yields are associated with macro variables remains open. F. Audrino and K. Filipova COMPSTAT 2010 – 7 / 32

Open questions Overview While just a small number of factors are sufficient to model the Introduction cross sectional variation of yields, a couple of questions still Motivation remain open. Example Two views Related literature ◮ What is the number of factors needed to build a good ⊲ Open questions model for the time series dynamics? Contributions Regimes Threshold models ◮ How yields are associated with macro variables? Modeling framework Model estimation ◮ Is there any predictability of the macro variables on top of Empirical Results the latent factors? If yes, then how many and which Conclusion macroeconomic factors should be included in the model? ◮ Do these variables always have the same impact on the yields with different maturities? F. Audrino and K. Filipova COMPSTAT 2010 – 8 / 32

Contributions Overview We propose regime-switching multifactor model model for the Introduction term structure dynamics over time which Motivation Example � for every maturity we are able to identify or infer, in a Two views Related literature purely data-driven way, the most important macroeconomic Open questions ⊲ Contributions and latent variables driving both the local dynamics and Regimes the regime shifts; Threshold models Modeling framework � is able to replicate the most important stylized facts; Model estimation Empirical Results � while it remains highly competitive in terms of in- and Conclusion out-of-sample forecasting performance. As such, the modeling framework offers a clear interpretation and regime specification. F. Audrino and K. Filipova COMPSTAT 2010 – 9 / 32

Regime-switching models Overview Regime-switching models describe better the nonlinearities in the Introduction yields’ drift and the volatility found in the historical interest rate Motivation data. Example Two views Related literature Related literature: Ang and Bekaert (2002), Bansal and Zhou Open questions Contributions (2002), Dai, Singleton, and Yang (2007), Bansal, Tauchen, and ⊲ Regimes Threshold models Zhou (2004), Audrino and De Giorgi (2007) , Audrino (2006), Modeling framework Rudebusch and Wu (2007); Ang, Bekaert, and Wei (2007); ... Model estimation Empirical Results However instead of using the common Markovian Conclusion regime–switching framework, the regimes could be constructed as multiple tree-structured thresholds partitioning the predictor space into relevant disjoint regions. [Tong and Lim (1980); Audrino and B¨ uhlmann (2001); Audrino (2006); Audrino and Trojani (2006)] F. Audrino and K. Filipova COMPSTAT 2010 – 10 / 32

Why threshold models? Overview � The probability to be at any given time in a specific regime Introduction is related to some relevant macroeconomic and/or term Motivation Example structure variables. [monetary policy conduction] Two views Related literature � The regimes are determined endogenously. [forecasting] Open questions Contributions Regimes � We are able to disentangle macroeconomic from monetary ⊲ Threshold models policy changes. [clear regime interpretation] Modeling framework Model estimation � Provide better out-of-sample fit than the Markovian regime Empirical Results switching. [see, for example, Audrino (2006), Audrino and Conclusion Medeiros (2010)] F. Audrino and K. Filipova COMPSTAT 2010 – 11 / 32

Overview Introduction Modeling ⊲ framework Our approach Specification Conditional dynamics Model estimation Modeling framework Empirical Results Conclusion F. Audrino and K. Filipova COMPSTAT 2010 – 12 / 32

Our approach in brief Overview To infer the yield curve behavior, we use a model with four Introduction distinct features: Modeling framework ⊲ Our approach � to capture the cross sectional dynamics of the yield curve Specification we employ latent term structure factors; Conditional dynamics Model estimation � we allow heteroskedasticity in the error term; Empirical Results Conclusion � motivated by the interpretability and the improved forecasting performance of the macro-factor literature in comparison to the pure finance approach, we incorporate macroeconomic variables; � our model accommodates regime-switching behavior, but still allows interpretation and clear endogenous regime specification. F. Audrino and K. Filipova COMPSTAT 2010 – 13 / 32

Model specification Overview Let ∆ y ( t, n τ ) ≡ y ( t, n τ ) − y ( t − 1 , n τ ) denote the first difference Introduction of yields at time t with maturity n τ . We assume the following Modeling framework model for the term structure dynamics Our approach ⊲ Specification Conditional ∆ y ( t, n τ ) = µ (Φ t − 1 ,n τ ; ψ n τ ) + ε t,n τ , τ = 1 , . . . , T, dynamics Model estimation where Empirical Results � µ (Φ t − 1 ,n τ ; ψ n τ ) is a parametric function representing the Conclusion conditional mean; � � ε t,n τ = h (Φ t − 1 ,n τ ; ψ n τ ) z t is the error term of the yields’ returns with maturity n τ . ( z t ) t ∈ Z is a sequence of iid random variables with zero mean and unit variance, and h (Φ t − 1 ,n τ ; ψ n τ ) is the time-varying conditional variance. F. Audrino and K. Filipova COMPSTAT 2010 – 14 / 32