Introduction Data and Empirical Method Empirical Results Conclusion Determinants of Bond Risk Premia Jing-zhi Huang and Zhan Shi Smeal College of Business Penn State University Waterloo Research Institute in Insurance, Securities and Quantitative Finance University of Waterloo May 15, 2012 Huang and Shi (Penn State Smeal) Determinants of Bond Risk Premia 1 / 31
Introduction Data and Empirical Method Empirical Results Conclusion Outline Introduction 1 Motivation What we do Data and Empirical Method 2 Data Used Methods for Model Selection The Proposed Two-Step Model Selection Empirical Results 3 In-sample Analysis Out of Sample Analysis Conclusion 4 Huang and Shi (Penn State Smeal) Determinants of Bond Risk Premia 2 / 31
Introduction Data and Empirical Method Motivation Empirical Results What we do Conclusion Focus of the Study Prediction of (default-free) bond excess returns: r ( n ) t +1 − y (1) = rx ( n ) t +1 = γ ′ Z t + ǫ t +1 (1) t where r ( n ) t +1 : an n-yr zero-cpn Treasury bond’s 1-yr log holding period return over [ t , t + 1] y (1) : the log yield of a 1-yr zero-cpn at time t t rx ( n ) t +1 : excess return of an n-yr zero over [ t , t + 1] Z t : forecasting variables Huang and Shi (Penn State Smeal) Determinants of Bond Risk Premia 3 / 31
Introduction Data and Empirical Method Motivation Empirical Results What we do Conclusion Examples of Predictors Identified Empirically: Yield curve factors Forward Spreads: Fama and Bliss (1987) Yield Spreads: Campbell and Shiller (1991) Forward Rates: Stambaugh (1988), Cochrane and Piazzesi (2005) Factors estimated from a DTSM: Duffee (2011) Decomposition of yields: Cieslak-Povala (2010) Macroeconomic factors Predetermined Economic Measures: Duffee (2007) (using inflation, GDP growth, 3m T-bill) Factors extracted from a set of macros: Ludvigson and Ng (2009) Interest rate derivatives factors Realized jump measures constructed from Treasury futures prices: Wright and Zhou (2009) Huang and Shi (Penn State Smeal) Determinants of Bond Risk Premia 4 / 31
Introduction Data and Empirical Method Motivation Empirical Results What we do Conclusion Recent Empirical Evidence Cochrane-Piazzesi (2005; CP): Z t =5 fwd rates R 2 = 30 ∼ 35% by a linear comb of the fwd rates Ludvigson-Ng (2009; LN): Z t =Factors estimated from a set of 131 macro R 2 = 26% by the LN factor alone Containing substantial info beyond CP: raising the R 2 from 31% to 44% Duffee (2011): Z t =5 factors estimated from a DTSM R 2 = 37% by the factors Wright and Zhou (2009): Z t = Realized jump measures R 2 ∼ 15% by the Jump mean R 2 = 60 − 62% when augmented w/ the CP factor cf : R 2 = 41 − 46% Cieslak-Povala (2010): cycle factor � Huang and Shi (Penn State Smeal) Determinants of Bond Risk Premia 5 / 31
Introduction Data and Empirical Method Motivation Empirical Results What we do Conclusion Recent Empirical Evidence (cont’d) The notion of the “hidden” forecasting factor (CP, LN, Duffee) Has substantial forecasting power for bond risk premia But has little impact on yields and “hidden” from the term structure E.g., Duffee’s 5th factor “has an imperceptible affect on yields but has substantial forecast power for future bond excess returns” Implications for term structure modeling: Affine TSMs: the important determinants of expected future yields are the important determinants of current yields Duffee (2011) and Barillas (2010) build DTSM where a factor affects dynamics but not current bond prices Huang and Shi (Penn State Smeal) Determinants of Bond Risk Premia 6 / 31
Introduction Data and Empirical Method Motivation Empirical Results What we do Conclusion Objectives Explore the predictability in bond markets beyond what have been documented from macroeconomic aggregates by Ludvigson-Ng (2008) Extract new macro factors w/ higher forecast power for risk premia using a shrinkage-type method Say more about the source of additional predictability Examine the link between the new predictors and existing ones (Cochrane-Piazzesi, Ludvigson-Ng, Duffee, Wright-Zhou, and Cieslak-Povala) Investigate the robustness of the explanatory power of macro variables for forecasting bond risk premia Provide new implications for term structure modeling Huang and Shi (Penn State Smeal) Determinants of Bond Risk Premia 7 / 31
Introduction Data and Empirical Method Motivation Empirical Results What we do Conclusion Preview of the Main Results Identifying a single macro factor with an R 2 up to 43%: Parsimonious and easy to interpret Related to economic measures in employment, housing and inflation Like other documented factors w/ forecast power, this factor Unspanned (affecting dynamics but not current bond prices) Subsuming both the Ludvigson-Ng (2009) single macro and Cooper-Priestley (2009) output gap factors Different from Duffee’s hidden factor, Wright-Zhou’s jump factor, and Cieslak-Povala’s cycle factor R 2 ∼ 54 − 58% The above 3 factors + our housing fac: ¯ Provide evidence on the robustness of this predictability (out of sample and small-sample analysis) Huang and Shi (Penn State Smeal) Determinants of Bond Risk Premia 8 / 31
Introduction Data Used Data and Empirical Method Methods for Model Selection Empirical Results The Proposed Two-Step Model Selection Conclusion Data Used 131 monthly macroeconomic time series used by Ludvigson-Ng From Global Insight Basic Economic database or the Fed Sample period: Jan. 1964 - Dec. 2007 8 categories: (1) output; (2) labor market; (3) housing sector; (4) orders and inventories; (5) money and credit; (6) bond and FX markets; (7) prices; and (8) stock market. Transformed data to ensure stationarity Treasury bond yields the Fama-Bliss dataset of CRSP monthly yields with maturities of 1 to 5 years Huang and Shi (Penn State Smeal) Determinants of Bond Risk Premia 9 / 31
Introduction Data Used Data and Empirical Method Methods for Model Selection Empirical Results The Proposed Two-Step Model Selection Conclusion Lasso Run the OLS using all macro variables available Over-fitting (poor out-of-sample performance) The resulting OLS predictor not intuitive Consider the following penalized least squares (PLS) func � N || y − X β || 2 + λ | β i | , (2) i =1 where λ ≥ 0 is a tuning parameter. The resulting estimator called the “least absolute shrinkage and selection operator” (lasso) estimator (Tibshirani, 1996) Many “useless” X variables dropped out Interpretability: The resultant model is much less complex than the OLS Forecasting accuracy: Improving the forecast power Huang and Shi (Penn State Smeal) Determinants of Bond Risk Premia 10 / 31
Introduction Data Used Data and Empirical Method Methods for Model Selection Empirical Results The Proposed Two-Step Model Selection Conclusion Two Variations of Lasso The Adaptive Lasso (Zou, 2006): � β ∈ R N || y − X β || 2 + λ min w i | β i | . (3) i where w i allows for different tuning parameters used for different predictors. The Group Lasso (Yuan and Lin, 2006): � β ∈ R N || y − X β || 2 + λ min || β h || . (4) h where h is the group index. Huang and Shi (Penn State Smeal) Determinants of Bond Risk Premia 11 / 31
Introduction Data Used Data and Empirical Method Methods for Model Selection Empirical Results The Proposed Two-Step Model Selection Conclusion Motivation for Using the Group Lasso A large set of macro variables Macroeconomic data often have cluster structure, where the clusters consist of “similar” time series Selected factors more intuitive Potential forecast power of lagged variables Limitations of factor analysis The analysis focusing on predictors themselves (unsupervised) (In statistical learning, a problem is supervised if the goal is to predict the value of an outcome based on numerous input measures) Factors involving linear combinations of “too many” macros Factors’ economic interpretation not always clear Huang and Shi (Penn State Smeal) Determinants of Bond Risk Premia 12 / 31
Introduction Data Used Data and Empirical Method Methods for Model Selection Empirical Results The Proposed Two-Step Model Selection Conclusion Supervised Adaptive Group Lasso (SAGLasso) We propose a two-step procedure (SAGLasso): 1 In each group/cluster, apply the adaptive lasso Y variable used: arx (a vector of average excess bond returns across maturity) 2 Apply the group lasso at the cluster level 3 Construct the single predictor using those selected groups Huang and Shi (Penn State Smeal) Determinants of Bond Risk Premia 13 / 31
Introduction Data and Empirical Method In-sample Analysis Empirical Results Out of Sample Analysis Conclusion Group Factors Selected after the 2nd Step Four out of eight groups selected: t ˆ g h t = X h β h , h = 1 , . . . , 4 . ˆ (5) (corresponding to the original groups #2, 3, 6, and 7) g 1 t (Employment and Income): Wachter (2006) g 2 t (Housing): Piazzesi et al. (2007) g 3 t (Bond Market) g 4 t (Prices): Brandt and Wang (2003) Single factor: 4 � � X h ˜ ˜ β g G ≡ h . (6) h =1 consisting of only 21 (out of 131) series and 38 variables (including lags) Huang and Shi (Penn State Smeal) Determinants of Bond Risk Premia 14 / 31
Recommend
More recommend
