Risk, Ambiguity, and Anomalies in the Fixed Income Market

Open Access
Shi, Zhan
Graduate Program:
Business Administration
Doctor of Philosophy
Document Type:
Date of Defense:
May 02, 2014
Committee Members:
  • Jingzhi Huang, Dissertation Advisor
  • Jingzhi Huang, Committee Chair
  • Heber Farnsworth, Committee Member
  • Joel Matthew Vanden, Committee Member
  • Jared Williams, Committee Member
  • Runze Li, Committee Member
  • Knightian uncertainty
  • asset pricing
  • equity premium
  • term premium
  • credit spreads
This dissertation contains five essays on the implications of risks and ambiguity for asset pricing puzzles, especially in the fixed income market. The first essay studies the effects of time-varying Knightian uncertainty (ambiguity) on equilibrium asset prices; the second and third essays focus on the term premia in the nominal and real Treasury bond markets; The last two examine the performance of structural models of credit risk in explaining the levels and changes of corporate yield spreads. In the first essay, I consider a continuous-time Lucas exchange economy in which an ambiguity-averse agent applies a discount rate that is adjusted not only for the current magnitude of ambiguity but also for the risk associated with its future fluctuations. As such, both the ambiguity level and volatility help raise asset premia and accommodate richer dynamics of asset prices. With a novel measure for the ambiguity level, I show that the estimated model is able to explain a wide range of asset markets anomalies, including the equity premium puzzle, the risk-free rate puzzle, the credit spread puzzle, and the expectations puzzle. In particular, this paper establishes both theoretical and empirical linkages of ambiguity with the unspanned predictability in the Treasury market. Furthermore, the proposed ambiguity measure is found to exhibit significant predictive power for excess returns on equities and bonds as well as for corporate yield spreads, a finding that justifies uncertainty channels highlighted in the model. The remaining four essays are based on work that is coauthored with Professor Jingzhi Huang. In the second chapter, we provide new and robust evidence on the power of macro variables for forecasting bond risk premia by using a recently developed model selection method--the supervised adaptive group "least absolute shrinkage and selection operator" (lasso) approach. We identify a single macro factor that can not only subsume the macro factors documented in the existing literature but also can substantially raise their forecasting power for future bond excess returns. Specifically, we find that the new macro factor, a linear combination of four group factors (including employment, housing, and price indices), can explain the variation in excess returns on bonds with maturities ranging from 2 to 5 years up to 43%. The new factor is countercyclical and furthermore picks up unspanned predictability in bond excess returns. Namely, the new macro factor contains substantial information on expected excess returns (as well as expected future short rates) but has negligible impact on the cross section of bond yields. In the third essay, we document a number of new empirical findings about the dynamic behavior and economic determinants of risk premia on real bonds. Specifically, we find that the real bond risk premium changes over time and fluctuates between positive and negative values. We also find that the real term structure itself contains a component that drives risk premia but is undetectable from cross section of bond yields. In addition, we present evidence on the link between real bond premia and macroeconomic variables. More specifically, we find that macro factors associated with real estate and consumer income and expenditure can capture a large portion of forecastable variation in excess returns on real bonds. These empirical findings have important implications for both affine term structure models and consumption-based asset pricing models of real bonds. The fourth essay provides new insights into the equity-credit market integration puzzle. Empirical evidence has documented that while variables suggested by structural credit risk models can explain only a small portion of corporate bond spread changes (Collin-Dufresne, Goldstein, and Martin 2001), these models provide quite accurate predictions of hedge ratios for corporate bond returns (Schaefer and Strebulaev 2008). These two stylized facts together are often considered to have conflicting implications for the level of integration between equity and credit markets -- given the fundamental relationship between corporate bond spread changes and returns. we provide a rational explanation of this anomaly by demonstrating that the two aforementioned seemingly conflicting findings can be reconciled with each other within the standard structural modeling framework. In particular, we show empirically that sensitivities of spread changes to leverage ratio or equity predicted by the Merton (1974) model are not rejected in time-series tests -- namely, the Merton hedge ratios for spread changes are too consistent with data. That is, the equity-credit market integration puzzle can be explained from a traditional hedging perspective. In the last essay, we empirically examine the hedging performance of structural models using data on corporate bond transaction prices over the period July 2002--December 2012 from the Trade Reporting and Compliance Engine (TRACE) database. While there is a large literature on the pricing performance of structural credit risk models, there is little empirical evidence on the empirical performance of these models on hedging corporate bonds. We find that the Merton (1974) model is not as useful as univariate regression models for the purpose of hedging corporate bond returns with equity. Further, for investment-grade bonds, hedging with Treasury bonds with a hedge ratio of unity is more effective than the Merton delta hedging with equity. However, we find that the Merton model is more useful for the purpose of hedging corporate bond spread changes, especially for high-yield bonds. Lastly, we also investigate the pricing performance of the Merton model. We find that on average the model overestimates (underestimates) prices (yield spreads) of bonds in our sample. Specifically, the model overestimates prices of corporate bonds by 1.87% on average. To sum, the evidence based on more recent data on transaction prices indicates that the Merton model still underpredicts yield spreads, especially for short-maturity or investment-grade bonds.