Consumption risk and the cross-section of government bond returns

In this paper we provide a consumption-based explanation of risk in nominal US Treasury bond portfolios. We use a consumption-CAPM with Epstein–Zin–Weil recursive preferences. Our model introduces two sources of risk: uncertainty about current consumption (reflected in contemporaneous consumption growth) and uncertainty about prospects of consumption in a long run (reflected in innovations to expectations about future consumption growth). We use a novel approach to estimate pricing factors in our model: we employ a factor-augmented VAR model with common factors, extracted from a large panel of macroeconomic and financial data, as state variables. We find that the important source of risk in US bonds is related to uncertainty in prospects in future consumption and it induces a positive and significant risk premium. We find as well that covariance risk related to innovations in expectations about future consumption growth is greater for long term bond portfolios than for short term bond portfolios, which is consistent with a duration measure of risk and justifies why long term bonds require greater premium than short term bonds. Our model explains well the cross-sectional variation in average excess returns of bonds with different maturities over the period 1975–2011 and compares favorably with competing models.     

Long-run risk in durable consumption

Durable consumption growth is persistent and predicted by the price-dividend ratio. This provides strong and direct evidence for the existence of a highly persistent expected component. Durable consumption growth is left-skewed and exhibits time-varying volatility. I model durable consumption growth as containing a persistent expected component and driven by counter-cyclical volatility, nondurable consumption as a random walk, and dividend growth as exposed to the expected component of durable consumption growth. Together with nonseparable Epstein-Zin preferences, the model demonstrates that long-run risk in durable consumption can explain major asset market phenomena. The model also generates an upward-sloping real term structure.     

Asset pricing in production economies with extrapolative expectations

Introducing extrapolative bias into a standard production-based model with recursive preferences reconciles salient stylized facts about business cycles (low consumption volatility, high investment volatility relative to output) and financial markets (high equity premium, volatile stock returns, low and smooth risk-free rate) with plausible levels of risk aversion and intertemporal elasticity of substitution. Furthermore, the model captures return predictability based upon dividend yield, Q, and investment. Intuitively, extrapolative bias increases the variation in the wealth–consumption ratio, which is heavily priced under recursive preferences; adjustment costs decrease the covariance between marginal utility and asset returns. Empirical support for key implications of the model is also provided.     

Housing,consumption and asset pricing

This paper considers a consumption-based asset pricing model where housing is explicitly modeled both as an asset and as a consumption good. Nonseparable preferences describe households’ concern with composition risk, that is, fluctuations in the relative share of housing in their consumption basket. Since the housing share moves slowly, a concern with composition risk induces low frequency movements in stock prices that are not driven by news about cash flow. Moreover, the model predicts that the housing share can be used to forecast excess returns on stocks. We document that this indeed true in the data. The presence of composition risk also implies that the riskless rate is low which further helps the model improve on the standard CCAPM.     

The term structure of interest rates in a DSGE model with recursive preferences

A dynamic stochastic general equilibrium (DSGE) model in which households have Epstein and Zin recursive preferences is solved with perturbation. The parameters governing preferences and technology are estimated by maximum likelihood using macroeconomic data and the term structure of interest rates. The estimates imply a large risk aversion, an elasticity of intertemporal substitution higher than one, and substantial adjustment costs. Furthermore, the paper identifies the tensions within the model by estimating it on subsets of these data. The analysis concludes by pointing out potential extensions that may improve the model's fit.     

Intertemporally dependent preferences and the volatility of consumption and wealth

In this article we construct a model in which a consumer's utilitydepends on the consumption history. We describe a general equilibriumframework similar to Cox, Ingersoll, and Ross (1985a). A simpleexample is then solved in closed form in this general equilibriumsetting to rationalize the observed stickiness of the consumptionseries relative to the fluctuations in stock market wealth.The sample paths of consumption generated from this model implylower variability in consumption growth rates compared to thosegenerated by models with separable utility functions. We thenpresent partial equilibrium model similar to Merton (1969, 1971)and extend Merton's results on optimal consumption and portfoliorules to accommodate nonseparability in preferences. Asset pricingimplications of our framework are briefly explored.     

Heterogeneous time preferences and interest rates—the preferred habitat theory revisited

The influence of heterogeneous time preferences on the term structure is studied in the framework of a continuous-time pure exchange economy, in which agents have, apart from differential time preferences, the same degree of relative risk aversion. A closed-form solution for the financial equilibrium is obtained. In equilibrium, one long-term bond and one short-term bond form a complete market. Agents use these bonds to finance their consumption plans. The long-term bond is bought by agents with a long habitat. The short rate is a weighted average of the short rates which prevail in homogeneous economies populated by one type of agent only. It is shown by example that heterogeneity of time preferences can produce additional humps in the yield curve.     

Real term structure forecasts of consumption growth

This paper employs an empirically tractable affine term structure model of real interest rates to examine the predictive ability of the real short-term interest rate and its term spread with a longer-term interest rate to predict future real consumption growth. The estimates of the model provide support of the consumption smoothing hypothesis. The paper shows that the real term structure is spanned by two mean-reverting state variables. The mean-reverting property of these variables can consistently explain the forecasting ability of the short-term real rate and term spread to forecast future consumption growth rate, over different horizons ahead. Although the risks associated with changes in these variables are both priced in the market, they are not volatile enough to obscure the information of the real term structure about future real consumption growth.     

A Simulation Approach to Dynamic Portfolio Choice with an Application to Learning About Return Predictability

We present a simulation-based method for solving discrete-timeportfolio choice problems involving non-standard preferences,a large number of assets with arbitrary return distribution,and, most importantly, a large number of state variables withpotentially path-dependent or non-stationary dynamics. The methodis flexible enough to accommodate intermediate consumption,portfolio constraints, parameter and model uncertainty, andlearning. We first establish the properties of the method forthe portfolio choice between a stock index and cash when thestock returns are either iid or predictable by the dividendyield. We then explore the problem of an investor who takesinto account the predictability of returns but is uncertainabout the parameters of the data generating process. The investorchooses the portfolio anticipating that future data realizationswill contain useful information to learn about the true parametervalues.     

Inflation and productive activity in a multiple-matching model of money

This paper investigates the relationship between money growth, inflation, and productive activity in a dynamic general-equilibrium, multiple-matching framework where trade frictions are manifested by limited consumption variety. Productive activity and matching in the goods market are endogenized by a time allocation decision of work and search effort. We find that a high degree of complementarity between participation in the labor and goods markets creates a channel by which inflation can positively influence production and output. This feature arises when household preferences for consumption variety is sufficiently large and it can also lead to the multiplicity of monetary equilibria.     

Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles

We model consumption and dividend growth rates as containing (1) a small long‐run predictable component, and (2) fluctuating economic uncertainty (consumption volatility). These dynamics, for which we provide empirical support, in conjunction with Epstein and Zin's (1989) preferences, can explain key asset markets phenomena. In our economy, financial markets dislike economic uncertainty and better long‐run growth prospects raise equity prices. The model can justify the equity premium, the risk‐free rate, and the volatility of the market return, risk‐free rate, and the price–dividend ratio. As in the data, dividend yields predict returns and the volatility of returns is time‐varying.     

Taylor rules, McCallum rules and the term structure of interest rates

Recent empirical research shows that a reasonable characterization of federal-funds-rate targeting behavior is that the change in the target rate depends on the maturity structure of interest rates and exhibits little dependence on lagged target rates. See, for example, Cochrane and Piazzesi [2002. The Fed and interest rates—a high-frequency identification. American Economic Review 92, 90-95.]. The result echoes the policy rule used by McCallum [1994a. Monetary policy and the term structure of interest rates. NBER Working Paper No. 4938.] to rationalize the empirical failure of the ‘expectations hypothesis’ applied to the term structure of interest rates. That is, rather than forward rates acting as unbiased predictors of future short rates, the historical evidence suggests that the correlation between forward rates and future short rates is surprisingly low. McCallum showed that a desire by the monetary authority to adjust short rates in response to exogenous shocks to the term premiums imbedded in long rates (i.e. “yield-curve smoothing”), along with a desire for smoothing interest rates across time, can generate term structures that account for the puzzling regression results of Fama and Bliss [1987. The information in long-maturity forward rates. The American Economic Review 77, 680-392.]. McCallum also clearly pointed out that this reduced-form approach to the policy rule, although naturally forward looking, needed to be studied further in the context of other response functions such as the now standard Taylor [1993. Discretion versus policy rules in practice. Carnegie-Rochester Conference Series on Public Policy 39, 195-214.] Rule. We explore both the robustness of McCallum's result to endogenous models of the term premium and also its connections to the Taylor Rule. We model the term premium endogenously using two different models in the class of affine term-structure models studied in Duffie and Kan [1996. A yield-factor model of interest rates. Mathematical Finance 57, 405-443.]: a stochastic volatility model and a stochastic price-of-risk model. We then solve for equilibrium term structures in environments in which interest rate targeting follows a rule such as the one suggested by McCallum (i.e., the “McCallum Rule”). We demonstrate that McCallum's original result generalizes in a natural way to this broader class of models. To understand the connection to the Taylor Rule, we then consider two structural macroeconomic models which have reduced forms that correspond to the two affine models and provide a macroeconomic interpretation of abstract state variables (as in Ang and Piazzessi [2003. A no-arbitrage vector autoregression of term structure dynamics with macroeconomic and latent variables. Journal of Monetary Economics 50, 745-787.]). Moreover, such structural models allow us to interpret the parameters of the term-structure model in terms of the parameters governing preferences, technologies, and policy rules. We show how a monetary policy rule will manifest itself in the equilibrium asset-pricing kernel and, hence, the equilibrium term structure. We then show how this policy can be implemented with an interest-rate targeting rule. This provides us with a set of restrictions under which the Taylor and McCallum Rules are equivalent in the sense if implementing the same monetary policy. We conclude with some numerical examples that explore the quantitative link between these two models of monetary policy.     

Growth uncertainty,generalized disappointment aversion and production-based asset pricing

We study a production economy with regime switching in the conditional mean and volatility of productivity growth. The representative agent has generalized disappointment aversion (GDA) preferences. We show that volatility risk in productivity growth carries a positive and sizable risk premium in levered equity. Our model can endogenously generate long-run risks in the volatility of consumption growth observed in the data. We show that introducing leverage with a procyclical dividend process consistent with the data is critical for the GDA preferences to have a large impact on equity returns.     

Information Quality and Long‐Run Risk: Asset Pricing Implications

I study the asset pricing implications of the quality of public information about persistent productivity shocks in a general equilibrium model with Kreps–Porteus preferences. Low information quality is associated with a high equity premium, a low volatility of consumption growth, and a low volatility of the risk‐free interest rate. The relationship between information quality and the equity premium differs from that in endowment economies. My calibration improves substantially upon the Bansal–Yaron model in terms of the moments of the wealth–consumption ratio and the return on aggregate wealth.     

Evaluation of long-dated assets: The role of parameter uncertainty

Under expected utility, the uncertainty that affects the parameters of the random walk of consumption growth has no effect on the value of short-term claims and makes the term structure of risk-free rates decreasing. The term structure of aggregate risk premia is increasing when the uncertain cumulants of log consumption are independent. We apply these generic results to the case of an uncertain probability of catastrophes, and to the case of an uncertain trend or volatility of growth. Adding some persistence to unobservable shocks into our benchmark model, we show that the term structure of risk premia is hump-shaped.     

Structural breaks, parameter uncertainty, and term structure puzzles

We show that uncertainty about parameters of the short rate model can account for the rejections of the expectations hypothesis for the term structure of interest rates. We assume that agents employ Bayes rule to learn parameter values in the context of a model that is subject to stochastic structural breaks. We show that parameter uncertainty also implies that the verdict on the expectations hypothesis varies systematically with the term of the long bond and the particular test employed, in the same way that is found in empirical tests.     

Risk,uncertainty, and asset prices

We identify the relative importance of changes in the conditional variance of fundamentals (which we call “uncertainty”) and changes in risk aversion in the determination of the term structure, equity prices, and risk premiums. Theoretically, we introduce persistent time-varying uncertainty about the fundamentals in an external habit model. The model matches the dynamics of dividend and consumption growth, including their volatility dynamics and many salient asset market phenomena. While the variation in price–dividend ratios and the equity risk premium is primarily driven by risk aversion, uncertainty plays a large role in the term structure and is the driver of countercyclical volatility of asset returns.     

Composition of wealth,conditioning information,and the cross-section of stock returns

Value stocks covary with aggregate consumption more than growth stocks during periods when financial wealth is low relative to consumption. However, the conditional value premium does not exhibit such countercyclical behavior. Consequently, a one-factor conditional consumption-based asset pricing model can be rejected without making any arbitrary assumptions on the dynamics of the price of risk or the conditional moments. Empirical evidence is somewhat more consistent with a consumption-based model augmented with an aggregate wealth growth factor, which can be motivated by either recursive preferences or relative wealth concerns.     

Monetary Policy Uncertainty and the Response of the Yield Curve to Policy Shocks

This paper studies the nonlinear response of the term structure of interest rates to monetary policy shocks and presents a new stylized fact. We show that uncertainty about monetary policy changes the way the term structure responds to monetary policy. A policy tightening leads to a significantly smaller increase in long-term bond yields if policy uncertainty is high at the time of the shock. We also look at the decomposition of bond yields into expectations about future policy and the term premium. The weaker response of yields is driven by the fall in term premia, which fall more strongly if uncertainty about policy is high. Conditional on a monetary policy shock, higher uncertainty about monetary policy tends to make securities with longer maturities relatively more attractive to investors. As a consequence, investors demand even lower term premia. These findings are robust to the measurement of monetary policy uncertainty, the definition of the monetary policy shock, and to changing the model specification.     

Nonseparable Preferences, Fiscal Policy Puzzles, and Inferior Goods

Nonseparable preferences over consumption and leisure can generate an increase in private consumption in response to government spending, as found in the data, in a frictionless business cycle model. However, the conditions on preferences required for these result to obtain hold if and only if the consumption good is inferior. Similarly, positive co-movement of consumption and hours worked occurs if and only if either consumption or leisure is inferior.