Long-run Consumption Risk Research Articles

Firm Networks and Asset Returns

Abstract Changes in the propagation of shocks along firm networks are important to understanding aggregate and cross-sectional features of stock returns. When calibrated to match key characteristics of supplier–customer networks in the United States, a model in which firms are interlinked via enduring relationships generates long-run consumption risks, high and volatile risk premiums, and a small and stable risk-free rate. The model also matches cross-sectional patterns of portfolio returns sorted by firm centrality, a feature unaccounted for by standard asset pricing models. (JEL C67, E30, G12, L14)

Existence of the Wealth-Consumption Ratio in Asset Pricing Models with Recursive Preferences

Abstract Modern asset pricing models combine recursive preferences with complex dynamics for the underlying consumption process. The existence of solutions is for many of these models an unsettled question. This paper introduces a novel technique to prove existence and nonexistence, as well as uniqueness for models with recursive preferences. The approach applies to many models of interest, including those with long-run consumption risks, with stochastic volatility and jumps, with time-varying consumption disasters, and with smooth ambiguity aversion and learning. Collectively, the proven results settle the existence question for many of today’s leading asset pricing models.

Long Run Risks in FX Markets: Are They There?

This paper documents a tight connection between long run consumption risks (LRRs), currency excess returns and traditional global currency risk factors. We adopt a novel identification strategy that estimates country level LRRs using asset market data alone. With this identification strategy in hand, we find that: (1) currencies that suffer a bad relative LRR shock appreciate on impact before depreciating over the long run, (2) the High-Minus-Low (HML) carry trade sorts currencies on the basis of global LRR exposures, (3) the dollar carry trade outperforms on impact before underperforming over the long run in response to positive US relative LRR shocks, (4) US relative LRR shocks drive global currency risk factors. We interpret these facts as evidence in favour of an international LRR model where US LRRs drive global shocks to the world economy.

Does the Long-Run Risk Explain the Cross-Section of Corporate Bond Returns?

We test whether long-run consumption risk can explain the cross-section of corporate bond risk premiums. We find that a one-factor model with long-run consumption growth explains the risk premiums on bond portfolios sorted on credit spreads, maturity, credit rating, downside risk, idiosyncratic volatility, and the betas with respect to shocks to financial intermediary's capital of He, Kelly, and Manela (2017). Furthermore, the estimated risk aversion coefficient declines as we increase the horizon to measure consumption growth, and a model with relatively low values of risk-aversion can match the observed risk premiums if we use 24-month growth rate as a risk factor.

Short-run risk, business cycle, and the value premium

We jointly explain the equity and value premium variations in a model with both short-run (SRR) and long-run (LRR) consumption risk. In our empirical analysis, we find that SRR varies with the business cycle, and it has a substantial predictive power for market excess returns and the value premium—both in-sample and out-of-sample. The LRR component also differs significantly from zero, and value stocks have a larger exposure to both LRR and SRR than growth stocks. To explain these patterns in asset returns, we propose an extended LRR model. The model can be solved using log-linear approximations with economically small errors.

Short-run Risk, Business Cycle, and the Value Premium

We jointly explain the variations of the equity and value premium in a model with both short-run (SRR) and long-run (LRR) consumption risk. In our preliminary empirical analysis, we find that SRR varies with the business cycle and it has a substantial predictive power for market excess returns and the value premium|both in-sample and out-of-sample. The LRR component also differs significantly from zero, and value stocks have a larger exposure to both LRR and SRR than growth stocks. To explain these patterns in asset returns, we propose an extended and analytically tractable LRR model.

The "In(de-)flated" Value Premium

The value premium has disappeared over the last decade and this paper provides a risk-based explanation for its disappearance. I document a positive linear relationship among the value premium and the expected inflation at both high frequency and lower business cycle frequency. A heterogeneous cash flow model featuring inflation non-neutrality is proposed to justify the observed pattern. The estimated results suggest that value firms are more exposed to high-frequency fluctuations in aggregate consumption growth but less exposed to the low-frequency consumption risk. This finding is consistent with the documented inflation-return relationship but it contrasts with the previous findings suggesting that value firms are more sensitive to long-run consumption risk. Simulation-based results show that the positive linear relationship among the value premium and the expected inflation can be recovered when inflation is non-neutral and the relationship turns into uncorrelated when inflation is neutral. Therefore we argue that inflation non-neutrality can justify the positive relationship among inflation and value premium. Meanwhile, value firms tend to under-perform growth firms when the inflation is in low range, and it leads to the disappearance of the value premium.

Trend Growth Shocks and Asset Prices

This paper addresses the link between shocks to productivity trend growth and long-run consumption risk in a production economy model with recursive utility. Quantifying trend growth shocks, I find that persistent fluctuations in trend growth are the key driver of sizable long-run consumption risk. I compare this result to two conventional assumptions on a productivity process: 1) a deterministic trend with a cycle and 2) a random walk with drift. Persistent trend growth shocks generate larger long-run consumption risk than both highly persistent cycle shocks and random walk shocks. As a result, agents in the face of the trend growth shocks tend to save more and demand a higher equity premium. In addition, fluctuations in aggregate productivity growth is largely attributable to movements in trend growth.

A two-step indirect inference approach to estimate the long-run risk asset pricing model

The long-run consumption risk model provides a theoretically appealing explanation for prominent asset pricing puzzles, but its intricate structure presents a challenge for econometric analysis. This paper proposes a two-step indirect inference approach that disentangles the estimation of the model’s macro-economic dynamics and the investor’s preference parameters. A Monte Carlo study explores the feasibility and efficiency of the estimation strategy. We apply the method to recent U.S. data and provide a critical re-assessment of the long-run risk model’s ability to reconcile the real economy and financial markets. This two-step indirect inference approach is potentially useful for the econometric analysis of other prominent consumption-based asset pricing models that are equally difficult to estimate.

A two-step indirect inference approach to estimate the long-run risk asset pricing model

Abstract The long-run consumption risk model provides a theoretically appealing explanation for prominent asset pricing puzzles, but its intricate structure presents a challenge for econometric analysis. This paper proposes a two-step indirect inference approach that disentangles the estimation of the model’s macro-economic dynamics and the investor’s preference parameters. A Monte Carlo study explores the feasibility and efficiency of the estimation strategy. We apply the method to recent U.S. data and provide a critical re-assessment of the long-run risk model’s ability to reconcile the real economy and financial markets. This two-step indirect inference approach is potentially useful for the econometric analysis of other prominent consumption-based asset pricing models that are equally difficult to estimate.

Firm Networks and Asset Returns

This paper argues that changes in the propagation of idiosyncratic shocks along firm networks are important to understanding variations in asset returns. When calibrated to match key features of supplier-customer networks in the United States, an equilibrium model in which investors have recursive preferences and firms are interlinked via enduring relationships generates long-run consumption risks. Additionally, the model matches cross-sectional patterns of portfolio returns sorted by network centrality, a feature unaccounted for by standard asset pricing models.

Estimating the Long-Run Risk Asset Pricing Model with a Two-Step Indirect Inference Approach

The long-run consumption risk (LRR) model provides a theoretically appealing explanation for prominent asset pricing puzzles, but its intricate structure presents a challenge for econometric analysis. This paper proposes a two-step indirect inference approach that disentangles the estimation of the model's macroeconomic dynamics and that of the investor's risk preferences, and that avoids the drawbacks of previous approaches. A Monte Carlo study explores the feasibility and efficiency of the estimation strategy. We apply the proposed method to recent U.S. data and provide an empirical assessment of the LRR model's ability to reconcile the real economy and financial markets.

Short-Run and Long-Run Consumption Risks, Dividend Processes and Asset Returns

We examine the implications of short-run and long-run consumption risks on the momentum and long-term contrarian profits and the value premium in a unified economic framework. By introducing time-varying firm cash flow exposures to the short-run and long-run shocks in consumption growth, we find the otherwise standard intertemporal asset pricing model goes a long way toward generating the momentum and long-term contrarian profits and the value premium. The model also reproduces the size effect, the pairwise correlations between the profitabilities of these investment strategies, and the performance of the standard CAPM and the consumption CAPM in explaining these well-documented return behaviors.

Short-Run and Long-Run Consumption Risks, Dividend Processes, and Asset Returns

We examine the implications of short-run and long-run consumption risks on the momentum and long-term contrarian profits and the value premium in a unified economic framework. By introducing time-varying firm cash flow exposures to the short-run and long-run shocks in consumption growth, we find the otherwise standard intertemporal asset pricing model goes a long way toward generating the momentum and long-term contrarian profits and the value premium. The model also reproduces the size effect, the pairwise correlations between the profitabilities of these investment strategies, and the performance of the standard CAPM and the consumption CAPM in explaining these well-documented return behaviors.

The Equilibrium Term Structure of Equity and Interest Rates

We develop an equilibrium asset pricing model with Epstein-Zin recursive preferences that accounts for major stylized facts of the term structure of bond and equity risk premia. While the term structure of bond risk premia tends to be upward-sloping on average, the term structure of equity risk premia is known to be downward-sloping. {{p}} The equilibrium asset pricing model with long-run consumption risks has difficulty matching these stylized facts simultaneously. The standard calibration of these models follows Bansal and Yaron (2004), in which agents prefer the early resolution of uncertainty and have the inter-temporal elasticity of substitution greater than one; this calibration implies an upward-sloping term structure of equity risk premia and a downward-sloping term structure of real bond risk premia. Although the standard model can match a downward-sloping term structure of equity risk premia by amplifying the short-run risk of dividend growth, it does not fully reconcile with empirical evidence implying an upward-sloping average yield curve and a downward-sloping term structure of Sharpe ratios of dividend strips. We extend a standard model in two dimensions. First, we incorporate time-varying market prices of risks by allowing marginal utility of consumption to be nonlinearly dependent on risk factors. Second, we endogenously determine expected cash flows and expected inflation as potentially nonlinear functions of risk factors. With these extensions, our model can match the average slope of both bond and equity risk premia together with the term structure of Sharpe ratios of dividend strips. At the same time, the model generates the behavior of the aggregate stock market return in line with the data.

Intertemporal Substitution and Equity Premium *

This article presents a model that incorporates habit formation and long-run risks into the Epstein–Zin preferences, and reveals intertemporal substitution as a distinctive channel, separate from risk aversion, in generating key asset market phenomena. With habit formation, both the risk aversion and intertemporal substitution channels enhance the market price of short-run consumption risk. With long-run risks, intertemporal substitution reduces the market prices of long-run consumption risks, working against risk aversion. The contrasting effects of the intertemporal substitution channel drive key differences in the model implications of habit formation and long-run risks.

Dividend multifactor process, long-run risk and payout ratios

The purpose of this paper is to examine the theoretical relationship between the multidimensionality of risk and dividend policy, in an intertemporal context. After assuming that dividends are generated by a multifactor process, we use the fundamental framework of the consumption capital asset pricing model to explore the effect of long-run risk on dividend payout ratios (dividends divided by earnings). Our approach is similar to any multifactor model that, given the N factor process, derives useful equilibrium conditions. Our main result shows that the dividend payout ratio is negatively related to N sensitive coefficients, given by the long-run covariance between dividends and economic factors. This suggests that the multidimensionality of long-run consumption risk influences dividend policy. In brief, the model proposes that the target payout ratio can be determined with a simple and easy-to-apply formula that takes into account the long-run sensitivity of dividends to various economic factors.

Editors’ Introduction

Editors’ Introduction

Comment on “Growth uncertainty, generalized disappointment aversion and production-based asset pricing”

A model that jointly explains aggregate asset price and macroeconomic dynamics has been elusive. The literature in macrofinance has evolved significantly since the early efforts of, e.g., Jermann (1998), Tallarini (2000), and Boldrin et al. (2001), but we still have not arrived at an agreed uponworkhorse macro-finance model: fitting onemoment better often leads to fitting other moments worse, calibrations are typically quite aggressive in order to quantitatively account for the data, and parsimony is increasingly giving way to parameter proliferation and ‘black-box’ models where it is harder to fully understand all the mechanisms at play. Relative to this, Liu and Miao (2015) take a more classic, parsimonious approach. They consider a standard real business cycle model with a representative firm and a representative agent, where the technology process is estimated in a straightforward way from the data. While the firm has a standard Cobb–Douglas production function with convex capital adjustment costs, the agent is endowed with generalized disappointment aversion (GDA) preferences and the exogenous technology growth process has timevarying mean and volatility. Introducing GDA preferences into a standard production-based model is the marginal contribution of the paper. Like Epstein and Zin (1989) preferences, GDA preferences allow for a preference for early resolution of uncertainty, and so endogenous long-run consumption risks are priced (see Kaltenbrunner and Lochstoer 2010). Time-varying mean and volatility in the technology process under Epstein–Zin (EZ) utility has been considered in prior literature (e.g., Croce 2014, Malkhozov 2014), as has disappointment aversion (DA) preferences (Campanale et al., 2010). Relative to the latter, which also features first-order risk aversion, GDA preferences can generate endogenously counter-cyclical risk aversion (Routledge and Zin 2010), which typically generates counter-cyclical risk premiums. Time-varying discount rates can in turn help to increase the volatility of the aggregate dividend claim, which is a sticking point in the literature. Liu and Miao have three main results. The first mirrors that of Tallarini (2000) and subsequent studies using EZ or DA preferences: increasing agents' sensitivity to risk (through higher firstand/or second-order risk aversion) has quantitatively

Investor Information, Long-Run Risk, and the Term Structure of Equity

We study the role of information in asset-pricing models with long-run cash flow risk. When investors can distinguish short- from long-run consumption risks (full information), the model generates a sizable equity risk premium only if the equity term structure slopes up, contrary to the data. In general, the short- and long-run components are unidentified. We propose a sparsity-based bounded rationality model of long-run risk that is both parsimonious and fully identified from historical data. In contrast to full information, the model generates a sizable market risk premium simultaneously with a downward-sloping equity term structure, as in the data.