Long‐Run Risk and Its Implications for the Equity Premium Puzzle: New Evidence from a Multivariate Framework

This paper investigates the empirical evidence of long‐run risk and its implications for the equity premium puzzle. We find that the long‐run risk model is generally weakly identified and that standard inferences tend to underestimate the uncertainty of long‐run risk. We extend the LM‐type test of Ma and Nelson (2010) that remains valid under weak identification to the bivariate VARMA‐GARCH model of consumption and dividend growth. The results cast doubt on the validity of long‐run risk as an explanation for the equity premium puzzle. We also evaluate the approach of Bansal, Kiku, and Yaron (2007a), which extracts long‐run risk by regressing consumption growth and its volatility on predictive variables. The results using the Bonferroni Q‐test of Campbell and Yogo (2006) suggest that consumption and dividend growth are generally unpredictable by the price‐dividend ratio and risk‐free rate. This casts doubt on the validity of the BKY approach.     

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.     

Uncertainty,Time‐Varying Fear,and Asset Prices

I construct an equilibrium model that captures salient properties of index option prices, equity returns, variance, and the risk‐free rate. A representative investor makes consumption and portfolio choice decisions that are robust to his uncertainty about the true economic model. He pays a large premium for index options because they hedge important model misspecification concerns, particularly concerning jump shocks to cash flow growth and volatility. A calibration shows that empirically consistent fundamentals and reasonable model uncertainty explain option prices and the variance premium. Time variation in uncertainty generates variance premium fluctuations, helping explain their power to predict stock returns.     

Asset Pricing with Countercyclical Household Consumption Risk

We show that shocks to household consumption growth are negatively skewed, persistent, countercyclical, and drive asset prices. We construct a parsimonious model where heterogeneous households have recursive preferences. A single state variable drives the conditional cross‐sectional moments of household consumption growth. The estimated model fits well the unconditional cross‐sectional moments of household consumption growth and the moments of the risk‐free rate, equity premium, price‐dividend ratio, and aggregate dividend and consumption growth. The model‐implied risk‐free rate and price‐dividend ratio are procyclical, while the market return has countercyclical mean and variance. Finally, household consumption risk explains the cross section of excess returns.     

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.     

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.     

Rare disaster risk and the expected equity risk premium

Consistent with the predictions of rare disaster models, we find that a proxy for the time‐varying probability of rare disasters helps to explain fluctuations in expectations of the equity risk premium. Our proxy for disaster risk is a recently developed measure of global political instability, and the expected market risk premium is from Value Line analysts' expected stock returns. Consistent with long‐run risk models, uncertainty about expected GDP growth and expected consumption growth is also significantly positively related to the expected market risk premium. We obtain similar results when we use the earnings–price ratio and the dividend–price ratio as proxies for the expected market risk premium.     

Stock Market Volatility and Learning

We show that consumption‐based asset pricing models with time‐separable preferences generate realistic amounts of stock price volatility if one allows for small deviations from rational expectations. Rational investors with subjective beliefs about price behavior optimally learn from past price observations. This imparts momentum and mean reversion into stock prices. The model quantitatively accounts for the volatility of returns, the volatility and persistence of the price‐dividend ratio, and the predictability of long‐horizon returns. It passes a formal statistical test for the overall fit of a set of moments provided one excludes the equity premium.     

Consumption Volatility Risk

We show that time variation in macroeconomic uncertainty affects asset prices. Consumption volatility is a negatively priced source of risk for a wide variety of test portfolios. At the firm level, exposure to consumption volatility risk predicts future returns, generating a spread across quintile portfolios in excess of 7% annually. This premium is explained by cross‐sectional differences in the sensitivity of dividend volatility to consumption volatility. Stocks with volatile cash flows in uncertain aggregate times require higher expected returns.     

Do dividend initiations signal a reduction in risk? Evidence from the option market

We investigate whether dividends convey information about the risk of a company by examining the reaction of implied volatility in the option market to the announcement of a dividend initiation. Implied volatility decreases after the announcement and the magnitude of the decline in volatility is positively related to both the magnitude of cumulative abnormal returns (CAR) in the equity markets and the size of the dividend. Additionally, firms with weaker (stronger) corporate governance experience larger (smaller) declines in implied volatility. Cross sectional analysis shows that a one-standard deviation decline in measures of risk increases the 2-day CAR by 74–137 basis points. Our results suggest that dividend initiations signal declining firm risk.     

Imperfect Information and Stock Market Volatility

The purpose of this paper is to (1) develop a model to show how imperfect information can create excess volatility in asset returns and (2) provide empirical evidence consistent with the model. In this framework, variations in information quality cause the market prices to fluctuate more than the corresponding economic fundamentals. Using high‐frequency data from 1988 to 2002, the empirical evidence supports the predictions of the model by showing that economic volatility, defined as squared deviations of the quarterly gross domestic product (GDP) growth rate from its long‐run trend, can explain about half of the variation in S&P 500‐stock index quarterly volatility.     

Equity Returns and Business Cycles in Small Open Economies

This is the first paper in the dynamic stochastic general equilibrium literature to match key business cycle moments and long‐run equity returns in a small open economy with production. These results are achieved by introducing four modifications to a standard real business cycle model: (i) borrowing and lending costs are imposed to increase the volatility of the marginal rate of substitution over time, (ii) capital adjustment costs are assumed to make equity returns more volatile, (iii) GHH preferences are employed to smooth consumption, and (iv) a working capital constraint to generate countercyclical trade balances. Our results are based on data from Argentina, Brazil, and Chile.     

Predictability in Consumption Growth and Equity Returns: A Bayesian Investigation

We use a Bayesian method to estimate a consumption-based asset pricing model featuring long-run risks. Although the model is generally consistent with consumption and dividend growth moments in annual data, the conditional mean of consumption growth (a latent process) is not persistent enough to satisfy the restriction that the price-dividend ratio be an affine function of the latent process. The model also requires relatively high intertemporal elasticity of substitution to match the low volatility of the risk-free return. These two restrictions lead to the equity volatility puzzle. The model accounts for only 50% of the total variation in asset returns.     

Income Insurance and the Equilibrium Term Structure of Equity

Output, wages, and dividends feature term structures of variance ratios that are respectively flat, increasing, and decreasing. Income insurance from shareholders to workers explains these term structures. Risk‐sharing smooths wages but only concerns transitory risk and hence enhances short‐run dividend risk. As a result, actual labor‐share variation largely forecasts the risk, premium, and slope of dividend strips. A simple general equilibrium model in which labor rigidity affects dividend dynamics and the price of short‐run risk reconciles standard asset pricing facts with the term structures of the equity premium, volatility, and macroeconomic variables, which are at odds in leading models.     

Procyclicality of the comovement between dividend growth and consumption growth

Duffee (2005) shows that the amount of consumption risk (i.e., the conditional covariance between market returns and consumption growth) is procyclical. In light of this “Duffee Puzzle,” I empirically demonstrate that the conditional covariance between dividend growth (i.e., the immediate cash flow part of market returns) and consumption growth is (1) procyclical and (2) a consistent source of procyclicality in the puzzle. Moreover, I solve an external habit formation model that incorporates realistic joint dynamics of dividend growth and consumption growth. The procyclical dividend-consumption comovement entails two new procyclical terms in the amount of consumption risk via cash flow and valuation channels, respectively. These two procyclical terms play an important role in generating a realistic magnitude of consumption risk. In contrast to extant habit formation models, the conditional equity premium no longer increases monotonically when a negative consumption shock arrives because it might lower the amount of risk while increasing the price of risk.     

Dividend Dynamics,Learning, and Expected Stock Index Returns

We present a latent variable model of dividends that predicts, out‐of‐sample, 39.5% to 41.3% of the variation in annual dividend growth rates between 1975 and 2016. Further, when learning about dividend dynamics is incorporated into a long‐run risks model, the model predicts, out‐of‐sample, 25.3% to 27.1% of the variation in annual stock index returns over the same time horizon, with learning contributing approximately half of the predictability in returns. These findings support the view that investors' aversion to long‐run risks and their learning about these risks are important in determining stock index prices and expected returns.     

The Interest Rate Risk Exposure of Financial Intermediaries: A Review of the Theory and Empirical Evidence

The paper surveys current and previous research on financial institutions' interest rate risk exposure. The implications of such exposure are discussed and motivating insights are emphasized. Various theoretical frameworks and models are presented. For each one an overview of the studies and any relationship to each other is provided. In a cross‐industry analysis, other idiosyncratic risk factors are considered and their importance is delineated. A number of empirical relations are established. More specifically, there is an inverse relationship between interest rate changes and common stock returns of financial institutions. The intermediaries' apparent yield sensitivity is mainly attributed to the duration gap inherent in their balance sheet structure. Furthermore, the aforesaid equity sensitivity due to other possible dynamics such as dividend yield, unanticipated inflation and regulatory lags is also considered. Changes in economic regimes have altered volatility in market yields with a subsequent effect, positive or negative, on financial intermediaries' equity returns. The issue of the risk‐return compensation is further analyzed, and findings suggest that the interest rate risk is priced by capital markets. Finally, a few other issues are identified as avenues for future research.     

Stock and bond returns with Moody Investors

We present a tractable, linear model for the simultaneous pricing of stock and bond returns that incorporates stochastic risk aversion. In this model, analytic solutions for endogenous stock and bond prices and returns are readily calculated. After estimating the parameters of the model by the general method of moments, we investigate a series of classic puzzles of the empirical asset pricing literature. In particular, our model is shown to jointly accommodate the mean and volatility of equity and long term bond risk premia as well as salient features of the nominal short rate, the dividend yield, and the term spread. Also, the model matches the evidence for predictability of excess stock and bond returns. However, the stock–bond return correlation implied by the model is somewhat higher than that in the data.     

Historic Changes in the High Yield Bond Market

In a history that now stretches about four decades, the high yield (HY) market has experienced growth in issuance and out‐standings that is remarkable both for its level (about 13% per annum, with HY bonds now accounting for about 25% of the total corporate bond market) and its cyclicality and sensitivity to the broad economy. The HY market has also experienced a notable shift away from B‐rated bonds and toward both lower‐risk Ba‐rated bonds and, to a lesser extent, more risky Caa‐rated bonds. Consistent with this development, studies of the performance of HY bonds show Ba‐rated bonds experiencing not only lower risk, but also higher returns than Caa‐rated bonds, which have produced surprisingly low average returns along with exceptionally high volatility. At the same time, studies of the correlation of HY bond returns with returns on other major asset classes report that all classes of HY bonds (but particularly the riskier B‐ and Caa‐rated bonds) have consistently stronger relationships with common stocks (especially small‐cap stocks) than with Treasuries and investment‐grade bonds. Analysis of the volatility of HY bond returns over time shows that during periods of stability in the economy and financial markets, the volatility of HY bond returns has been very similar to that of investment‐grade bonds. But during periods of political or economic uncertainty, the volatility of HY bonds has become two or three times that of investment‐grade bonds, approaching the volatility of common stocks. The main driver of the significant increase in the risk of the aggregate HY bond market during periods of uncertainty has been Caa‐rated bonds, whose risk pattern has been remarkably similar to that of small‐cap common stocks. Analysis of the credit risk spread (or CRS) series for both the composite HY bond market and each of its rating categories shows markedly non‐normal distributions with significant positive “skewness”—that is, periods of exceptionally high spreads (that are not counterbalanced by periods of exceptionally low spreads). The authors also report a consistently strong relationship of the CRS series with default rates and the general state of the economy, with major peaks occurring during or shortly after economic recessions. Near the end of 2008, however, there was a clear break in this relationship when the CRS reached an historic peak of 2,000 basis points, or more than five standard deviations above its long‐term mean, while the default rate (at 4%) was below its long‐term average. The authors offer two explanations for this break in CRS‐default rate relationship: the jump in the CRS caused by the extreme flight to quality and drop in liquidity for all risky securities during the second half of 2008; and the use of covenant‐lite securities and other sources of financial flexibility that appear to have enabled many HY issuers to defer defaults (if not avoid them entirely).     

Local Trends in Price‐to‐Dividend Ratios—Assessment,Predictive Value,and Determinants

Persistent variations of the log price‐to‐dividend ratio (PD) and their economic determinants have attracted a lively discussion in the literature. We suggest a gradually time‐varying state process to govern the persistence of the PD. The adopted state‐space approach offers favorable model diagnostics and finds particular support in out‐of‐sample stock return prediction. We show that this slowly evolving mean process is jointly shaped by the consumption risk, the demographic structure, and the proportion of firms with traditional dividend payout policy during the past 60 years. In particular, the volatility of consumption growth plays the dominant role.