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.     

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.     

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.     

Inflation and the stock market: Understanding the “Fed Model”

The so-called Fed model postulates that the dividend or earnings yield on stocks should equal the yield on nominal Treasury bonds, or at least that the two should be highly correlated. In US data there is indeed a strikingly high time series correlation between the yield on nominal bonds and the dividend yield on equities. This positive correlation is often attributed to the fact that both bond and equity yields comove strongly and positively with expected inflation. Contrary to some of the extant literature, we show that this effect is consistent with modern asset pricing theory incorporating uncertainty about real growth prospects and habit-based risk aversion. In the US, high expected inflation has tended to coincide with periods of heightened uncertainty about real economic growth and unusually high risk aversion, both of which rationally raise equity yields.     

Time-varying risk aversion and asset prices

This paper uses a variant of the consumption-based representative agent model in Campbell and Cochrane [Campbell, J.Y., Cochrane, J.H., 1999. By force of habit: Consumption-based explanation of aggregate stock market behavior. Journal of Political Economy 107, 205–251] to study how investors’ time-varying risk aversion affects asset prices. First, we show that a countercyclical variation of risk aversion drives a procyclical conditional risk premium. Second, we show that with a small value for the volatility of the log surplus consumption ratio, a large value of risk aversion may not determine whether the equity premium and the risk-free rate puzzles can be resolved or not. Third, we show that countercyclical risk aversion may not help explain the predictability of long-horizon stock returns, the univariate mean-reversion of stock prices and the “leverage effect” in return volatility.     

Accounting quality,information risk and the term structure of implied volatility around earnings announcements

We examine the association between accounting quality, which is used as a proxy for firm information risk, and the behavior of the term structure of implied option volatility around earnings announcements. By employing a large sample of US firms having options traded on their equity during 1996–2010, we find that lower (higher) accounting quality is significantly associated with stronger (weaker) changes in the steepness of the term structure of implied volatility curve around quarterly earnings announcements. This finding (which is robust to controls for business-stemming uncertainty regarding future firm performance) is consistent with a stronger differential of short vs. long-term uncertainty for higher information risk firms, indicating greater uncertainty on the future economic performance of poorer vs. stronger accounting quality firms. We also establish the trading implications of these findings by demonstrating a (profitable in-sample) self-financed option trading strategy that is based on the quality of the accounting information released on earnings announcement days.     

On the systematic volatility of unpriced earnings

Some important puzzles in macro finance can be resolved in a model featuring systematically varying volatility of unpriced shocks to firms? earnings. In the data, the correlation between corporate debt and stock market valuations is low. The model accounts for this via the opposing effect of unpriced earnings risk on levered debt and equity prices. The model also explains the low (or nonexistent) risk-reward relation for the market portfolio of levered equity via the opposing effects of unpriced and priced uncertainty (both components of stock volatility) on the levered equity risk premium. Versions of the model calibrated to empirical measures of both types of fundamental risk can quantitatively substantiate these explanations. Variation in residual earning dispersion accounts for a significant fraction of observed disagreement between debt and equity valuations and of realized stock volatility. The implication that the two components of risk should forecast the levered equity risk premium with opposite signs is also supported in the data. The results are a notable advance for risk-based asset pricing.     

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.     

Explaining share price disparity with parameter uncertainty: Evidence from Chinese A- and H-shares

The price disparity between the A- and H-share markets for dual-listed firms in China is one of the most intriguing puzzles in the Mainland and Hong Kong financial markets. In this paper, we revisit this price disparity puzzle using the channel of parameter uncertainty. In the presence of information asymmetry and market segmentation, investors have different views on a firm’s asset volatility, and hence different valuations of the same reference firm. We estimate a structural model for equity pricing using a Bayesian approach, in which the uncertainty of investor model parameters is represented by the posterior standard deviation of the firm’s asset volatility. Our regression analysis shows that in addition to other market-based and macro factors, parameter uncertainty explains variations in price disparity.     

Noise, equity prices, and hedging: A new approach

The existence of noise trading in equity markets has possible economic implications for arbitrage, and asset pricing. In terms of pricing, noise trading can lead to excess volatility which has been shown to influence the value of options and futures. Furthermore, option research shows that modeling volatility leads to improved hedging performance. To this end, we derive a general hedging model for equity index futures in the presence of noise trading. Our analysis shows how the level and dynamics of noise trading should influence a hedger's behavior. Finally, we empirically test our model using the NASDAQ-100 index futures and FTSE 100 index futures over the period of January 1998 to May 2003.     

State uncertainty in stock markets: How big is the impact on the cost of equity?

We propose a novel Bayesian framework to incorporate uncertainty about the state of the market. Among others, one advantage of the framework is the ability to model a large collection of time-varying parameters simultaneously. When we apply the framework to estimate the cost of equity we find economically significant effects of state uncertainty. A state-independent pricing model overestimates the cost of equity by about 4% per annum for a utility firm and by as much as 3% for industries. We also observe that the expected return, volatility, risk loading, and pricing error all display state-dependent dynamics that coincide with the business cycle. More interestingly, the forecasted market and Fama–French factor risk premiums can predict the future real GDP growth rate even though the model does not use any macroeconomic variables, which suggests that the proposed Bayesian framework captures the state-dependent dynamics well.     

Equity yields

We study a new data set of dividend futures with maturities up to ten years across three world regions: the US, Europe, and Japan. We use these asset prices to construct equity yields, analogous to bond yields. We decompose the equity yields to obtain a term structure of expected dividend growth rates and a term structure of risk premia, which decomposes the equity risk premium by maturity. We find that the slope of the term structure of risk premia is pro-cyclical, whereas the slope of the term structure of expected dividend growth rates is counter-cyclical. The comovement of yields across regions is, on average, higher for long-maturity yields than for short-maturity yields, whereas the variation in this comovement is much higher for short-maturity yields.     

Optimal portfolios when volatility can jump

We consider an asset allocation problem in a continuous-time model with stochastic volatility and jumps in both the asset price and its volatility. First, we derive the optimal portfolio for an investor with constant relative risk aversion. The demand for jump risk includes a hedging component, which is not present in models without volatility jumps. We further show that the introduction of derivative contracts can have substantial economic value. We also analyze the distribution of terminal wealth for an investor who uses the wrong model, either by ignoring volatility jumps or by falsely including such jumps, or who is subject to estimation risk. Whenever a model different from the true one is used, the terminal wealth distribution exhibits fatter tails and (in some cases) significant default risk.     

Asset pricing with a financial sector

In this paper, we study the quantitative asset pricing implications of a financial intermediary that faces a leverage constraint. We use a recursive method to construct the global solution that accounts for occasionally binding constraints. Quantitatively, our model generates a high and countercyclical equity premium, a low and smooth risk-free interest rate, and a procyclical and persistent price–dividend ratio, despite an independently and identically distributed consumption growth process and a moderate risk aversion of 10. As a distinct prediction from our model, we find that when the intermediary is financially constrained, the interest rate spread between interbank and household loans spikes. This pattern is consistent with the empirical evidence that high TED spread coincides with low stock price and high stock market volatility.     

Dividend Dynamics and the Term Structure of Dividend Strips

Many leading asset pricing models are specified so that the term structure of dividend volatility is either flat or upward sloping. These models predict that the term structures of expected returns and volatilities on dividend strips (i.e., claims to dividends paid over a prespecified interval) are also upward sloping. However, the empirical evidence suggests otherwise. This discrepancy can be reconciled if these models replace their proposed dividend dynamics with processes that generate stationary leverage ratios. Under such policies, shareholders are forced to divest (invest) when leverage is low (high), which shifts risk from long‐ to short‐horizon dividend strips.     

Ambiguous Information,Portfolio Inertia,and Excess Volatility

I study the effects of risk and ambiguity (Knightian uncertainty) on optimal portfolios and equilibrium asset prices when investors receive information that is difficult to link to fundamentals. I show that the desire of investors to hedge ambiguity leads to portfolio inertia and excess volatility. Specifically, when news is surprising, investors may not react to price changes even if there are no transaction costs or other market frictions. Moreover, I show that small shocks to cash flow news, asset betas, or market risk premia may lead to drastic changes in the stock price and hence to excess volatility.     

Assessing the compensation for volatility risk implicit in interest rate derivatives

We use the risk neutral volatilities which market participants use to price dollar, euro and pound swaptions to the aim of assessing the size and the sign of the daily compensation for interest rate volatility risk between October 1998 and August 2006. The measurement of the unobservable volatility risk premium rests on a simple garch model, which generates the parameters of the volatility process under the physical measure and produces paths of future volatilities, whose averages represent the realized volatility forecasts. Results show that interest rate volatility has embodied a large — negative — compensation for volatility risk, in line with other studies focusing on different asset classes. We also document that the volatility risk premium has exhibited a term structure across the analyzed maturity spectrum and that it has changed through time, but much less than risk neutral volatilities. Compensation for volatility risk is positively related to risk neutral volatility, although the relation is not completely linear, and it is influenced, as expected, by the level of the short term rate and its realized volatility. Also a small but robust number of macroeconomic surprises affect compensation for volatility risk, with macroeconomic uncertainty in one country spilling over to other currencies. Estimates of the risk aversion coefficient computed over the same sample as the volatility risk premium suggest that (minus) the volatility risk premium can be almost directly read as risk aversion.     

Machine learning and asset allocation

Investors have access to a large array of structured and unstructured data. We consider how these data can be incorporated into financial decisions through the lens of the canonical asset allocation decision. We characterize investor preference for simplicity in models of the data used in the asset allocation decision. The simplicity parameters then guide asset allocation along with the usual risk aversion parameter. We use three distinct and diverse macroeconomic data sets to implement the model to forecast equity returns (the equity risk premium). The data sets we use are (a) price‐dividend ratios, (b) an array of macroeconomic series, and (c) text data from the Federal Reserve's Federal Open Market Committee (FOMC) meetings.     

Valuation Risk and Asset Pricing

Standard representative‐agent models fail to account for the weak correlation between stock returns and measurable fundamentals, such as consumption and output growth. This failing, which underlies virtually all modern asset pricing puzzles, arises because these models load all uncertainty onto the supply side of the economy. We propose a simple theory of asset pricing in which demand shocks play a central role. These shocks give rise to valuation risk that allows the model to account for key asset pricing moments, such as the equity premium, the bond term premium, and the weak correlation between stock returns and fundamentals.