Abstract not found

We provide an empirical evaluation of the Long-Run Risks (LRR) model, and highlight important differences in the asset pricing implications of the LRR model relative to the habit model. We feature three key results: (i) consistent with the LRR model there is considerable evidence in the data for time-varying expected consumption growth and consumption volatility, (ii) the LRR model matches the key asset markets data features, (iii) in the data and in the LRR model accordingly, lagged consumption growth does not predict the future price-dividend ratio, while in the habit-model it counterfactually predicts the future price-dividend with an R 2 of over 40%. Overall, we find considerable empirical support for the LRR model.

Uncertainty plays a key role in economics, finance, and decision sciences. Financial markets, in particular derivative markets, provide fertile ground for understanding how perceptions of economic uncertainty and cashflow risk manifest themselves in asset prices. We demonstrate that the variance premium, defined as the difference between the squared VIX index and expected realized variance, captures attitudes toward uncertainty. We show conditions under which the variance premium displays significant time variation and return predictability. A calibrated, generalized Long-Run Risks model generates a variance premium with time variation and return predictability that is consistent with the data, while simultaneously matching the levels and volatilities of the market return and risk free rate. Our evidence indicates an important role for transient non-Gaussian shocks to fundamentals that affect agents ’ views of economic uncertainty and prices. We thank seminar participants at Wharton, the CREATES workshop ‘New Hope for the C-CAPM?’,

In fixed income markets, volatility is unspanned if volatility risk cannot be hedged with bonds. We first show that all affine term structure models with state space RM+ ×RN−M can be drift normalized and show when the standard variance normalization can be obtained. Using this normalization, we find conditions for a wide class of affine term structure models to exhibit unspanned stochastic volatility (USV). We show that the USV conditions restrict both the mean reversions of risk factors and the cross section of conditional yield volatilities. The restrictions imply that previously studied affine USV models are unlikely to be able to generate the observed cross section of yield volatilities. However, more general USV models can match the cross section of bond volatilities. 1.

developed the Long-Run Risk (LRR) model which emphasizes the role of long-run risks -low-frequency movements in consumption growth rates and volatility, in accounting for a wide-range of asset pricing puzzles. In this article we present a generalized LRR model, which allows us to study the role of cyclical fluctuations and macroeconomic crises on asset prices and expected returns. The Bansal and Yaron (2004) LRR model contains (i) a persistent expected consumption growth component, (ii) long-run variation in consumption volatility, and (iii) preference for early resolution of uncertainty. To evaluate the role of cyclical risks, we incorporate a cyclical component in consumption growth -this component is stationary in levels. To study financial market crises, we also entertain jumps in consumption growth and volatility. We find that the magnitude of risk compensation for cyclical risks in consumption critically depends on the magnitude of the inter-temporal elasticity of substitution (IES). When the IES is larger than one, cyclical risks carry a very small risk-premium When IES is close to zero, the risk compensation for cyclical risks is large, however, in this case the risk-free rate is implausibly high (in excess of 10 percent). It is, therefore, unlikely that the compensation for cyclical risk is of economically significant magnitude. This implication is also consistent with Robert E. Jr. To study financial market crisis, we first explore jumps in the cyclical component of the generalized LRR model; Robert Barro, Emi Nakamura, Jón Steinsson and José Ursúa Consistent with the LRR model, Lars Hansen, John Heaton and Nan Li (2008) document that there is predictable variation in consumption growth at longhorizons. Georg Kaltenbrunner and Lars Lochstoer (Forthcoming) show that a standard production-based model endogenously generates long-run predictable variation in consumption growth. Earlier work shows that LRR model can explain an important set of asset pricing puzzles -for the term structure and related puzzles see Monika I. Generalized Long-Run Risks Model We generalize the Bansal and Yaron (2004) model and allow for cyclical variations in aggregate consumption and dividends. Specifically, the level of log consumption (ct) consists of a deterministic trend, a stochastic trend (y t ), and a transitory component (s t ). That is, c t = µt + y t + s t . The growth rate of the 1

We propose two performance measures for asset pricing models and apply them to representative agent models with recursive preferences, habits, and jumps. The measures describe the pricing kernel’s dispersion (the entropy of the title) and dynamics (horizon dependence, a measure of how entropy varies over different time horizons). We show how each model generates entropy and horizon dependence, and compare their magnitudes to estimates derived from asset returns. This exercise — and transparent loglinear approximations — clarify the mechanisms underlying these models. It also reveals, in some cases, tension between entropy, which should be large enough to account for observed excess returns, and horizon dependence, which should be small enough to account for mean yield spreads.

Asset price movements in many cases seem de-linked from aggregate economic fundamentals. Forexample, RaviBansal andIvanShaliastovich (2008a) show that frequent large moves in asset prices, i.e. jumps, on average are not correlated with movements in macro-variables (see Table 1 below). Motivated by this, we present a general equilibrium model in which variation in investor confidence about expected growth determines risk premia and hence asset prices. This confidence risk channel can account for (i) the lack of connection between large asset-price moves and macro-variables such as consumption, (ii)large declinesinassetprices, thatis, the left tail of the return distribution, and (iii) observed predictability of equity returns and consumption growth by the price to dividend ratio. In essence, we present a model in which behaviorally motivated shifts in expectations play an important role for the asset prices. Our economy set-up follows a standard longrun risks specification of Ravi Bansal and Amir Yaron (2004), and features Gaussian consumption growth process with time-varying expected growth and volatility; there are no large moves orjumpsintheunderlyingconsumptionanddividenddynamics. Expectedgrowth isnotdirectly observable, and investors learn about it using the cross-section of signals. The time-varying cross-sectional varianceof thesignals determines the quality of the information, and therefore the confidence that investors place in their growth forecast. In the long-run risks framework, the fluctuations in confidence risk determines risk premia and asset prices. We model investors as being recency-biased in their expectation formation, that is, they overweigh recent observations as in Werner De Bondt and Richard Thaler (1990). This is important, as in the standard Kalman-Filter based expectation formation, periods of low information quality get down-weighted, which diminishes the role of the confidence risk channel.

We show that volatility movements have first-order implications for consumption dynamics and asset prices. Volatility news affects the stochastic discount factor and carries a separate risk premium. In the data, volatility risks are persistent and are strongly correlated with discount-rate news. This evidence has important implications for the return on aggregate wealth and the cross-sectional differences in risk premia. Estimation of our volatility risks based model yields an economically plausible positive correlation between the return to human capital and equity, while this correlation is implausibly negative when volatility risk is ignored. Our model setup implies a dynamics capital asset pricing model (DCAPM) which underscores the importance of volatility risk in addition to cash-flow and discount-rate risks. We show that our DCAPM accounts for the level and dispersion of risk premia across book-to-market and size sorted portfolios, and that equity portfolios carry positive volatility-risk premia. We thank seminar participants at NBER Spring 2012 Asset-Pricing Meeting, AFA 2012, SED

In a challenge to models that link the equity premium to rare disasters, Backus, Chernov, and Martin (2011) show that data on options imply negative events that are far smaller than these models suggest. We show that this result depends critically on the assumption that the probability of the rare event is constant. That is, a model with stochastic jumps in consumption can simultaneously explain options data and the equity premium. Indeed, such a model delivers an excellent fit to implied volatilities, despite being calibrated to match the equity premium and equity volatility alone.

Abstract Why do value stocks have higher expected returns than growth stocks, in spite of having lower risk? Why do these stocks exhibit positive abnormal performance while growth stocks exhibit negative abnormal performance? This paper offers a rareevents based explanation, that can also account for facts about the aggregate market. Patterns in time-series predictability offer independent evidence for the model's conclusions.