Run Risk Model Research Articles

Measuring Long Run Risks for Brazil

We study the temporal structure of risk prices, risk exposures and expected market returns for Brazil assuming the economy follows a long run risks model. The model consists on an endowment economy where aggregate consumption and dividend growth contain predictable components, and a representative agent has Epstein-Zin recursive preferences with CES specification. We show that aggregate consumption in Brazil is sufficiently predictable to generate risk premia associated with Epstein-Zin preferences in excess of traditional compensations induced by power utility. Moreover, risk compensation is dominated by permanent shocks both in the short and long run, as Epstein-Zin preferences mitigate the price of temporary shocks' risk.

Robust Test of Long Run Risk and Valuation Risk Model

This paper tests the long run risk and valuation risk model using a robust estimation procedure. The persistent long run component of consumption growth process is proxied by a news based index that is created using a random forest algorithm. This news index is shown to predict aggregate long term consumption growth with an R-square of 57% and is robust to inclusion of other commonly used predictors. I theoretically derive an estimatable bias term in adjusted Euler equation of the model that arises due to measurement error in consumption data and show that this bias term is non-zero. Using a three pass estimation procedure that accounts for this bias, I show that the long run risk and valuation risk model fails to explain cross section of equity returns. This contrasts to the results from regular two pass Fama-MacBeth estimation procedure that implies that the same model explains the cross section of asset returns with statistically significant risk premia estimates.

From Which Consumption-Based Asset Pricing Models Can Investors Profit? Evidence from Model-Based Priors

This paper compares consumption-based asset pricing models based on the forecasting performance of investors who use economic constraints derived from the models to predict the equity premium. Three prominent asset pricing models are considered: Habit Formation, Long Run Risk, and Prospect Theory. I propose a simple Bayesian framework through which the investors impose the economic constraints as model-based priors on the parameters of their predictive regressions. An investor whose prior beliefs are rooted in the Long Run Risk model achieves more accurate forecasts overall. The greatest difference in performance occurs during the bull market of the late 1990s. During this period, the weak predictability of the equity premium implied by the Long Run Risk model helps the investor to not prematurely anticipate falling stock prices.

Risks for the long run: Estimation with time aggregation

The discrepancy between the decision and data-sampling intervals, known as time aggregation, confounds the identification of long-, short-run growth, and volatility risks in asset prices. This paper develops a method to simultaneously estimate the model parameters and the decision interval of the agent by exploiting identifying restrictions of the Long Run Risk (LRR) model that account for time aggregation. The LRR model finds considerable empirical support in the data; the estimated decision interval of the agents is 33 days. Our estimation results establish that long-run growth and volatility risks are important for asset prices.

From Which Consumption-Based Asset Pricing Models Can Investors Profit? Evidence from Model-Based Priors

This paper compares consumption-based asset pricing models based on the forecasting performance of investors who use economic constraints derived from the models to predict the equity premium. Three prominent asset pricing models are considered: Habit Formation, Long Run Risk, and Prospect Theory. I propose a simple Bayesian framework through which the investors impose the economic constraints as model-based priors on the parameters of their predictive regressions. An investor whose prior beliefs are rooted in the Long Run Risk model achieves more accurate forecasts overall. The greatest difference in performance occurs during the bull market of the late 1990s. During this period, the weak predictability of the equity premium implied by the Long Run Risk model helps the investor to not prematurely anticipate falling stock prices.

Long Run Consumption Growth Predictability

We document evidence of long run consumption growth predictability. We show that the news-based consumption measure developed in Matthies and Liu (2014) strongly predicts consumption growth over long horizons. The news-based measure explains up to 30 percent of the consumption growth variation at the 5 year horizon with a t-statistic significant at the 1% level. Our results are robust to alternative error and model specifications. These findings are consistent with the assumptions embedded in the Long Run Risk model. We show that alternative consumption growth predictors are not able to generate long run predictability.

News-Based Macroeconomic Asset Pricing

News contains valuable conditioning information that captures time-varying investor concern over different aspects of the macroeconomy. We create separate news measures to approximate investor concern about consumption growth, inflation, and unemployment by associating front-page articles in the Wall Street Journal with the respective macroeconomic factors. For each macroeconomic variable, we construct a news conditional macro model and compare its cross-sectional pricing power against that of the corresponding macro 1-factor beta-model. Next, we focus on our consumption-based news measure and simulate a long-short trading strategy based on news beta-loadings of NYSE and AMEX stocks. Strategy returns are significant and robust to adjusting for Fama French 3-factor risk. Finally, we show our news measures capture aspects of investor concern related to changes in macroeconomic forecasts. We discuss the implications of our consumption-based news measure for three important macro asset pricing models: Habit, Rare Disaster, and Long Run Risk. Our empirical findings do not support the Habit or Rare Disaster models. However, we find evidence in favor of the Long Run Risk model.

Incomplete Information in a Long Run Risks Model of Asset Pricing

We study the effects of incorporating incomplete information in the recently developed long run risks model of asset pricing. Studying the effects of incomplete information in such a setting is tractable, especially in the homoskedastic case with no fluctuating economic uncertainty. The incomplete information model is solved using approximate analytical methods as in the complete information framework analyzed in the literature. Model implications on moments of endogenous variables of interest including rates of return are compared in the long run risks model with and without incomplete information.

Predictability in the Long Run Risks Model

I analyse predictability of returns by the dividend-price ratio in the long-run risks model of Bansal and Yaron (2004). I find that the model does not generate predictability patterns consistently with the data. I connect this shortcoming to specific features of the long-run risks processes.

Money and Currency Market Implications of the Long Run Risk Models

Using postwar US and UK data, we study the implied interest rates and exchange rates in a simple Long Run Risk (LRR) model with two countries. When a closed economy is considered, emprical estimates show that, as in standard CCAPM models, the movements of the risk free rate implied by a baseline LRR model are entirely determined by the variations of the expected consumption growth. Nevertheless, differently from the standard CCAPM, the long run component of consumption growth is a key element to capture the counter-cyclical variations of the money market rates. Turning to an open economy setting, we find evidence that a baseline LRR model accounts for foreign exchange market movements.

Long Run Risks, the Macroeconomy, and Asset Prices

Ravi Bansal and Amir Yaron (2004) developed the Long Run Risk (LRR) model which emphasizes the role of long run risks, that is, 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 intertemporal 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 variations 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 risks is of economically significant magnitude. This implication is also consistent Long Run Risks and asset MaRkets †

Long Run and the Temporal Aggregation of Risks

The long-run risk model introduced by R.Bansal and A.Yaron (2004) assumes the existence of a small predictable component in consumption growth and an elasticity of intertemporal substitution of the representative agent larger than one for the substitution effect to dominate the income one. Previous tests fail to detect predictability in mean consumption growth fluctuations and the estimated value for the elasticity of intertemporal substitution is smaller than one. We argue that these apparent inconsistencies are due to a severe error-in-variables problem generated by the heterogeneity in the persistence levels of shocks to consumption growth. In this paper the original long run risk model is extended introducing a novel persistence based decomposition which can be considered as a refined permanent-transitory decomposition where the transitory shock is further split into orthogonal components. This new decomposition provides an effective method to represent a time series as a linear combination of innovations classified by their level of persistence and their time of arrival. Correspondingly the relations between equity return variations, cash flow risk and persistent fluctuations in the consumption mean are disaggregated across different levels of persistence and the complete term structure of risk return tradeoffs is computed. Quite remarkably, the empirical tests performed within this extended setup find evidence of consumption growth predictability, produce sizeable estimated for the equity premia and explain the value premium as an effect of the differential exposure of cash flows to consumption risk.

Asset Pricing with Long Run Risk and Stochastic Differential Utility: An Analytic Approach

The analytic method of Chen, Cosimano, and Himonas (CCH 2009) is extended to prove that the continuous time version of the long run risk model of Bansal and Yaron (2004) has an analytic solution. The long run risk model is dependent on the recursive utility introduced by Duffie and Epstein (1992a, 1992b) which leads to a nonlinear differential equation. The solution to this differential equation is an analytic function, so that the lifetime utility is represented by a power series near the stationary mean of the long run risk variable. The radius of convergence for this power series is determined to be at least seven standard deviations of the long run risk variable. Consequently, the lifetime utility can be quickly and accurately solved using a higher order Taylor polynomial approximation. With the solution to the lifetime utility the analytic method is then used to solve the linear ODE for the price-dividend function near the stationary mean of the long run risk variable with a radius of convergence at least one third of that for the lifetime utility. The short term properties of the long run risk model are compared with that of the external habit model of Campbell and Cochrane (1999). Finally, an alternative method from Hansen and Scheinkman (2009) is used to find the asymptotic rate of return on stocks for the long run risk model.

Rational Pessimism, Rational Exuberance, and Asset Pricing Models

The paper estimates and examines the empirical plausibiltiy of asset pricing models that attempt to explain features of financial markets such as the size of the equity premium and the volatility of the stock market. In one model, the long run risks model of Bansal and Yaron (2004), low frequency movements and time varying uncertainty in aggregate consumption growth are the key channels for understanding asset prices. In another, as typified by Campbell and Cochrane (1999), habit formation, which generates time-varying risk-aversion and consequently time-variation in risk-premia, is the key channel. These models are fitted to data using simulation estimators. Both models are found to fit the data equally well at conventional significance levels, and they can track quite closely a new measure of realized annual volatility. Further scrutiny using a rich array of diagnostics suggests that the long run risk model is preferred.