Stochastic discount factor bounds and rare events: a review

We aim to provide a review of the stochastic discount factor bounds usually applied to diagnose asset pricing models. In particular, we mainly discuss the bounds used to analyze the disaster model of Barro (2006). Our attention is focused in this disaster model since the stochastic discount factor bounds that are applied to study the performance of disaster models usually consider the approach of Barro (2006). We first present the entropy bounds that provide a diagnosis of the analyzed disaster model which are the methods of Almeida and Garcia (2012, 2016); Ghosh et al. (2016). Then, we discuss how their results according to the disaster model are related to each other and also present the findings of other methodologies that are similar to these bounds but provide different evidence about the performance of the framework developed by Barro (2006).

Income inequality in a job-search model with heterogeneous discount factors: (revised version, forthcoming 2006, Revista Economia)

This paper investigates the income inequality generated by a jobsearch process when di§erent cohorts of homogeneous workers are allowed to have di§erent degrees of impatience. Using the fact the average wage under the invariant Markovian distribution is a decreasing function of the discount factor (Cysne (2004, 2006)), I show that the Lorenz curve and the between-cohort Gini coe¢ cient of income inequality can be easily derived in this case. An example with arbitrary measures regarding the wage o§ers and the distribution of time preferences among cohorts provides some insights into how much income inequality can be generated, and into how it varies as a function of the probability of unemployment and of the probability that the worker does not Önd a job o§er each period.

Estimating the stochastic discount factor without a utility function

Using the Pricing Equation in a panel-data framework, we construct a novel consistent estimator of the stochastic discount factor (SDF) which relies on the fact that its logarithm is the serial-correlation ìcommon featureîin every asset return of the economy. Our estimator is a simple function of asset returns, does not depend on any parametric function representing preferences, is suitable for testing di§erent preference speciÖcations or investigating intertemporal substitution puzzles, and can be a basis to construct an estimator of the risk-free rate. For post-war data, our estimator is close to unity most of the time, yielding an average annual real discount rate of 2.46%. In formal testing, we cannot reject standard preference speciÖcations used in the literature and estimates of the relative risk-aversion coe¢ cient are between 1 and 2, and statistically equal to unity. Using our SDF estimator, we found little signs of the equity-premium puzzle for the U.S.

A stochastic discount factor approach to asset pricing using panel data

Using the Pricing Equation, in a panel-data framework, we construct a novel consistent estimator of the stochastic discount factor (SDF) mimicking portfolio which relies on the fact that its logarithm is the ìcommon featureîin every asset return of the economy. Our estimator is a simple function of asset returns and does not depend on any parametric function representing preferences, making it suitable for testing di§erent preference speciÖcations or investigating intertemporal substitution puzzles.

A stochastic discount factor approach to asset pricing using panel data asymptotics

Using the Pricing Equation in a panel-data framework, we construct a novel consistent estimator of the stochastic discount factor (SDF) which relies on the fact that its logarithm is the "common feature" in every asset return of the economy. Our estimator is a simple function of asset returns and does not depend on any parametric function representing preferences. The techniques discussed in this paper were applied to two relevant issues in macroeconomics and finance: the first asks what type of parametric preference-representation could be validated by asset-return data, and the second asks whether or not our SDF estimator can price returns in an out-of-sample forecasting exercise. In formal testing, we cannot reject standard preference specifications used in the macro/finance literature. Estimates of the relative risk-aversion coefficient are between 1 and 2, and statistically equal to unity. We also show that our SDF proxy can price reasonably well the returns of stocks with a higher capitalization level, whereas it shows some difficulty in pricing stocks with a lower level of capitalization.

The forward- and the equity-premium puzzles: two symptoms of the same illness?

In this paper we revisit the relationship between the equity and the forward premium puzzles. We construct return-based stochastic discount factors under very mild assumptions and check whether they price correctly the equity and the foreign currency risk premia. We avoid log-linearizations by using moments restrictions associated with euler equations to test the capacity of our return-based stochastic discount factors to price returns on the relevant assets. Our main finding is that a pricing kernel constructed only using information on American domestic assets accounts for both domestic and international stylized facts that escape consumption based models. In particular, we fail to reject the null hypothesis that the foreign currency risk premium has zero price when the instrument is the own current value of the forward premium.

Constructing common-factor portfolios

In this paper we construct common-factor portfolios using a novel linear transformation of standard factor models extracted from large data sets of asset returns. The simple transformation proposed here keeps the basic properties of the usual factor transformations, although some new interesting properties are further attached to them. Some theoretical advantages are shown to be present. Also, their practical importance is confirmed in two applications: the performance of common-factor portfolios are shown to be superior to that of asset returns and factors commonly employed in the finance literature.

Nonparametric tail risk, macroeconomics and stock returns: predictability and risk premia

This paper proposes a new novel to calculate tail risks incorporating risk-neutral information without dependence on options data. Proceeding via a non parametric approach we derive a stochastic discount factor that correctly price a chosen panel of stocks returns. With the assumption that states probabilities are homogeneous we back out the risk neutral distribution and calculate five primitive tail risk measures, all extracted from this risk neutral probability. The final measure is than set as the first principal component of the preliminary measures. Using six Fama-French size and book to market portfolios to calculate our tail risk, we find that it has significant predictive power when forecasting market returns one month ahead, aggregate U.S. consumption and GDP one quarter ahead and also macroeconomic activity indexes. Conditional Fama-Macbeth two-pass cross-sectional regressions reveal that our factor present a positive risk premium when controlling for traditional factors.

An SDF approach to hedge funds’ tail risk: evidence from Brazilian funds

The main purpose of this paper is to propose a methodology to obtain a hedge fund tail risk measure. Our measure builds on the methodologies proposed by Almeida and Garcia (2015) and Almeida, Ardison, Garcia, and Vicente (2016), which rely in solving dual minimization problems of Cressie Read discrepancy functions in spaces of probability measures. Due to the recently documented robustness of the Hellinger estimator (Kitamura et al., 2013), we adopt within the Cressie Read family, this specific discrepancy as loss function. From this choice, we derive a minimum Hellinger risk-neutral measure that correctly prices an observed panel of hedge fund returns. The estimated risk-neutral measure is used to construct our tail risk measure by pricing synthetic out-of-the-money put options on hedge fund returns of ten specific categories. We provide a detailed description of our methodology, extract the aggregate Tail risk hedge fund factor for Brazilian funds, and as a by product, a set of individual Tail risk factors for each specific hedge fund category.

Consumption smoothing in Latin America: an empirical assessment of present value models

The study aims to assess the empirical adherence of the permanent income theory and the consumption smoothing view in Latin America. Two present value models are considered, one describing household behavior and the other open economy macroeconomics. Following the methodology developed in Campbell and Schiller (1987), Bivariate Vector Autoregressions are estimated for the saving ratio and the real growth rate of income concerning the household behavior model and for the current account and the change in national cash ‡ow regarding the open economy model. The countries in the sample are considered separately in the estimation process (individual system estimation) as well as jointly (joint system estimation). Ordinary Least Squares (OLS) and Seemingly Unrelated Regressions (SURE) estimates of the coe¢cients are generated. Wald Tests are then conducted to verify if the VAR coe¢cient estimates are in conformity with those predicted by the theory. While the empirical results are sensitive to the estimation method and discount factors used, there is only weak evidence in favor of the permanent income theory and consumption smoothing view in the group of countries analyzed.

Ensaios sobre o fator estocástico de descontos

Este trabalho propõe maneiras alternativas para a estimação consistente de uma medida abstrata, crucial para o estudo de decisões intertemporais, o qual é central a grande parte dos estudos em macroeconomia e finanças: o Fator Estocástico de Descontos (SDF, sigla em Inglês). Pelo emprego da Equação de Apreçamento constrói-se um inédito estimador consistente do SDF que depende do fato de que seu logaritmo é comum a todos os ativos de uma economia. O estimador resultante é muito simples de se calcular, não depende de fortes hipóteses econômicas, é adequado ao teste de diversas especificações de preferência e para a investigação de paradoxos de substituição intertemporal, e pode ser usado como base para a construção de um estimador para a taxa livre de risco. Alternativas para a estratégia de identificação são aplicadas e um paralelo entre elas e estratégias de outras metodologias é traçado. Adicionando estrutura ao ambiente inicial, são apresentadas duas situações onde a distribuição assintótica pode ser derivada. Finalmente, as metodologias propostas são aplicadas a conjuntos de dados dos EUA e do Brasil. Especificações de preferência usualmente empregadas na literatura, bem como uma classe de preferências dependentes do estado, são testadas. Os resultados são particularmente interessantes para a economia americana. A aplicação de teste formais não rejeita especificações de preferências comuns na literatura e estimativas para o coeficiente relativo de aversão ao risco se encontram entre 1 e 2, e são estatisticamente indistinguíveis de 1. Adicionalmente, para a classe de preferência s dependentes do estado, trajetórias altamente dinâmicas são estimadas para a tal coeficiente, as trajetórias são confinadas ao intervalo [1,15, 2,05] e se rejeita a hipótese de uma trajetória constante.

The forward- and the equity-premium puzzles: two symptoms of the same illness?

We build a pricing kernel using only US domestic assets data and check whether it accounts for foreign markets stylized facts that escape consumption based models. By interpreting our stochastic discount factor as the projection of a pricing kernel from a fully specified model in the space of returns, our results indicate that a model that accounts for the behavior of domestic assets goes a long way toward accounting for the behavior of foreign assets. We address predictability issues associated with the forward premium puzzle by: i) using instruments that are known to forecast excess returns in the moments restrictions associated with Euler equations, and; ii) by pricing Lustig and Verdelhan (2007)'s foreign currency portfolios. Our results indicate that the relevant state variables that explain foreign-currency market asset prices are also the driving forces behind U.S. domestic assets behavior.

The forward- and the equity-premium puzzles: two symptoms of the same illness?

Using information on US domestic financial data only, we build a stochastic discount factor—SDF— and check whether it accounts for foreign markets stylized facts that escape consumption based models. By interpreting our SDF as the projection of a pricing kernel from a fully specified model in the space of returns, our results indicate that a model that accounts for the behavior of domestic assets goes a long way toward accounting for the behavior of foreign assets prices. We address predictability issues associated with the forward premium puzzle by: i) using instruments that are known to forecast excess returns in the moments restrictions associated with Euler equations, and; ii) by pricing Lustig and Verdelhan (2007)’s foreign currency portfolios. Our results indicate that the relevant state variables that explain foreign-currency market asset prices are also the driving forces behind U.S. domestic assets behavior.

Fator estocástico de desconto: as cotas de variância, métricas de distância e suas extensões

The concept of stochastic discount factor pervades the Modern Theory of Asset Pricing. Initially, such object allows unattached pricing models to be discussed under the same terms. However, Hansen and Jagannathan have shown there is worthy information to be brought forth from such powerful concept which undelies asset pricing models. From security market data sets, one is able to explore the behavior of such random variable, determining a useful variance bound. Furthermore, through that instrument, they explore one pitfall on modern asset pricing: model misspecification. Those major contributions, alongside with some of its extensions, are thoroughly investigated in this exposition.

The forward- and the equity-premium puzzles: two symptoms of the same illness?

Using information on US domestic financial data only, we build a stochastic discount factor—SDF— and check whether it accounts for foreign markets stylized facts that escape consumption based models. By interpreting our SDF as the projection of a pricing kernel from a fully specified model in the space of returns, our results indicate that a model that accounts for the behavior of domestic assets goes a long way toward accounting for the behavior of foreign assets prices. We address predictability issues associated with the forward premium puzzle by: i) using instruments that are known to forecast excess returns in the moments restrictions associated with Euler equations, and; ii) by comparing this out-of-sample results with the one obtained performing an in-sample exercise, where the return-based SDF captures sources of risk of a representative set of developed and emerging economies government bonds. Our results indicate that the relevant state variables that explain foreign-currency market asset prices are also the driving forces behind U.S. domestic assets behavior.